%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA129-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:45 PM UTC 2026
% Result : Unsatisfiable 0.73s 0.97s
% Output : Proof 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA129-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.31 % Computer : n026.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Mon May 4 22:38:40 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.73/0.97 % SZS status Unsatisfiable
% 0.73/0.97 % SZS output start Proof
% 0.73/0.97 tff(b_type, type, (
% 0.73/0.97 b: ( $i * $i ) > $o)).
% 0.73/0.97 tff(s_type, type, (
% 0.73/0.97 s: $i > $i)).
% 0.73/0.97 tff(z_type, type, (
% 0.73/0.97 z: $i)).
% 0.73/0.97 tff(r_type, type, (
% 0.73/0.97 r: ( $i * $i ) > $o)).
% 0.73/0.97 tff(elem_1_type, type, (
% 0.73/0.97 elem_1: $i)).
% 0.73/0.97 tff(inj_0_type, type, (
% 0.73/0.97 inj_0: $i > $i)).
% 0.73/0.97 tff(1,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.73/0.97 tff(2,plain,
% 0.73/0.97 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(3,plain,
% 0.73/0.97 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(4,plain,
% 0.73/0.97 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(5,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 0.73/0.97 tff(6,plain,
% 0.73/0.97 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.73/0.97 tff(7,plain,(
% 0.73/0.97 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.73/0.97 inference(skolemize,[status(sab)],[6])).
% 0.73/0.97 tff(8,plain,
% 0.73/0.97 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.73/0.97 tff(9,plain,
% 0.73/0.97 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.73/0.97 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.73/0.97 tff(10,plain,
% 0.73/0.97 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.73/0.97 inference(quant_inst,[status(thm)],[])).
% 0.73/0.97 tff(11,plain,
% 0.73/0.97 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.73/0.97 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.73/0.97 tff(12,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))), introduced(assumption)).
% 0.73/0.97 tff(13,assumption,(r(s(z), z)), introduced(assumption)).
% 0.73/0.97 tff(14,assumption,(r(z, s(z))), introduced(assumption)).
% 0.73/0.97 tff(15,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.73/0.97 tff(16,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 0.73/0.97 tff(17,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 0.73/0.97 tff(18,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 0.73/0.97 tff(19,plain,
% 0.73/0.97 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))),
% 0.73/0.97 inference(bind,[status(th)],[])).
% 0.73/0.97 tff(20,plain,
% 0.73/0.97 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.97 inference(quant_intro,[status(thm)],[19])).
% 0.73/0.97 tff(21,plain,
% 0.73/0.97 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.97 inference(rewrite,[status(thm)],[])).
% 0.73/0.97 tff(22,plain,
% 0.73/0.97 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r(X0, X1)) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> (((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> (((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))))), rewrite((((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))))),
% 0.73/0.98 inference(bind,[status(th)],[])).
% 0.73/0.98 tff(23,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.98 inference(quant_intro,[status(thm)],[22])).
% 0.73/0.98 tff(24,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 0.73/0.98 tff(25,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.73/0.98 tff(26,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.73/0.98 tff(27,plain,(
% 0.73/0.98 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.98 inference(skolemize,[status(sab)],[26])).
% 0.73/0.98 tff(28,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.73/0.98 tff(29,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(30,plain,
% 0.73/0.98 (((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(31,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[30])).
% 0.73/0.98 tff(32,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[31, 29])).
% 0.73/0.98 tff(33,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(34,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.73/0.98 tff(35,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[34, 28, 18, 13, 17])).
% 0.73/0.98 tff(36,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(37,plain,
% 0.73/0.98 (~r(z, s(s(z)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[36, 17, 13])).
% 0.73/0.98 tff(38,assumption,(z = s(s(z))), introduced(assumption)).
% 0.73/0.98 tff(39,plain,
% 0.73/0.98 (s(s(z)) = z),
% 0.73/0.98 inference(symmetry,[status(thm)],[38])).
% 0.73/0.98 tff(40,plain,
% 0.73/0.98 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.73/0.98 inference(bind,[status(th)],[])).
% 0.73/0.98 tff(41,plain,
% 0.73/0.98 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.73/0.98 inference(quant_intro,[status(thm)],[40])).
% 0.73/0.98 tff(42,plain,
% 0.73/0.98 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(43,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 0.73/0.98 tff(44,plain,
% 0.73/0.98 (![X: $i] : (~(s(X) = z))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.73/0.98 tff(45,plain,(
% 0.73/0.98 ![X: $i] : (~(s(X) = z))),
% 0.73/0.98 inference(skolemize,[status(sab)],[44])).
% 0.73/0.98 tff(46,plain,
% 0.73/0.98 (![X: $i] : (~(s(X) = z))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.73/0.98 tff(47,plain,
% 0.73/0.98 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(48,plain,
% 0.73/0.98 (~(s(s(z)) = z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.73/0.98 tff(49,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[48, 39])).
% 0.73/0.98 tff(50,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(51,plain,
% 0.73/0.98 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.73/0.98 inference(bind,[status(th)],[])).
% 0.73/0.98 tff(52,plain,
% 0.73/0.98 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.98 inference(quant_intro,[status(thm)],[51])).
% 0.73/0.98 tff(53,plain,
% 0.73/0.98 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(54,plain,
% 0.73/0.98 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.73/0.98 inference(bind,[status(th)],[])).
% 0.73/0.98 tff(55,plain,
% 0.73/0.98 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.98 inference(quant_intro,[status(thm)],[54])).
% 0.73/0.98 tff(56,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 0.73/0.98 tff(57,plain,
% 0.73/0.98 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.73/0.98 tff(58,plain,
% 0.73/0.98 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.73/0.98 tff(59,plain,(
% 0.73/0.98 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.98 inference(skolemize,[status(sab)],[58])).
% 0.73/0.98 tff(60,plain,
% 0.73/0.98 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.73/0.98 tff(61,plain,
% 0.73/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(62,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(63,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.73/0.98 tff(64,plain,
% 0.73/0.98 (b(z, s(s(z))) | r(z, s(s(z)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[63, 60, 50])).
% 0.73/0.98 tff(65,plain,
% 0.73/0.98 (b(z, s(s(z)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[64, 37])).
% 0.73/0.98 tff(66,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.73/0.98 tff(67,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.73/0.98 tff(68,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(69,plain,
% 0.73/0.98 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(70,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[69])).
% 0.73/0.98 tff(71,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[70, 68])).
% 0.73/0.98 tff(72,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(73,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.73/0.98 tff(74,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[73, 28, 66, 16, 67])).
% 0.73/0.98 tff(75,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(76,plain,
% 0.73/0.98 (~r(s(s(s(z))), s(s(z)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[75, 66, 16])).
% 0.73/0.98 tff(77,plain,
% 0.73/0.98 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 0.73/0.98 inference(commutativity,[status(thm)],[])).
% 0.73/0.98 tff(78,plain,
% 0.73/0.98 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 0.73/0.98 inference(symmetry,[status(thm)],[77])).
% 0.73/0.98 tff(79,plain,
% 0.73/0.98 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[78])).
% 0.73/0.98 tff(80,plain,
% 0.73/0.98 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(81,plain,
% 0.73/0.98 (inj_0(s(s(z))) = s(z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[80, 9])).
% 0.73/0.98 tff(82,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 0.73/0.98 tff(83,plain,
% 0.73/0.98 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[82])).
% 0.73/0.98 tff(84,plain,
% 0.73/0.98 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 0.73/0.98 inference(symmetry,[status(thm)],[83])).
% 0.73/0.98 tff(85,plain,
% 0.73/0.98 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(86,plain,
% 0.73/0.98 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[85, 9])).
% 0.73/0.98 tff(87,plain,
% 0.73/0.98 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.73/0.98 inference(symmetry,[status(thm)],[86])).
% 0.73/0.98 tff(88,plain,
% 0.73/0.98 (s(s(s(z))) = s(s(z))),
% 0.73/0.98 inference(symmetry,[status(thm)],[82])).
% 0.73/0.98 tff(89,plain,
% 0.73/0.98 (s(s(s(z))) = s(z)),
% 0.73/0.98 inference(transitivity,[status(thm)],[88, 87, 84, 81])).
% 0.73/0.98 tff(90,plain,
% 0.73/0.98 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(91,plain,
% 0.73/0.98 (inj_0(s(z)) = z),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[90, 9])).
% 0.73/0.98 tff(92,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.73/0.98 tff(93,plain,
% 0.73/0.98 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[92])).
% 0.73/0.98 tff(94,plain,
% 0.73/0.98 (s(s(z)) = z),
% 0.73/0.98 inference(transitivity,[status(thm)],[87, 93, 91])).
% 0.73/0.98 tff(95,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[48, 94])).
% 0.73/0.98 tff(96,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(97,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[96, 89])).
% 0.73/0.98 tff(98,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(99,plain,
% 0.73/0.98 (~(s(s(s(z))) = s(s(z)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[98, 79])).
% 0.73/0.98 tff(100,plain,
% 0.73/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(101,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(102,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.73/0.98 tff(103,plain,
% 0.73/0.98 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[102, 60])).
% 0.73/0.98 tff(104,plain,
% 0.73/0.98 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[103, 99])).
% 0.73/0.98 tff(105,plain,
% 0.73/0.98 (b(s(s(s(z))), s(s(z)))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[104, 76])).
% 0.73/0.98 tff(106,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 0.73/0.98 tff(107,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(108,plain,
% 0.73/0.98 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(109,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[108])).
% 0.73/0.98 tff(110,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[109, 107])).
% 0.73/0.98 tff(111,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(112,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.73/0.98 tff(113,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[112, 28, 13, 16, 106, 17])).
% 0.73/0.98 tff(114,plain,((~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(115,plain,
% 0.73/0.98 (~r(s(s(z)), z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[114, 17, 13, 16])).
% 0.73/0.98 tff(116,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 0.73/0.98 tff(117,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 0.73/0.98 tff(118,plain,
% 0.73/0.98 (((~![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))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(119,plain,
% 0.73/0.98 ((~![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))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(120,plain,
% 0.73/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.73/0.98 tff(121,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[120, 60, 48, 117, 116])).
% 0.73/0.98 tff(122,plain,(b(s(s(z)), z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(123,plain,
% 0.73/0.98 (b(s(s(z)), z)),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[122, 115])).
% 0.73/0.98 tff(124,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.73/0.98 tff(125,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(126,plain,
% 0.73/0.98 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(127,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.73/0.98 inference(monotonicity,[status(thm)],[126])).
% 0.73/0.98 tff(128,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.73/0.98 inference(transitivity,[status(thm)],[127, 125])).
% 0.73/0.98 tff(129,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(130,plain,
% 0.73/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.73/0.98 tff(131,plain,
% 0.73/0.98 ($false),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[130, 28, 124, 66, 16])).
% 0.73/0.98 tff(132,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.98 tff(133,plain,
% 0.73/0.98 (~r(s(s(z)), s(s(s(z))))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[132, 66, 16])).
% 0.73/0.98 tff(134,plain,
% 0.73/0.98 (((~![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)))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(135,plain,
% 0.73/0.98 ((~![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)))))),
% 0.73/0.98 inference(quant_inst,[status(thm)],[])).
% 0.73/0.98 tff(136,plain,
% 0.73/0.98 ((~![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))))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.73/0.98 tff(137,plain,
% 0.73/0.98 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[136, 60])).
% 0.73/0.98 tff(138,plain,
% 0.73/0.98 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[137, 98])).
% 0.73/0.98 tff(139,plain,
% 0.73/0.98 (b(s(s(z)), s(s(s(z))))),
% 0.73/0.98 inference(unit_resolution,[status(thm)],[138, 133])).
% 0.73/0.98 tff(140,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 0.73/0.98 tff(141,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.73/0.98 tff(142,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 0.73/0.98 tff(143,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.73/0.98 tff(144,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.73/0.98 tff(145,plain,
% 0.73/0.98 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.73/0.98 inference(bind,[status(th)],[])).
% 0.73/0.98 tff(146,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.98 inference(quant_intro,[status(thm)],[145])).
% 0.73/0.98 tff(147,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(148,plain,
% 0.73/0.98 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3))) <=> (((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 0.73/0.98 inference(bind,[status(th)],[])).
% 0.73/0.98 tff(149,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.98 inference(quant_intro,[status(thm)],[148])).
% 0.73/0.98 tff(150,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 0.73/0.98 tff(151,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.73/0.98 tff(152,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.73/0.98 tff(153,plain,(
% 0.73/0.98 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.98 inference(skolemize,[status(sab)],[152])).
% 0.73/0.98 tff(154,plain,
% 0.73/0.98 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.73/0.98 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.73/0.98 tff(155,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(156,plain,
% 0.73/0.98 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.73/0.98 inference(rewrite,[status(thm)],[])).
% 0.73/0.98 tff(157,plain,
% 0.73/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[156])).
% 0.73/0.99 tff(158,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[157, 155])).
% 0.73/0.99 tff(159,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(160,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.73/0.99 tff(161,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[160, 154, 144, 143, 142, 141, 140])).
% 0.73/0.99 tff(162,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(163,plain,
% 0.73/0.99 (~b(s(s(s(z))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[162, 139, 123, 65, 105])).
% 0.73/0.99 tff(164,plain,
% 0.73/0.99 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(165,plain,
% 0.73/0.99 (~(s(s(s(z))) = z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[164, 46])).
% 0.73/0.99 tff(166,plain,
% 0.73/0.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![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))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(167,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(168,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.73/0.99 tff(169,plain,
% 0.73/0.99 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[168, 60, 165])).
% 0.73/0.99 tff(170,plain,
% 0.73/0.99 (r(s(s(s(z))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[169, 163])).
% 0.73/0.99 tff(171,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.73/0.99 tff(172,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.73/0.99 tff(173,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(174,plain,
% 0.73/0.99 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(175,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[174])).
% 0.73/0.99 tff(176,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[175, 173])).
% 0.73/0.99 tff(177,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(178,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.73/0.99 tff(179,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[178, 28, 172, 66, 171])).
% 0.73/0.99 tff(180,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(181,plain,
% 0.73/0.99 (~r(z, s(s(s(s(z)))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[180, 170, 66])).
% 0.73/0.99 tff(182,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(183,plain,
% 0.73/0.99 (s(s(s(s(z)))) = z),
% 0.73/0.99 inference(symmetry,[status(thm)],[182])).
% 0.73/0.99 tff(184,plain,
% 0.73/0.99 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(185,plain,
% 0.73/0.99 (~(s(s(s(s(z)))) = z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[184, 46])).
% 0.73/0.99 tff(186,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[185, 183])).
% 0.73/0.99 tff(187,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(188,plain,
% 0.73/0.99 (((~![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))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(189,plain,
% 0.73/0.99 ((~![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))))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(190,plain,
% 0.73/0.99 ((~![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)))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.73/0.99 tff(191,plain,
% 0.73/0.99 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[190, 60, 187])).
% 0.73/0.99 tff(192,plain,
% 0.73/0.99 (b(z, s(s(s(s(z)))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[191, 181])).
% 0.73/0.99 tff(193,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.73/0.99 tff(194,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(195,plain,
% 0.73/0.99 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(196,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[195])).
% 0.73/0.99 tff(197,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.73/0.99 inference(transitivity,[status(thm)],[196, 194])).
% 0.73/0.99 tff(198,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(199,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.73/0.99 tff(200,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[199, 28, 66, 171, 193])).
% 0.73/0.99 tff(201,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(202,plain,
% 0.73/0.99 (~r(s(s(s(s(z)))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[201, 170, 66])).
% 0.73/0.99 tff(203,plain,
% 0.73/0.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(204,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(205,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.73/0.99 tff(206,plain,
% 0.73/0.99 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[205, 60, 185])).
% 0.73/0.99 tff(207,plain,
% 0.73/0.99 (b(s(s(s(s(z)))), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[206, 202])).
% 0.73/0.99 tff(208,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(209,plain,
% 0.73/0.99 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(210,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[209])).
% 0.73/0.99 tff(211,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[210, 208])).
% 0.73/0.99 tff(212,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(213,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.73/0.99 tff(214,plain,
% 0.73/0.99 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[213, 154, 207, 123, 65, 192])).
% 0.73/0.99 tff(215,plain,
% 0.73/0.99 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 0.73/0.99 inference(commutativity,[status(thm)],[])).
% 0.73/0.99 tff(216,plain,
% 0.73/0.99 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[215])).
% 0.73/0.99 tff(217,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(218,plain,
% 0.73/0.99 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[217])).
% 0.73/0.99 tff(219,plain,
% 0.73/0.99 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 0.73/0.99 inference(symmetry,[status(thm)],[218])).
% 0.73/0.99 tff(220,plain,
% 0.73/0.99 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.73/0.99 inference(symmetry,[status(thm)],[11])).
% 0.73/0.99 tff(221,plain,
% 0.73/0.99 (s(s(s(z))) = s(z)),
% 0.73/0.99 inference(transitivity,[status(thm)],[220, 219, 81])).
% 0.73/0.99 tff(222,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[96, 221])).
% 0.73/0.99 tff(223,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(224,plain,
% 0.73/0.99 (~(s(s(s(s(z)))) = s(s(z)))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.73/0.99 tff(225,plain,
% 0.73/0.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(226,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(227,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.73/0.99 tff(228,plain,
% 0.73/0.99 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[227, 60])).
% 0.73/0.99 tff(229,plain,
% 0.73/0.99 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[228, 224])).
% 0.73/0.99 tff(230,plain,
% 0.73/0.99 (r(s(s(s(s(z)))), s(s(z)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[229, 214])).
% 0.73/0.99 tff(231,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 0.73/0.99 tff(232,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(233,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(234,plain,
% 0.73/0.99 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(235,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[234])).
% 0.73/0.99 tff(236,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[235, 233])).
% 0.73/0.99 tff(237,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(238,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.73/0.99 tff(239,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[238, 154, 144, 1, 232, 231, 141])).
% 0.73/0.99 tff(240,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(241,plain,
% 0.73/0.99 (~b(s(z), s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[240, 231, 1, 144, 141])).
% 0.73/0.99 tff(242,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 0.73/0.99 tff(243,plain,
% 0.73/0.99 (s(s(s(z))) = s(z)),
% 0.73/0.99 inference(symmetry,[status(thm)],[242])).
% 0.73/0.99 tff(244,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[96, 243])).
% 0.73/0.99 tff(245,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(246,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(247,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(248,plain,
% 0.73/0.99 (((~![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)))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(249,plain,
% 0.73/0.99 ((~![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)))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(250,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.73/0.99 tff(251,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[250, 60, 247, 246, 245])).
% 0.73/0.99 tff(252,plain,(b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(253,plain,
% 0.73/0.99 (r(s(z), s(s(s(z))))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[252, 241])).
% 0.73/0.99 tff(254,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.73/0.99 tff(255,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(256,plain,
% 0.73/0.99 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(257,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 0.73/0.99 inference(monotonicity,[status(thm)],[256])).
% 0.73/0.99 tff(258,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.73/0.99 inference(transitivity,[status(thm)],[257, 255])).
% 0.73/0.99 tff(259,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(260,plain,
% 0.73/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.73/0.99 tff(261,plain,
% 0.73/0.99 ((~b(s(z), z)) | (~b(s(s(z)), s(z)))),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[260, 154, 15, 142, 254])).
% 0.73/0.99 tff(262,plain,
% 0.73/0.99 (~b(s(z), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[261, 231])).
% 0.73/0.99 tff(263,assumption,(~r(s(z), z)), introduced(assumption)).
% 0.73/0.99 tff(264,assumption,(~b(s(z), z)), introduced(assumption)).
% 0.73/0.99 tff(265,plain,
% 0.73/0.99 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(266,plain,
% 0.73/0.99 (~(s(z) = z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[265, 46])).
% 0.73/0.99 tff(267,plain,
% 0.73/0.99 (((~![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))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(268,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.73/0.99 inference(quant_inst,[status(thm)],[])).
% 0.73/0.99 tff(269,plain,
% 0.73/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.73/0.99 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.73/0.99 tff(270,plain,
% 0.73/0.99 ($false),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[269, 60, 266, 264, 263])).
% 0.73/0.99 tff(271,plain,(b(s(z), z) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.99 tff(272,plain,
% 0.73/0.99 (r(s(z), z)),
% 0.73/0.99 inference(unit_resolution,[status(thm)],[271, 262])).
% 0.73/0.99 tff(273,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.73/0.99 tff(274,plain,
% 0.73/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 0.73/0.99 inference(rewrite,[status(thm)],[])).
% 0.73/0.99 tff(275,plain,
% 0.73/0.99 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(276,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[275])).
% 0.73/1.00 tff(277,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 0.73/1.00 inference(transitivity,[status(thm)],[276, 274])).
% 0.73/1.00 tff(278,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(279,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.73/1.00 tff(280,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[279, 28, 273, 13, 171])).
% 0.73/1.00 tff(281,plain,((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(282,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[281, 272, 253, 171])).
% 0.73/1.00 tff(283,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(284,plain,
% 0.73/1.00 (~b(s(s(z)), s(z))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[283, 192, 15, 123, 170, 1, 139, 105])).
% 0.73/1.00 tff(285,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 0.73/1.00 tff(286,plain,
% 0.73/1.00 (s(z) = s(s(z))),
% 0.73/1.00 inference(symmetry,[status(thm)],[285])).
% 0.73/1.00 tff(287,plain,
% 0.73/1.00 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[286])).
% 0.73/1.00 tff(288,plain,
% 0.73/1.00 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.73/1.00 inference(symmetry,[status(thm)],[287])).
% 0.73/1.00 tff(289,plain,
% 0.73/1.00 (s(z) = inj_0(s(s(z)))),
% 0.73/1.00 inference(symmetry,[status(thm)],[81])).
% 0.73/1.00 tff(290,plain,
% 0.73/1.00 (s(z) = z),
% 0.73/1.00 inference(transitivity,[status(thm)],[289, 288, 91])).
% 0.73/1.00 tff(291,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[266, 290])).
% 0.73/1.00 tff(292,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(293,plain,
% 0.73/1.00 (((~![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)))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(294,plain,
% 0.73/1.00 ((~![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)))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(295,plain,
% 0.73/1.00 ((~![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))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[294, 293])).
% 0.73/1.00 tff(296,plain,
% 0.73/1.00 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[295, 60, 292])).
% 0.73/1.00 tff(297,plain,
% 0.73/1.00 (r(s(s(z)), s(z))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[296, 284])).
% 0.73/1.00 tff(298,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.73/1.00 tff(299,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
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% 0.73/1.00 inference(modus_ponens,[status(thm)],[304, 303])).
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% 0.73/1.00 tff(308,plain,
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% 0.73/1.00 tff(309,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 0.73/1.00 tff(310,plain,
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% 0.73/1.00 tff(311,plain,
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% 0.73/1.00 tff(312,plain,
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% 0.73/1.00 inference(unit_resolution,[status(thm)],[165, 311])).
% 0.73/1.00 tff(313,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(314,plain,
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% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(316,plain,
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% 0.73/1.00 inference(modus_ponens,[status(thm)],[315, 314])).
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% 0.73/1.00 inference(unit_resolution,[status(thm)],[316, 60])).
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% 0.73/1.00 tff(323,plain,
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% 0.73/1.00 inference(rewrite,[status(thm)],[])).
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% 0.73/1.00 inference(modus_ponens,[status(thm)],[326, 325])).
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% 0.73/1.00 inference(commutativity,[status(thm)],[])).
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% 0.73/1.00 tff(331,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 0.73/1.00 tff(332,plain,
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% 0.73/1.00 tff(333,plain,
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% 0.73/1.00 tff(337,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(338,plain,
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% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(340,plain,
% 0.73/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
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% 0.73/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.73/1.00 tff(342,plain,
% 0.73/1.00 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[341, 60])).
% 0.73/1.00 tff(343,plain,
% 0.73/1.00 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[342, 338])).
% 0.73/1.00 tff(344,plain,
% 0.73/1.00 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[343, 328])).
% 0.73/1.00 tff(345,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 0.73/1.00 tff(346,plain,
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% 0.73/1.00 inference(rewrite,[status(thm)],[])).
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% 0.73/1.00 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
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% 0.73/1.00 inference(transitivity,[status(thm)],[348, 346])).
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% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(351,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.73/1.00 tff(352,plain,
% 0.73/1.00 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[351, 28, 345, 299])).
% 0.73/1.00 tff(353,plain,
% 0.73/1.00 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(354,plain,
% 0.73/1.00 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[353, 9])).
% 0.73/1.00 tff(355,assumption,(s(s(z)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.73/1.00 tff(356,plain,
% 0.73/1.00 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[355])).
% 0.73/1.00 tff(357,plain,
% 0.73/1.00 (s(z) = s(s(s(elem!1)))),
% 0.73/1.00 inference(transitivity,[status(thm)],[289, 356, 354])).
% 0.73/1.00 tff(358,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 0.73/1.00 tff(359,plain,
% 0.73/1.00 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[358])).
% 0.73/1.00 tff(360,plain,
% 0.73/1.00 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.73/1.00 inference(symmetry,[status(thm)],[359])).
% 0.73/1.00 tff(361,plain,
% 0.73/1.00 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(362,plain,
% 0.73/1.00 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[361, 9])).
% 0.73/1.00 tff(363,plain,
% 0.73/1.00 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.73/1.00 inference(symmetry,[status(thm)],[362])).
% 0.73/1.00 tff(364,plain,
% 0.73/1.00 (s(s(elem!1)) = z),
% 0.73/1.00 inference(transitivity,[status(thm)],[363, 360, 91])).
% 0.73/1.00 tff(365,plain,
% 0.73/1.00 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(366,plain,
% 0.73/1.00 (~(s(s(elem!1)) = z)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[365, 46])).
% 0.73/1.00 tff(367,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[366, 364])).
% 0.73/1.00 tff(368,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(369,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[368, 357])).
% 0.73/1.00 tff(370,plain,(~(s(s(z)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(371,plain,
% 0.73/1.00 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(372,plain,
% 0.73/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(373,plain,
% 0.73/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.73/1.00 tff(374,plain,
% 0.73/1.00 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[373, 60, 370, 352])).
% 0.73/1.00 tff(375,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(376,plain,
% 0.73/1.00 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(377,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[376])).
% 0.73/1.00 tff(378,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 0.73/1.00 inference(transitivity,[status(thm)],[377, 375])).
% 0.73/1.00 tff(379,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(380,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.73/1.00 tff(381,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[380, 28, 14, 106, 299])).
% 0.73/1.00 tff(382,plain,((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(383,plain,
% 0.73/1.00 (~r(s(s(z)), z)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[382, 299, 14])).
% 0.73/1.00 tff(384,plain,
% 0.73/1.00 (b(s(s(z)), z)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[122, 383])).
% 0.73/1.00 tff(385,assumption,(z = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.73/1.00 tff(386,plain,
% 0.73/1.00 (s(s(s(s(elem!1)))) = z),
% 0.73/1.00 inference(symmetry,[status(thm)],[385])).
% 0.73/1.00 tff(387,plain,
% 0.73/1.00 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(388,plain,
% 0.73/1.00 (~(s(s(s(s(elem!1)))) = z)),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[387, 46])).
% 0.73/1.00 tff(389,plain,
% 0.73/1.00 ($false),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[388, 386])).
% 0.73/1.00 tff(390,plain,(~(z = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.00 tff(391,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(392,plain,
% 0.73/1.00 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(393,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.73/1.00 inference(monotonicity,[status(thm)],[392])).
% 0.73/1.00 tff(394,plain,
% 0.73/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.73/1.00 inference(transitivity,[status(thm)],[393, 391])).
% 0.73/1.00 tff(395,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(396,plain,
% 0.73/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.73/1.00 tff(397,plain,
% 0.73/1.00 (~r(z, s(s(s(s(elem!1)))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[396, 28, 345, 14])).
% 0.73/1.00 tff(398,plain,
% 0.73/1.00 (((~![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))))))),
% 0.73/1.00 inference(rewrite,[status(thm)],[])).
% 0.73/1.00 tff(399,plain,
% 0.73/1.00 ((~![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))))))),
% 0.73/1.00 inference(quant_inst,[status(thm)],[])).
% 0.73/1.00 tff(400,plain,
% 0.73/1.00 ((~![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)))))),
% 0.73/1.00 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.73/1.00 tff(401,plain,
% 0.73/1.00 (b(z, s(s(s(s(elem!1)))))),
% 0.73/1.00 inference(unit_resolution,[status(thm)],[400, 60, 397, 390])).
% 0.73/1.01 tff(402,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 0.73/1.01 tff(403,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(404,plain,
% 0.73/1.01 (((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(405,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[404])).
% 0.73/1.01 tff(406,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.73/1.01 inference(transitivity,[status(thm)],[405, 403])).
% 0.73/1.01 tff(407,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(408,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.73/1.01 tff(409,plain,
% 0.73/1.01 ($false),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[408, 28, 345, 13, 402])).
% 0.73/1.01 tff(410,plain,((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.01 tff(411,plain,
% 0.73/1.01 (~r(s(s(s(s(elem!1)))), z)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[410, 345, 13])).
% 0.73/1.01 tff(412,assumption,(~r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 0.73/1.01 tff(413,assumption,(~b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 0.73/1.01 tff(414,plain,
% 0.73/1.01 (((~![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))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(415,plain,
% 0.73/1.01 ((~![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))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(416,plain,
% 0.73/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.73/1.01 tff(417,plain,
% 0.73/1.01 ($false),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[416, 60, 388, 413, 412])).
% 0.73/1.01 tff(418,plain,(b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)), inference(lemma,lemma(discharge,[]))).
% 0.73/1.01 tff(419,plain,
% 0.73/1.01 (b(s(s(s(s(elem!1)))), z)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[418, 411])).
% 0.73/1.01 tff(420,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(421,plain,
% 0.73/1.01 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(422,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[421])).
% 0.73/1.01 tff(423,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))))),
% 0.73/1.01 inference(transitivity,[status(thm)],[422, 420])).
% 0.73/1.01 tff(424,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(425,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.73/1.01 tff(426,plain,
% 0.73/1.01 ($false),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[425, 154, 419, 401, 384, 140, 374])).
% 0.73/1.01 tff(427,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.01 tff(428,plain,
% 0.73/1.01 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[427, 297, 14, 65, 13])).
% 0.73/1.01 tff(429,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 0.73/1.01 tff(430,plain,
% 0.73/1.01 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[429])).
% 0.73/1.01 tff(431,plain,
% 0.73/1.01 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(symmetry,[status(thm)],[354])).
% 0.73/1.01 tff(432,plain,
% 0.73/1.01 (s(s(s(elem!1))) = z),
% 0.73/1.01 inference(transitivity,[status(thm)],[431, 430, 91])).
% 0.73/1.01 tff(433,plain,
% 0.73/1.01 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(434,plain,
% 0.73/1.01 (~(s(s(s(elem!1))) = z)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[433, 46])).
% 0.73/1.01 tff(435,plain,
% 0.73/1.01 ($false),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[434, 432])).
% 0.73/1.01 tff(436,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.01 tff(437,plain,
% 0.73/1.01 (((~![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)))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(438,plain,
% 0.73/1.01 ((~![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)))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(439,plain,
% 0.73/1.01 ((~![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))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.73/1.01 tff(440,plain,
% 0.73/1.01 ((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))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[439, 60])).
% 0.73/1.01 tff(441,plain,
% 0.73/1.01 (b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[440, 436])).
% 0.73/1.01 tff(442,plain,
% 0.73/1.01 (b(s(s(s(s(elem!1)))), s(z))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[441, 428])).
% 0.73/1.01 tff(443,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 0.73/1.01 tff(444,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 0.73/1.01 tff(445,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(446,plain,
% 0.73/1.01 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(447,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[446])).
% 0.73/1.01 tff(448,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.73/1.01 inference(transitivity,[status(thm)],[447, 445])).
% 0.73/1.01 tff(449,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(450,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.73/1.01 tff(451,plain,
% 0.73/1.01 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[450, 154, 144, 444, 1, 443])).
% 0.73/1.01 tff(452,plain,
% 0.73/1.01 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[373, 60, 370, 451])).
% 0.73/1.01 tff(453,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(454,plain,
% 0.73/1.01 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(455,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[454])).
% 0.73/1.01 tff(456,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 0.73/1.01 inference(transitivity,[status(thm)],[455, 453])).
% 0.73/1.01 tff(457,plain,
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% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(458,plain,
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% 0.73/1.01 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.73/1.01 tff(459,plain,
% 0.73/1.01 (~b(s(z), s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[458, 154, 444, 1, 443, 232])).
% 0.73/1.01 tff(460,plain,
% 0.73/1.01 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(commutativity,[status(thm)],[])).
% 0.73/1.01 tff(461,plain,
% 0.73/1.01 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = s(s(s(s(elem!1))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[460])).
% 0.73/1.01 tff(462,plain,
% 0.73/1.01 (~(s(z) = s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[436, 461])).
% 0.73/1.01 tff(463,plain,
% 0.73/1.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(464,plain,
% 0.73/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(465,plain,
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% 0.73/1.01 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.73/1.01 tff(466,plain,
% 0.73/1.01 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[465, 60])).
% 0.73/1.01 tff(467,plain,
% 0.73/1.01 (b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[466, 462])).
% 0.73/1.01 tff(468,plain,
% 0.73/1.01 (r(s(z), s(s(s(s(elem!1)))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[467, 459])).
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% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(470,plain,
% 0.73/1.01 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.73/1.01 inference(rewrite,[status(thm)],[])).
% 0.73/1.01 tff(471,plain,
% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[470])).
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% 0.73/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.73/1.01 inference(transitivity,[status(thm)],[471, 469])).
% 0.73/1.01 tff(473,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(474,plain,
% 0.73/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 0.73/1.01 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.73/1.01 tff(475,plain,
% 0.73/1.01 ($false),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[474, 28, 468, 17, 452])).
% 0.73/1.01 tff(476,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.01 tff(477,plain,
% 0.73/1.01 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[476, 442, 1, 139, 17, 321])).
% 0.73/1.01 tff(478,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 0.73/1.01 tff(479,plain,
% 0.73/1.01 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(z))))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[478])).
% 0.73/1.01 tff(480,plain,
% 0.73/1.01 (s(s(s(elem!1))) = s(s(z))),
% 0.73/1.01 inference(transitivity,[status(thm)],[431, 479, 86])).
% 0.73/1.01 tff(481,plain,
% 0.73/1.01 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[480])).
% 0.73/1.01 tff(482,plain,
% 0.73/1.01 (s(s(elem!1)) = s(z)),
% 0.73/1.01 inference(transitivity,[status(thm)],[363, 481, 81])).
% 0.73/1.01 tff(483,plain,
% 0.73/1.01 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.73/1.01 inference(monotonicity,[status(thm)],[482])).
% 0.73/1.01 tff(484,plain,
% 0.73/1.01 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 0.73/1.01 inference(quant_inst,[status(thm)],[])).
% 0.73/1.01 tff(485,plain,
% 0.73/1.01 (inj_0(s(s(elem!1))) = s(elem!1)),
% 0.73/1.01 inference(unit_resolution,[status(thm)],[484, 9])).
% 0.73/1.02 tff(486,plain,
% 0.73/1.02 (s(elem!1) = inj_0(s(s(elem!1)))),
% 0.73/1.02 inference(symmetry,[status(thm)],[485])).
% 0.73/1.02 tff(487,plain,
% 0.73/1.02 (s(elem!1) = z),
% 0.73/1.02 inference(transitivity,[status(thm)],[486, 483, 91])).
% 0.73/1.02 tff(488,plain,
% 0.73/1.02 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 0.73/1.02 inference(quant_inst,[status(thm)],[])).
% 0.73/1.02 tff(489,plain,
% 0.73/1.02 (~(s(elem!1) = z)),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[488, 46])).
% 0.73/1.02 tff(490,plain,
% 0.73/1.02 ($false),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[489, 487])).
% 0.73/1.02 tff(491,plain,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.73/1.02 tff(492,plain,
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% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(493,plain,
% 0.73/1.02 ((~![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)))))),
% 0.73/1.02 inference(quant_inst,[status(thm)],[])).
% 0.73/1.02 tff(494,plain,
% 0.73/1.02 ((~![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))))),
% 0.73/1.02 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.73/1.02 tff(495,plain,
% 0.73/1.02 ((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))))),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[494, 60])).
% 0.73/1.02 tff(496,plain,
% 0.73/1.02 (b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[495, 491])).
% 0.73/1.02 tff(497,plain,
% 0.73/1.02 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[496, 477])).
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% 0.73/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(499,plain,
% 0.73/1.02 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(500,plain,
% 0.73/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 0.73/1.02 inference(monotonicity,[status(thm)],[499])).
% 0.73/1.02 tff(501,plain,
% 0.73/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.73/1.02 inference(transitivity,[status(thm)],[500, 498])).
% 0.73/1.02 tff(502,plain,
% 0.73/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.73/1.02 inference(quant_inst,[status(thm)],[])).
% 0.73/1.02 tff(503,plain,
% 0.73/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 0.73/1.02 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.73/1.02 tff(504,plain,
% 0.73/1.02 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[503, 28, 497, 344, 230])).
% 0.73/1.02 tff(505,assumption,(b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.73/1.02 tff(506,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.73/1.02 tff(507,plain,
% 0.73/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(508,plain,
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% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(509,plain,
% 0.73/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 0.73/1.02 inference(monotonicity,[status(thm)],[508])).
% 0.73/1.02 tff(510,plain,
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% 0.73/1.02 inference(transitivity,[status(thm)],[509, 507])).
% 0.73/1.02 tff(511,plain,
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% 0.73/1.02 inference(quant_inst,[status(thm)],[])).
% 0.73/1.02 tff(512,plain,
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% 0.73/1.02 inference(modus_ponens,[status(thm)],[511, 510])).
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% 0.73/1.02 inference(unit_resolution,[status(thm)],[512, 154, 444, 15, 506])).
% 0.73/1.02 tff(514,plain,
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% 0.73/1.02 inference(unit_resolution,[status(thm)],[513, 505])).
% 0.73/1.02 tff(515,plain,
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% 0.73/1.02 inference(rewrite,[status(thm)],[])).
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% 0.73/1.02 inference(quant_inst,[status(thm)],[])).
% 0.73/1.02 tff(517,plain,
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% 0.73/1.02 inference(modus_ponens,[status(thm)],[516, 515])).
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% 0.73/1.02 inference(unit_resolution,[status(thm)],[517, 60, 514, 12])).
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% 0.73/1.02 tff(520,plain,
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% 0.73/1.02 tff(521,plain,
% 0.73/1.02 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[458, 154, 444, 1, 232])).
% 0.73/1.02 tff(522,plain,
% 0.73/1.02 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[521, 505])).
% 0.73/1.02 tff(523,plain,
% 0.73/1.02 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.73/1.02 inference(unit_resolution,[status(thm)],[496, 522])).
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% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(525,plain,
% 0.73/1.02 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(526,plain,
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% 0.73/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
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% 0.73/1.02 inference(quant_inst,[status(thm)],[])).
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% 0.73/1.02 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.73/1.02 tff(530,plain,
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% 0.73/1.02 inference(unit_resolution,[status(thm)],[529, 28, 523, 520, 518])).
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% 0.73/1.02 tff(532,plain,
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% 0.73/1.02 (r(s(z), s(s(s(s(elem!1)))))),
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% 0.73/1.02 tff(534,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.73/1.02 tff(535,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
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% 0.73/1.02 tff(544,plain,
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% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(551,plain,
% 0.73/1.02 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.73/1.02 inference(rewrite,[status(thm)],[])).
% 0.73/1.02 tff(552,plain,
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[563, 337])).
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% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(592,plain,
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% 0.86/1.03 inference(monotonicity,[status(thm)],[591])).
% 0.86/1.03 tff(593,plain,
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% 0.86/1.03 inference(transitivity,[status(thm)],[592, 590])).
% 0.86/1.03 tff(594,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(595,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.86/1.03 tff(596,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[595, 28, 273, 67, 17])).
% 0.86/1.03 tff(597,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(598,plain,
% 0.86/1.03 (~r(s(s(s(z))), s(s(z)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[597, 587, 17])).
% 0.86/1.03 tff(599,plain,
% 0.86/1.03 (b(s(s(s(z))), s(s(z)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[104, 598])).
% 0.86/1.03 tff(600,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[162, 599, 589, 123, 65, 144])).
% 0.86/1.03 tff(601,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(602,plain,
% 0.86/1.03 (~b(s(s(z)), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[601, 17, 13, 15, 565, 16, 1])).
% 0.86/1.03 tff(603,plain,
% 0.86/1.03 (r(s(s(z)), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[138, 602])).
% 0.86/1.03 tff(604,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.86/1.03 tff(605,plain,
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% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(606,plain,
% 0.86/1.03 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(607,plain,
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% 0.86/1.03 inference(monotonicity,[status(thm)],[606])).
% 0.86/1.03 tff(608,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[607, 605])).
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% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(610,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.86/1.03 tff(611,plain,
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[610, 28, 124, 604, 16])).
% 0.86/1.03 tff(612,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(613,plain,
% 0.86/1.03 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[612, 603, 16])).
% 0.86/1.03 tff(614,plain,
% 0.86/1.03 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[343, 613])).
% 0.86/1.03 tff(615,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.86/1.03 tff(616,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(617,plain,
% 0.86/1.03 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(618,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[617])).
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% 0.86/1.03 inference(transitivity,[status(thm)],[618, 616])).
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% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.03 inference(modus_ponens,[status(thm)],[620, 619])).
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[621, 154, 1, 232, 615, 15, 566])).
% 0.86/1.03 tff(623,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(624,plain,
% 0.86/1.03 (~b(s(z), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[623, 614, 15, 1, 565])).
% 0.86/1.03 tff(625,plain,
% 0.86/1.03 (r(s(z), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[252, 624])).
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% 0.86/1.03 (~r(s(s(s(z))), s(s(z)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[597, 625, 17])).
% 0.86/1.03 tff(627,plain,
% 0.86/1.03 (b(s(s(s(z))), s(s(z)))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[104, 626])).
% 0.86/1.03 tff(628,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.86/1.03 tff(629,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
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% 0.86/1.03 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(631,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[630])).
% 0.86/1.03 tff(632,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[631, 629])).
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% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.03 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.86/1.03 tff(635,plain,
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[634, 28, 14, 628, 273])).
% 0.86/1.03 tff(636,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(637,plain,
% 0.86/1.03 (~r(z, s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[636, 625, 14])).
% 0.86/1.03 tff(638,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 0.86/1.03 tff(639,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 0.86/1.03 tff(640,plain,
% 0.86/1.03 (s(s(s(z))) = z),
% 0.86/1.03 inference(symmetry,[status(thm)],[639])).
% 0.86/1.03 tff(641,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[165, 640])).
% 0.86/1.03 tff(642,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(643,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 0.86/1.03 tff(644,plain,
% 0.86/1.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(645,plain,
% 0.86/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(646,plain,
% 0.86/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.86/1.03 tff(647,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[646, 60, 643, 642, 638])).
% 0.86/1.03 tff(648,plain,(b(z, s(s(s(z)))) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(649,plain,
% 0.86/1.03 (b(z, s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[648, 637])).
% 0.86/1.03 tff(650,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(651,plain,
% 0.86/1.03 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(652,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[651])).
% 0.86/1.03 tff(653,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[652, 650])).
% 0.86/1.03 tff(654,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(655,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.86/1.03 tff(656,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[655, 28, 124, 273, 299])).
% 0.86/1.03 tff(657,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(658,plain,
% 0.86/1.03 (~r(s(s(z)), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[657, 625, 603])).
% 0.86/1.03 tff(659,plain,
% 0.86/1.03 (b(s(s(z)), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[296, 658])).
% 0.86/1.03 tff(660,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.86/1.03 tff(661,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(662,plain,
% 0.86/1.03 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(663,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[662])).
% 0.86/1.04 tff(664,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[663, 661])).
% 0.86/1.04 tff(665,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(666,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.86/1.04 tff(667,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[666, 154, 1, 660, 231, 141, 140])).
% 0.86/1.04 tff(668,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(669,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 659, 649, 1, 627, 65])).
% 0.86/1.04 tff(670,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(671,plain,
% 0.86/1.04 (~r(s(z), s(s(z)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[670, 1, 14, 15, 16, 13, 12])).
% 0.86/1.04 tff(672,plain,
% 0.86/1.04 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 0.86/1.04 inference(commutativity,[status(thm)],[])).
% 0.86/1.04 tff(673,plain,
% 0.86/1.04 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.86/1.04 inference(symmetry,[status(thm)],[672])).
% 0.86/1.04 tff(674,plain,
% 0.86/1.04 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[673])).
% 0.86/1.04 tff(675,plain,
% 0.86/1.04 (~(s(z) = s(s(z)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[292, 674])).
% 0.86/1.04 tff(676,plain,
% 0.86/1.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(677,plain,
% 0.86/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(678,plain,
% 0.86/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.86/1.04 tff(679,plain,
% 0.86/1.04 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[678, 60])).
% 0.86/1.04 tff(680,plain,
% 0.86/1.04 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[679, 675])).
% 0.86/1.04 tff(681,plain,
% 0.86/1.04 (b(s(z), s(s(z)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[680, 671])).
% 0.86/1.04 tff(682,plain,
% 0.86/1.04 (~r(s(s(s(z))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[281, 273, 13])).
% 0.86/1.04 tff(683,plain,
% 0.86/1.04 (b(s(s(s(z))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[169, 682])).
% 0.86/1.04 tff(684,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 0.86/1.04 tff(685,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(686,plain,
% 0.86/1.04 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(687,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[686])).
% 0.86/1.04 tff(688,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[687, 685])).
% 0.86/1.04 tff(689,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(690,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.86/1.04 tff(691,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[690, 154, 144, 1, 684, 231, 141])).
% 0.86/1.04 tff(692,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(693,plain,
% 0.86/1.04 (~b(s(s(z)), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[692, 105, 684, 1, 139])).
% 0.86/1.04 tff(694,plain,
% 0.86/1.04 (r(s(s(z)), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[296, 693])).
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% 0.86/1.04 inference(rewrite,[status(thm)],[])).
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% 0.86/1.04 inference(rewrite,[status(thm)],[])).
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% 0.86/1.04 inference(monotonicity,[status(thm)],[696])).
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% 0.86/1.04 inference(transitivity,[status(thm)],[697, 695])).
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% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.04 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.86/1.04 tff(701,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[700, 28, 13, 106, 299])).
% 0.86/1.04 tff(702,plain,((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(703,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[702, 694, 13])).
% 0.86/1.04 tff(704,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[122, 703])).
% 0.86/1.04 tff(705,plain,
% 0.86/1.04 (~b(z, s(s(z)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[162, 704, 139, 105, 143])).
% 0.86/1.04 tff(706,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[64, 705])).
% 0.86/1.04 tff(707,plain,
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% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(708,plain,
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% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(709,plain,
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% 0.86/1.04 inference(monotonicity,[status(thm)],[708])).
% 0.86/1.04 tff(710,plain,
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% 0.86/1.04 inference(transitivity,[status(thm)],[709, 707])).
% 0.86/1.04 tff(711,plain,
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% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(712,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.86/1.04 tff(713,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[712, 28, 14, 706, 694])).
% 0.86/1.04 tff(714,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(715,plain,
% 0.86/1.04 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[714, 683, 14, 13, 681, 1, 16])).
% 0.86/1.04 tff(716,plain,
% 0.86/1.04 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[564, 715])).
% 0.86/1.04 tff(717,plain,
% 0.86/1.04 (~r(z, s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[636, 273, 14])).
% 0.86/1.04 tff(718,plain,
% 0.86/1.04 (b(z, s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[648, 717])).
% 0.86/1.04 tff(719,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(720,plain,
% 0.86/1.04 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(721,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[720])).
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% 0.86/1.04 inference(transitivity,[status(thm)],[721, 719])).
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% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.04 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.86/1.04 tff(725,plain,
% 0.86/1.04 (~r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[724, 28, 14, 298])).
% 0.86/1.04 tff(726,plain,
% 0.86/1.04 (b(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[191, 725])).
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% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
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% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(729,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[728])).
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% 0.86/1.04 inference(transitivity,[status(thm)],[729, 727])).
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% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.86/1.04 tff(733,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[732, 28, 14, 298])).
% 0.86/1.04 tff(734,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[206, 733])).
% 0.86/1.04 tff(735,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(736,plain,
% 0.86/1.04 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(737,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[736])).
% 0.86/1.04 tff(738,plain,
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% 0.86/1.04 inference(transitivity,[status(thm)],[737, 735])).
% 0.86/1.04 tff(739,plain,
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% 0.86/1.04 tff(740,plain,
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% 0.86/1.04 inference(modus_ponens,[status(thm)],[739, 738])).
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% 0.86/1.04 tff(743,plain,
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% 0.86/1.04 tff(744,plain,
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% 0.86/1.04 inference(rewrite,[status(thm)],[])).
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% 0.86/1.05 tff(747,plain,
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% 0.86/1.05 inference(monotonicity,[status(thm)],[746])).
% 0.86/1.05 tff(748,plain,
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% 0.86/1.05 inference(transitivity,[status(thm)],[747, 745])).
% 0.86/1.05 tff(749,plain,
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% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.05 inference(modus_ponens,[status(thm)],[749, 748])).
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% 0.86/1.05 tff(753,plain,
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% 0.86/1.05 tff(754,plain,
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% 0.86/1.05 inference(unit_resolution,[status(thm)],[343, 753])).
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% 0.86/1.05 (~r(s(s(z)), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[612, 754, 16])).
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% 0.86/1.05 (b(s(s(z)), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[138, 755])).
% 0.86/1.05 tff(757,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
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% 0.86/1.05 inference(rewrite,[status(thm)],[])).
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% 0.86/1.05 tff(765,plain,
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% 0.86/1.05 tff(766,plain,
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% 0.86/1.05 inference(unit_resolution,[status(thm)],[296, 765])).
% 0.86/1.05 tff(767,plain,
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% 0.86/1.05 inference(unit_resolution,[status(thm)],[712, 28, 14, 766])).
% 0.86/1.05 tff(768,plain,
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% 0.86/1.05 inference(unit_resolution,[status(thm)],[64, 767])).
% 0.86/1.05 tff(769,plain,
% 0.86/1.05 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[427, 768, 14, 766, 13])).
% 0.86/1.05 tff(770,plain,
% 0.86/1.05 (b(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[441, 769])).
% 0.86/1.05 tff(771,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(772,plain,
% 0.86/1.05 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
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% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[772])).
% 0.86/1.05 tff(774,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[773, 771])).
% 0.86/1.05 tff(775,plain,
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% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(776,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.86/1.05 tff(777,plain,
% 0.86/1.05 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[776, 154, 770, 1, 15, 716])).
% 0.86/1.05 tff(778,plain,
% 0.86/1.05 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[496, 777])).
% 0.86/1.05 tff(779,plain,
% 0.86/1.05 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[529, 28, 778, 754])).
% 0.86/1.05 tff(780,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 0.86/1.05 tff(781,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(782,plain,
% 0.86/1.05 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(783,plain,
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% 0.86/1.05 inference(monotonicity,[status(thm)],[782])).
% 0.86/1.05 tff(784,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[783, 781])).
% 0.86/1.05 tff(785,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(786,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.86/1.05 tff(787,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[786, 28, 535, 780, 273])).
% 0.86/1.05 tff(788,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(789,plain,
% 0.86/1.05 (~r(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[788, 778, 273])).
% 0.86/1.05 tff(790,plain,
% 0.86/1.05 (b(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[467, 789])).
% 0.86/1.05 tff(791,plain,
% 0.86/1.05 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[512, 154, 770, 15, 744])).
% 0.86/1.05 tff(792,plain,
% 0.86/1.05 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[791, 790])).
% 0.86/1.05 tff(793,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[517, 60, 792, 12, 779])).
% 0.86/1.05 tff(794,plain,((~r(s(z), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(795,plain,
% 0.86/1.05 (~r(s(z), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[794, 1, 15, 12, 14, 13, 16])).
% 0.86/1.05 tff(796,plain,
% 0.86/1.05 (b(s(z), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[252, 795])).
% 0.86/1.05 tff(797,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(798,plain,
% 0.86/1.05 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(799,plain,
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% 0.86/1.05 inference(monotonicity,[status(thm)],[798])).
% 0.86/1.05 tff(800,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[799, 797])).
% 0.86/1.05 tff(801,plain,
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% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.05 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.86/1.05 tff(803,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[802, 154, 139, 1, 232, 684, 105])).
% 0.86/1.05 tff(804,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(805,plain,
% 0.86/1.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[804, 1, 796, 681, 16])).
% 0.86/1.05 tff(806,plain,
% 0.86/1.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[564, 805])).
% 0.86/1.05 tff(807,plain,
% 0.86/1.05 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[623, 806, 15, 1, 796])).
% 0.86/1.05 tff(808,plain,
% 0.86/1.05 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[343, 807])).
% 0.86/1.05 tff(809,plain,
% 0.86/1.05 (~b(s(s(z)), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[585, 806, 15, 796, 16, 1])).
% 0.86/1.05 tff(810,plain,
% 0.86/1.05 (r(s(s(z)), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[138, 809])).
% 0.86/1.05 tff(811,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[612, 810, 808, 16])).
% 0.86/1.05 tff(812,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(813,plain,
% 0.86/1.05 (~b(s(s(s(z))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[812, 16, 15, 12, 14, 13])).
% 0.86/1.05 tff(814,plain,
% 0.86/1.05 (((~![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)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(815,plain,
% 0.86/1.05 ((~![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)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(816,plain,
% 0.86/1.05 ((~![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))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[815, 814])).
% 0.86/1.05 tff(817,plain,
% 0.86/1.05 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[816, 60])).
% 0.86/1.05 tff(818,plain,
% 0.86/1.05 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[817, 96])).
% 0.86/1.05 tff(819,plain,
% 0.86/1.05 (r(s(s(s(z))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[818, 813])).
% 0.86/1.05 tff(820,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.86/1.05 tff(821,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(822,plain,
% 0.86/1.05 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(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))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(823,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[822])).
% 0.86/1.05 tff(824,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[823, 821])).
% 0.86/1.05 tff(825,plain,
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% 0.86/1.05 tff(839,plain,
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% 0.86/1.05 tff(845,plain,
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% 0.86/1.06 tff(854,plain,
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% 0.86/1.06 tff(865,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(866,plain,
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% 0.86/1.06 tff(870,plain,
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% 0.86/1.06 inference(unit_resolution,[status(thm)],[838, 14, 820])).
% 0.86/1.06 tff(871,plain,
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% 0.86/1.06 inference(unit_resolution,[status(thm)],[648, 870])).
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% 0.86/1.06 inference(monotonicity,[status(thm)],[875])).
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% 0.86/1.06 inference(monotonicity,[status(thm)],[917])).
% 0.86/1.06 tff(919,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[918, 916])).
% 0.86/1.06 tff(920,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(921,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.86/1.06 tff(922,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[921, 28, 16, 106, 193])).
% 0.86/1.06 tff(923,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(924,plain,
% 0.86/1.06 (~r(s(s(s(s(z)))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[923, 895, 16])).
% 0.86/1.06 tff(925,plain,
% 0.86/1.06 (b(s(s(s(s(z)))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[206, 924])).
% 0.86/1.06 tff(926,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(927,plain,
% 0.86/1.06 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(928,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[927])).
% 0.86/1.07 tff(929,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[928, 926])).
% 0.86/1.07 tff(930,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(931,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[930, 929])).
% 0.86/1.07 tff(932,plain,
% 0.86/1.07 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[931, 154, 925, 887, 885, 915])).
% 0.86/1.07 tff(933,plain,
% 0.86/1.07 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[343, 932])).
% 0.86/1.07 tff(934,assumption,(~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.86/1.07 tff(935,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(936,plain,
% 0.86/1.07 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(937,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[936])).
% 0.86/1.07 tff(938,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[937, 935])).
% 0.86/1.07 tff(939,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(940,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.86/1.07 tff(941,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[940, 28, 820, 345, 780])).
% 0.86/1.07 tff(942,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(943,plain,
% 0.86/1.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[942, 780, 820])).
% 0.86/1.07 tff(944,plain,
% 0.86/1.07 (b(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[441, 943])).
% 0.86/1.07 tff(945,plain,
% 0.86/1.07 (~r(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[788, 780, 273])).
% 0.86/1.07 tff(946,plain,
% 0.86/1.07 (b(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[467, 945])).
% 0.86/1.07 tff(947,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(948,plain,
% 0.86/1.07 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(949,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[948])).
% 0.86/1.07 tff(950,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[949, 947])).
% 0.86/1.07 tff(951,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(952,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[951, 950])).
% 0.86/1.07 tff(953,plain,
% 0.86/1.07 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[952, 154, 946, 944, 15, 506])).
% 0.86/1.07 tff(954,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(955,plain,
% 0.86/1.07 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(956,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[955])).
% 0.86/1.07 tff(957,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[956, 954])).
% 0.86/1.07 tff(958,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(959,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.86/1.07 tff(960,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[959, 28, 780, 604])).
% 0.86/1.07 tff(961,plain,
% 0.86/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(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(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(962,plain,
% 0.86/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(963,plain,
% 0.86/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.86/1.07 tff(964,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[963, 60, 934, 960, 953])).
% 0.86/1.07 tff(965,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(966,plain,
% 0.86/1.07 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[965, 855, 15, 934, 933, 905, 820])).
% 0.86/1.07 tff(967,plain,
% 0.86/1.07 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[496, 966])).
% 0.86/1.07 tff(968,plain,
% 0.86/1.07 (~r(s(s(s(z))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[828, 14, 820])).
% 0.86/1.07 tff(969,plain,
% 0.86/1.07 (b(s(s(s(z))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[169, 968])).
% 0.86/1.07 tff(970,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(971,plain,
% 0.86/1.07 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(972,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[971])).
% 0.86/1.07 tff(973,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[972, 970])).
% 0.86/1.07 tff(974,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(975,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.86/1.07 tff(976,plain,
% 0.86/1.07 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[975, 28, 820, 345])).
% 0.86/1.07 tff(977,plain,
% 0.86/1.07 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(commutativity,[status(thm)],[])).
% 0.86/1.07 tff(978,plain,
% 0.86/1.07 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 0.86/1.07 inference(symmetry,[status(thm)],[977])).
% 0.86/1.07 tff(979,assumption,(s(s(s(z))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.86/1.07 tff(980,plain,
% 0.86/1.07 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.86/1.07 tff(981,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), introduced(assumption)).
% 0.86/1.07 tff(982,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[981, 980])).
% 0.86/1.07 tff(983,plain,((~(s(s(s(z))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(984,plain,
% 0.86/1.07 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[983, 491])).
% 0.86/1.07 tff(985,plain,
% 0.86/1.07 (((~![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))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(986,plain,
% 0.86/1.07 ((~![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))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(987,plain,
% 0.86/1.07 ((~![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)))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.86/1.07 tff(988,plain,
% 0.86/1.07 ((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)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[987, 60])).
% 0.86/1.07 tff(989,plain,
% 0.86/1.07 (b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[988, 984])).
% 0.86/1.07 tff(990,plain,
% 0.86/1.07 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[989, 976])).
% 0.86/1.07 tff(991,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(992,plain,
% 0.86/1.07 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(993,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[992])).
% 0.86/1.07 tff(994,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[993, 991])).
% 0.86/1.07 tff(995,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(996,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.86/1.07 tff(997,plain,
% 0.86/1.07 (~r(s(s(s(s(elem!1)))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[996, 28, 345, 14])).
% 0.86/1.07 tff(998,plain,
% 0.86/1.07 (b(s(s(s(s(elem!1)))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[418, 997])).
% 0.86/1.07 tff(999,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(1000,plain,
% 0.86/1.07 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1001,plain,
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% 0.86/1.08 inference(monotonicity,[status(thm)],[1000])).
% 0.86/1.08 tff(1002,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1001, 999])).
% 0.86/1.08 tff(1003,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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)))))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1004,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.86/1.08 tff(1005,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1004, 154, 998, 990, 443, 969, 871])).
% 0.86/1.08 tff(1006,plain,((~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1007,plain,
% 0.86/1.08 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1006, 967, 14, 820])).
% 0.86/1.08 tff(1008,plain,
% 0.86/1.08 (b(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[441, 1007])).
% 0.86/1.08 tff(1009,plain,
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% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1010,plain,
% 0.86/1.08 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1011,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1010])).
% 0.86/1.08 tff(1012,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1011, 1009])).
% 0.86/1.08 tff(1013,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1014,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.86/1.08 tff(1015,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1014, 28, 535, 13, 402])).
% 0.86/1.08 tff(1016,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1017,plain,
% 0.86/1.08 (~r(s(s(s(s(elem!1)))), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1016, 535, 13])).
% 0.86/1.08 tff(1018,plain,
% 0.86/1.08 (b(s(s(s(s(elem!1)))), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[418, 1017])).
% 0.86/1.08 tff(1019,assumption,(r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.86/1.08 tff(1020,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1021,plain,
% 0.86/1.08 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1022,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1021])).
% 0.86/1.08 tff(1023,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1022, 1020])).
% 0.86/1.08 tff(1024,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1025,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.86/1.08 tff(1026,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1025, 28, 535, 1019, 273])).
% 0.86/1.08 tff(1027,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1028,plain,
% 0.86/1.08 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1027, 535, 273])).
% 0.86/1.08 tff(1029,plain,
% 0.86/1.08 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[989, 1028])).
% 0.86/1.08 tff(1030,plain,
% 0.86/1.08 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1004, 154, 443, 143, 660])).
% 0.86/1.08 tff(1031,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1030, 1029, 1018])).
% 0.86/1.08 tff(1032,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1033,plain,
% 0.86/1.08 (~r(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1032, 967, 887, 885, 905, 13])).
% 0.86/1.08 tff(1034,plain,
% 0.86/1.08 (b(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[467, 1033])).
% 0.86/1.08 tff(1035,plain,
% 0.86/1.08 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[952, 154, 1034, 1008, 15, 855])).
% 0.86/1.08 tff(1036,plain,
% 0.86/1.08 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[963, 60, 934, 1035])).
% 0.86/1.08 tff(1037,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1038,plain,
% 0.86/1.08 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1039,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1038])).
% 0.86/1.08 tff(1040,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1039, 1037])).
% 0.86/1.08 tff(1041,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1042,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.86/1.08 tff(1043,plain,
% 0.86/1.08 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1042, 154, 139, 967, 897])).
% 0.86/1.08 tff(1044,plain,
% 0.86/1.08 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1043, 1034])).
% 0.86/1.08 tff(1045,assumption,(s(s(s(s(elem!1)))) = s(s(z))), introduced(assumption)).
% 0.86/1.08 tff(1046,plain,
% 0.86/1.08 (s(s(z)) = s(s(s(s(elem!1))))),
% 0.86/1.08 inference(symmetry,[status(thm)],[1045])).
% 0.86/1.08 tff(1047,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[370, 1046])).
% 0.86/1.08 tff(1048,plain,(~(s(s(s(s(elem!1)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1049,plain,
% 0.86/1.08 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1050,plain,
% 0.86/1.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1051,plain,
% 0.86/1.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.86/1.08 tff(1052,plain,
% 0.86/1.08 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1051, 60, 1048, 1044])).
% 0.86/1.08 tff(1053,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1054,plain,
% 0.86/1.08 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1055,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1054])).
% 0.86/1.08 tff(1056,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1055, 1053])).
% 0.86/1.08 tff(1057,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1058,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.86/1.08 tff(1059,plain,
% 0.86/1.08 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1058, 154, 15, 897, 883, 855])).
% 0.86/1.08 tff(1060,plain,
% 0.86/1.08 (r(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[229, 1059])).
% 0.86/1.08 tff(1061,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1062,plain,
% 0.86/1.08 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1063,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1062])).
% 0.86/1.08 tff(1064,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1063, 1061])).
% 0.86/1.08 tff(1065,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1066,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 0.86/1.08 tff(1067,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1066, 28, 1060, 1052, 1036])).
% 0.86/1.08 tff(1068,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(1069,plain,
% 0.86/1.08 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1068, 819, 15, 13, 14, 845, 16])).
% 0.86/1.08 tff(1070,plain,
% 0.86/1.08 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[564, 1069])).
% 0.86/1.08 tff(1071,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[742, 1070, 840, 830, 14])).
% 0.86/1.08 tff(1072,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[318, 1071])).
% 0.86/1.08 tff(1073,plain,
% 0.86/1.08 (~r(s(s(z)), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[881, 819, 14])).
% 0.86/1.08 tff(1074,plain,
% 0.86/1.08 (b(s(s(z)), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[296, 1073])).
% 0.86/1.08 tff(1075,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[612, 124, 16])).
% 0.86/1.08 tff(1076,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[343, 1075])).
% 0.86/1.08 tff(1077,plain,
% 0.86/1.08 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1068, 820, 15, 13, 14, 934, 16])).
% 0.86/1.08 tff(1078,plain,
% 0.86/1.08 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[564, 1077])).
% 0.86/1.08 tff(1079,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[742, 1078, 885, 887, 14])).
% 0.86/1.08 tff(1080,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[318, 1079])).
% 0.86/1.08 tff(1081,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1082,plain,
% 0.86/1.08 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1083,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[1082])).
% 0.86/1.08 tff(1084,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[1083, 1081])).
% 0.86/1.08 tff(1085,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(1086,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 0.86/1.08 tff(1087,plain,
% 0.86/1.08 (~b(s(z), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1086, 154, 1076, 15, 1080, 1078])).
% 0.86/1.08 tff(1088,plain,
% 0.86/1.08 (r(s(z), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[252, 1087])).
% 0.86/1.08 tff(1089,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1090,plain,
% 0.86/1.08 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(1091,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1090])).
% 0.86/1.09 tff(1092,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[1091, 1089])).
% 0.86/1.09 tff(1093,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(1094,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 0.86/1.09 tff(1095,plain,
% 0.86/1.09 (~r(s(z), s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1094, 28, 124, 1088])).
% 0.86/1.09 tff(1096,plain,
% 0.86/1.09 (b(s(z), s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[680, 1095])).
% 0.86/1.09 tff(1097,plain,
% 0.86/1.09 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 0.86/1.09 inference(commutativity,[status(thm)],[])).
% 0.86/1.09 tff(1098,plain,
% 0.86/1.09 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 0.86/1.09 inference(symmetry,[status(thm)],[1097])).
% 0.86/1.09 tff(1099,plain,
% 0.86/1.09 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(z))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1098])).
% 0.86/1.09 tff(1100,plain,
% 0.86/1.09 (~(s(s(s(s(elem!1)))) = s(s(z)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[370, 1099])).
% 0.86/1.09 tff(1101,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1102,plain,
% 0.86/1.09 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1103,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1102])).
% 0.86/1.09 tff(1104,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[1103, 1101])).
% 0.86/1.09 tff(1105,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(1106,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 0.86/1.09 tff(1107,plain,
% 0.86/1.09 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1106, 28, 124, 780])).
% 0.86/1.09 tff(1108,plain,
% 0.86/1.09 ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1051, 60, 1107])).
% 0.86/1.09 tff(1109,plain,
% 0.86/1.09 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1108, 1100])).
% 0.86/1.09 tff(1110,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1111,plain,
% 0.86/1.09 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1112,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1111])).
% 0.86/1.09 tff(1113,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[1112, 1110])).
% 0.86/1.09 tff(1114,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(1115,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.86/1.09 tff(1116,plain,
% 0.86/1.09 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1115, 28, 124, 780])).
% 0.86/1.09 tff(1117,plain,
% 0.86/1.09 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[373, 60, 370, 1116])).
% 0.86/1.09 tff(1118,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1119,plain,
% 0.86/1.09 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1120,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1119])).
% 0.86/1.09 tff(1121,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.86/1.09 tff(1122,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(1123,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.86/1.09 tff(1124,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1123, 28, 124, 820, 299])).
% 0.86/1.09 tff(1125,plain,((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(1126,plain,
% 0.86/1.09 (~r(s(s(z)), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1125, 124, 820])).
% 0.86/1.09 tff(1127,plain,
% 0.86/1.09 (b(s(s(z)), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[296, 1126])).
% 0.86/1.09 tff(1128,plain,
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% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1129,plain,
% 0.86/1.09 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1130,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1129])).
% 0.86/1.09 tff(1131,plain,
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% 0.86/1.09 inference(transitivity,[status(thm)],[1130, 1128])).
% 0.86/1.09 tff(1132,plain,
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% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(1133,plain,
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% 0.86/1.09 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.86/1.09 tff(1134,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1133, 154, 944, 684, 1127, 1117, 1109])).
% 0.86/1.09 tff(1135,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(1136,plain,
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% 0.86/1.09 tff(1137,plain,
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% 0.86/1.09 tff(1138,plain,
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% 0.86/1.09 inference(unit_resolution,[status(thm)],[1032, 1137, 887, 885, 1088, 13])).
% 0.86/1.09 tff(1139,plain,
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% 0.86/1.09 inference(unit_resolution,[status(thm)],[467, 1138])).
% 0.86/1.09 tff(1140,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1141,plain,
% 0.86/1.09 (((~b(s(s(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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1142,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[1141])).
% 0.86/1.09 tff(1143,plain,
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% 0.86/1.09 inference(transitivity,[status(thm)],[1142, 1140])).
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% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.09 inference(modus_ponens,[status(thm)],[1144, 1143])).
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% 0.86/1.09 inference(unit_resolution,[status(thm)],[1145, 154, 1139, 1137, 1076, 15])).
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% 0.86/1.09 tff(1148,plain,
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% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(1151,plain,
% 0.86/1.09 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
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% 0.86/1.09 inference(monotonicity,[status(thm)],[1151])).
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% 0.86/1.10 tff(1159,plain,
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% 0.86/1.10 inference(unit_resolution,[status(thm)],[229, 1158])).
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% 0.86/1.10 inference(unit_resolution,[status(thm)],[1066, 28, 1159, 1157, 1147])).
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% 0.86/1.10 tff(1162,plain,
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% 0.86/1.10 inference(unit_resolution,[status(thm)],[879, 154, 143, 142, 141, 140])).
% 0.86/1.10 tff(1169,plain,
% 0.86/1.10 (r(z, s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[648, 1168])).
% 0.86/1.10 tff(1170,plain,
% 0.86/1.10 (~r(z, s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[838, 1169, 820])).
% 0.86/1.10 tff(1171,assumption,(~r(z, s(z))), introduced(assumption)).
% 0.86/1.10 tff(1172,assumption,(z = s(z)), introduced(assumption)).
% 0.86/1.10 tff(1173,plain,
% 0.86/1.10 (s(z) = z),
% 0.86/1.10 inference(symmetry,[status(thm)],[1172])).
% 0.86/1.10 tff(1174,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[266, 1173])).
% 0.86/1.10 tff(1175,plain,(~(z = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(1176,assumption,(~b(z, s(z))), introduced(assumption)).
% 0.86/1.10 tff(1177,plain,
% 0.86/1.10 (((~![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)))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1178,plain,
% 0.86/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(1179,plain,
% 0.86/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 0.86/1.10 tff(1180,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1179, 60, 1176, 1175, 1171])).
% 0.86/1.10 tff(1181,plain,(r(z, s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(1182,plain,
% 0.86/1.10 (b(z, s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1181, 1170])).
% 0.86/1.10 tff(1183,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1184,plain,
% 0.86/1.10 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1185,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[1184])).
% 0.86/1.10 tff(1186,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[1185, 1183])).
% 0.86/1.10 tff(1187,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(1188,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.86/1.10 tff(1189,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1188, 154, 1182, 143, 231, 141, 140])).
% 0.86/1.10 tff(1190,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(1191,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1190, 1167, 65, 820, 231, 123, 143])).
% 0.86/1.10 tff(1192,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(1193,plain,
% 0.86/1.10 (~r(s(z), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1192, 819, 1074, 830, 1165, 13, 16])).
% 0.86/1.10 tff(1194,plain,
% 0.86/1.10 (b(s(z), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[680, 1193])).
% 0.86/1.10 tff(1195,plain,
% 0.86/1.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1058, 154, 15, 1194, 1074, 1072])).
% 0.86/1.10 tff(1196,plain,
% 0.86/1.10 (r(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[229, 1195])).
% 0.86/1.10 tff(1197,plain,
% 0.86/1.10 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1006, 443, 14, 820])).
% 0.86/1.10 tff(1198,plain,
% 0.86/1.10 (b(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[441, 1197])).
% 0.86/1.10 tff(1199,plain,
% 0.86/1.10 (~r(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1032, 443, 887, 885, 273, 13])).
% 0.86/1.10 tff(1200,plain,
% 0.86/1.10 (b(s(z), s(s(s(s(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[467, 1199])).
% 0.86/1.10 tff(1201,plain,
% 0.86/1.10 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[952, 154, 1200, 1198, 15, 506])).
% 0.86/1.10 tff(1202,plain,
% 0.86/1.10 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[963, 60, 934, 1201])).
% 0.86/1.10 tff(1203,plain,
% 0.86/1.10 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1042, 154, 144, 1200, 443, 684])).
% 0.86/1.10 tff(1204,plain,
% 0.86/1.10 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1051, 60, 1048, 1203])).
% 0.86/1.10 tff(1205,plain,
% 0.86/1.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1058, 154, 15, 684, 883, 506])).
% 0.86/1.10 tff(1206,plain,
% 0.86/1.10 (r(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[229, 1205])).
% 0.86/1.10 tff(1207,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1066, 28, 1206, 1204, 1202])).
% 0.86/1.10 tff(1208,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(1209,plain,
% 0.86/1.10 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1208, 1072, 15, 845, 1163, 1194, 1165, 13, 14, 819])).
% 0.86/1.10 tff(1210,plain,
% 0.86/1.10 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[496, 1209])).
% 0.86/1.10 tff(1211,plain,
% 0.86/1.10 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[965, 1210, 15, 845, 1072, 1165, 819])).
% 0.86/1.10 tff(1212,plain,
% 0.86/1.10 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[343, 1211])).
% 0.86/1.10 tff(1213,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1214,plain,
% 0.86/1.10 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1215,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[1214])).
% 0.86/1.10 tff(1216,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[1215, 1213])).
% 0.86/1.10 tff(1217,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(1218,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 0.86/1.10 tff(1219,plain,
% 0.86/1.10 (~b(z, s(s(s(s(z)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1218, 154, 830, 1212, 840, 1070])).
% 0.86/1.10 tff(1220,plain,
% 0.86/1.10 (r(z, s(s(s(s(z)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[191, 1219])).
% 0.86/1.10 tff(1221,plain,
% 0.86/1.10 (~r(z, s(s(s(s(z)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[913, 106, 16])).
% 0.86/1.10 tff(1222,plain,
% 0.86/1.10 (b(z, s(s(s(s(z)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[191, 1221])).
% 0.86/1.10 tff(1223,plain,
% 0.86/1.10 (~r(s(s(s(s(z)))), z)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[923, 106, 16])).
% 0.86/1.10 tff(1224,plain,
% 0.86/1.10 (b(s(s(s(s(z)))), z)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[206, 1223])).
% 0.86/1.10 tff(1225,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1226,plain,
% 0.86/1.10 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1227,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[1226])).
% 0.86/1.10 tff(1228,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[1227, 1225])).
% 0.86/1.10 tff(1229,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(1230,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 0.86/1.10 tff(1231,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1230, 154, 1224, 143, 615, 566, 1222])).
% 0.86/1.10 tff(1232,plain,((~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(1233,plain,
% 0.86/1.10 (~r(s(s(z)), z)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1232, 1212, 830, 1070, 16])).
% 0.86/1.10 tff(1234,plain,
% 0.86/1.10 (b(s(s(z)), z)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[122, 1233])).
% 0.86/1.10 tff(1235,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1236,plain,
% 0.86/1.10 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1237,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[1236])).
% 0.86/1.10 tff(1238,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[1237, 1235])).
% 0.86/1.10 tff(1239,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(1240,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 0.86/1.10 tff(1241,plain,
% 0.86/1.10 (~b(z, s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1240, 154, 1163, 830, 840, 1234])).
% 0.86/1.10 tff(1242,plain,
% 0.86/1.10 (r(z, s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[64, 1241])).
% 0.86/1.10 tff(1243,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.86/1.10 tff(1244,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1245,plain,
% 0.86/1.10 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(1246,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[1245])).
% 0.86/1.10 tff(1247,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[1246, 1244])).
% 0.86/1.10 tff(1248,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(1249,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 0.86/1.10 tff(1250,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1249, 28, 172, 18, 1243])).
% 0.86/1.10 tff(1251,plain,((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1252,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1251, 1242, 1220, 1196])).
% 0.86/1.11 tff(1253,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1254,plain,
% 0.86/1.11 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1253, 15, 13, 14, 12])).
% 0.86/1.11 tff(1255,plain,
% 0.86/1.11 (((~![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))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1256,plain,
% 0.86/1.11 ((~![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))))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(1257,plain,
% 0.86/1.11 ((~![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)))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.86/1.11 tff(1258,plain,
% 0.86/1.11 ((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)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1257, 60])).
% 0.86/1.11 tff(1259,plain,
% 0.86/1.11 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1258, 223])).
% 0.86/1.11 tff(1260,plain,
% 0.86/1.11 (b(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1259, 1254])).
% 0.86/1.11 tff(1261,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1262,plain,
% 0.86/1.11 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1263,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[1262])).
% 0.86/1.11 tff(1264,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[1263, 1261])).
% 0.86/1.11 tff(1265,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(1266,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 0.86/1.11 tff(1267,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1266, 28, 820, 13, 171])).
% 0.86/1.11 tff(1268,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1269,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1268, 171, 13])).
% 0.86/1.11 tff(1270,plain,
% 0.86/1.11 (b(s(s(s(z))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[818, 1269])).
% 0.86/1.11 tff(1271,plain,
% 0.86/1.11 (~r(s(s(z)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[382, 106, 14])).
% 0.86/1.11 tff(1272,plain,
% 0.86/1.11 (b(s(s(z)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[296, 1271])).
% 0.86/1.11 tff(1273,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1274,plain,
% 0.86/1.11 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1275,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[1274])).
% 0.86/1.11 tff(1276,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.86/1.11 inference(transitivity,[status(thm)],[1275, 1273])).
% 0.86/1.11 tff(1277,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(1278,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 0.86/1.11 tff(1279,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1278, 28, 106, 171, 67])).
% 0.86/1.11 tff(1280,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1281,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1280, 106, 171])).
% 0.86/1.11 tff(1282,plain,
% 0.86/1.11 (b(s(s(s(z))), s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[104, 1281])).
% 0.86/1.11 tff(1283,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 0.86/1.11 tff(1284,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1285,plain,
% 0.86/1.11 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1286,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[1285])).
% 0.86/1.11 tff(1287,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[1286, 1284])).
% 0.86/1.11 tff(1288,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(1289,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 0.86/1.11 tff(1290,plain,
% 0.86/1.11 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1289, 154, 1, 1283, 15])).
% 0.86/1.11 tff(1291,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1290, 1282, 1272])).
% 0.86/1.11 tff(1292,plain,((~r(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1293,plain,
% 0.86/1.11 (~r(s(s(z)), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1292, 1270, 1260, 15, 171, 14])).
% 0.86/1.11 tff(1294,plain,
% 0.86/1.11 (b(s(s(z)), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[122, 1293])).
% 0.86/1.11 tff(1295,plain,
% 0.86/1.11 (~r(z, s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[180, 66, 171])).
% 0.86/1.11 tff(1296,plain,
% 0.86/1.11 (b(z, s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[191, 1295])).
% 0.86/1.11 tff(1297,plain,
% 0.86/1.11 (~r(s(s(s(s(z)))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[201, 66, 171])).
% 0.86/1.11 tff(1298,plain,
% 0.86/1.11 (b(s(s(s(s(z)))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[206, 1297])).
% 0.86/1.11 tff(1299,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.86/1.11 tff(1300,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1301,plain,
% 0.86/1.11 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1302,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[1301])).
% 0.86/1.11 tff(1303,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[1302, 1300])).
% 0.86/1.11 tff(1304,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 0.86/1.11 tff(1306,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1305, 154, 1299, 1283, 142, 140, 254])).
% 0.86/1.11 tff(1307,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1308,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1307, 1298, 1296, 1283, 142, 140])).
% 0.86/1.11 tff(1309,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1310,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1309, 857, 1294, 1260, 171])).
% 0.86/1.11 tff(1311,plain,
% 0.86/1.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[564, 1310])).
% 0.86/1.11 tff(1312,plain,
% 0.86/1.11 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[623, 1311, 15, 1270, 232])).
% 0.86/1.11 tff(1313,plain,
% 0.86/1.11 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[343, 1312])).
% 0.86/1.11 tff(1314,plain,
% 0.86/1.11 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[427, 857, 14, 299, 13])).
% 0.86/1.11 tff(1315,plain,
% 0.86/1.11 (b(s(s(s(s(elem!1)))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[441, 1314])).
% 0.86/1.11 tff(1316,plain,
% 0.86/1.11 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[776, 154, 1315, 1270, 15, 1311])).
% 0.86/1.11 tff(1317,plain,
% 0.86/1.11 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[496, 1316])).
% 0.86/1.11 tff(1318,plain,
% 0.86/1.11 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[959, 28, 1317, 1313])).
% 0.86/1.11 tff(1319,plain,
% 0.86/1.11 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[963, 60, 845, 1318])).
% 0.86/1.11 tff(1320,plain,
% 0.86/1.11 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[529, 28, 1317, 1313])).
% 0.86/1.11 tff(1321,plain,
% 0.86/1.11 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[517, 60, 12, 1320])).
% 0.86/1.11 tff(1322,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1307, 734, 726, 1283, 142, 140])).
% 0.86/1.11 tff(1323,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1324,plain,
% 0.86/1.11 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1323, 857, 1294, 1260, 14])).
% 0.86/1.11 tff(1325,plain,
% 0.86/1.11 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[318, 1324])).
% 0.86/1.11 tff(1326,plain,
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% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1327,plain,
% 0.86/1.11 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1328,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[1327])).
% 0.86/1.11 tff(1329,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[1328, 1326])).
% 0.86/1.11 tff(1330,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(1331,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 0.86/1.11 tff(1332,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1331, 154, 1315, 15, 1325, 1321, 1319])).
% 0.86/1.11 tff(1333,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1334,plain,
% 0.86/1.11 (~r(s(s(z)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1333, 171, 14, 12, 232, 15, 13])).
% 0.86/1.11 tff(1335,plain,
% 0.86/1.11 (b(s(s(z)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[296, 1334])).
% 0.86/1.11 tff(1336,plain,
% 0.86/1.11 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1289, 154, 1270, 1260, 15])).
% 0.86/1.11 tff(1337,plain,
% 0.86/1.11 (~b(s(s(s(z))), s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1336, 1335])).
% 0.86/1.11 tff(1338,plain,
% 0.86/1.11 (r(s(s(s(z))), s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[104, 1337])).
% 0.86/1.11 tff(1339,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1340,plain,
% 0.86/1.11 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1341,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[1340])).
% 0.86/1.11 tff(1342,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[1341, 1339])).
% 0.86/1.11 tff(1343,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(1344,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.86/1.11 tff(1345,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1344, 28, 18, 171, 67])).
% 0.86/1.11 tff(1346,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1347,plain,
% 0.86/1.11 (~r(z, s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1346, 1338, 171])).
% 0.86/1.11 tff(1348,plain,
% 0.86/1.11 (b(z, s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[64, 1347])).
% 0.86/1.11 tff(1349,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1309, 1348, 1294, 1260, 171])).
% 0.86/1.11 tff(1350,plain,
% 0.86/1.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[564, 1349])).
% 0.86/1.11 tff(1351,plain,
% 0.86/1.11 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1323, 1348, 1294, 1260, 14])).
% 0.86/1.11 tff(1352,plain,
% 0.86/1.11 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[318, 1351])).
% 0.86/1.11 tff(1353,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[583, 154, 1270, 232, 15, 1352, 1350])).
% 0.86/1.11 tff(1354,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(1355,plain,
% 0.86/1.11 (~r(s(s(s(z))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1354, 232, 15, 14, 12, 13])).
% 0.86/1.11 tff(1356,plain,
% 0.86/1.11 (b(s(s(s(z))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[169, 1355])).
% 0.86/1.11 tff(1357,plain,
% 0.86/1.11 (~r(s(z), s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[36, 18, 13])).
% 0.86/1.11 tff(1358,plain,
% 0.86/1.11 (b(s(z), s(s(z)))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[680, 1357])).
% 0.86/1.11 tff(1359,plain,
% 0.86/1.11 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 0.86/1.11 inference(commutativity,[status(thm)],[])).
% 0.86/1.11 tff(1360,plain,
% 0.86/1.11 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[1359])).
% 0.86/1.11 tff(1361,plain,
% 0.86/1.11 (~(s(z) = s(s(s(s(z)))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[313, 1360])).
% 0.86/1.11 tff(1362,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1363,plain,
% 0.86/1.11 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(1364,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[1363])).
% 0.86/1.12 tff(1365,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.86/1.12 tff(1366,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1367,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.86/1.12 tff(1368,plain,
% 0.86/1.12 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1367, 28, 13, 193])).
% 0.86/1.12 tff(1369,plain,
% 0.86/1.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1370,plain,
% 0.86/1.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1371,plain,
% 0.86/1.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 0.86/1.12 tff(1372,plain,
% 0.86/1.12 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1371, 60])).
% 0.86/1.12 tff(1373,plain,
% 0.86/1.12 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1372, 1368, 1361])).
% 0.86/1.12 tff(1374,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1375,plain,
% 0.86/1.12 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1376,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[1375])).
% 0.86/1.12 tff(1377,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.12 inference(transitivity,[status(thm)],[1376, 1374])).
% 0.86/1.12 tff(1378,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1379,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.86/1.12 tff(1380,plain,
% 0.86/1.12 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1379, 28, 13, 193])).
% 0.86/1.12 tff(1381,plain,
% 0.86/1.12 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[317, 1380, 313])).
% 0.86/1.12 tff(1382,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1383,plain,
% 0.86/1.12 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1384,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[1383])).
% 0.86/1.12 tff(1385,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[1384, 1382])).
% 0.86/1.12 tff(1386,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1387,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 0.86/1.12 tff(1388,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1387, 154, 1283, 15, 684, 231, 506])).
% 0.86/1.12 tff(1389,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(1390,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1389, 1381, 1373, 231, 684, 1283])).
% 0.86/1.12 tff(1391,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(1392,plain,
% 0.86/1.12 (~r(s(s(s(s(z)))), z)),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1391, 231, 13, 1283, 684])).
% 0.86/1.12 tff(1393,plain,
% 0.86/1.12 (b(s(s(s(s(z)))), z)),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[206, 1392])).
% 0.86/1.12 tff(1394,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1395,plain,
% 0.86/1.12 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1396,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[1395])).
% 0.86/1.12 tff(1397,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[1396, 1394])).
% 0.86/1.12 tff(1398,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1399,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 0.86/1.12 tff(1400,plain,
% 0.86/1.12 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1399, 154, 232, 1393, 143, 15])).
% 0.86/1.12 tff(1401,plain,
% 0.86/1.12 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[343, 1400])).
% 0.86/1.12 tff(1402,plain,
% 0.86/1.12 (~b(s(s(s(s(z)))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1389, 231, 15, 1283, 684])).
% 0.86/1.12 tff(1403,plain,
% 0.86/1.12 (r(s(s(s(s(z)))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[318, 1402])).
% 0.86/1.12 tff(1404,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1405,plain,
% 0.86/1.12 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1406,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[1405])).
% 0.86/1.12 tff(1407,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[1406, 1404])).
% 0.86/1.12 tff(1408,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1409,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.86/1.12 tff(1410,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1409, 28, 820, 604, 298])).
% 0.86/1.12 tff(1411,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(1412,plain,
% 0.86/1.12 (~r(s(s(s(z))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1411, 1401, 1403])).
% 0.86/1.12 tff(1413,plain,
% 0.86/1.12 (b(s(s(s(z))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[818, 1412])).
% 0.86/1.12 tff(1414,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1415,plain,
% 0.86/1.12 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1416,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[1415])).
% 0.86/1.12 tff(1417,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[1416, 1414])).
% 0.86/1.12 tff(1418,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1419,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 0.86/1.12 tff(1420,plain,
% 0.86/1.12 (~b(s(s(z)), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1419, 154, 1413, 232, 684, 231])).
% 0.86/1.12 tff(1421,plain,
% 0.86/1.12 (r(s(s(z)), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[138, 1420])).
% 0.86/1.12 tff(1422,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1423,plain,
% 0.86/1.12 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1424,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[1423])).
% 0.86/1.12 tff(1425,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[1424, 1422])).
% 0.86/1.12 tff(1426,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(1427,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 0.86/1.12 tff(1428,plain,
% 0.86/1.12 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1427, 28, 1421, 1401])).
% 0.86/1.12 tff(1429,plain,
% 0.86/1.12 (b(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[229, 1428])).
% 0.86/1.12 tff(1430,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1431,plain,
% 0.86/1.12 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(1432,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[1431])).
% 0.96/1.13 tff(1433,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[1432, 1430])).
% 0.96/1.13 tff(1434,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(1435,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 0.96/1.13 tff(1436,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1435, 154, 1283, 15, 684, 231, 1429])).
% 0.96/1.13 tff(1437,plain,((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(1438,plain,
% 0.96/1.13 (~b(s(s(z)), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1437, 1358, 15, 1283, 232, 143, 13])).
% 0.96/1.13 tff(1439,plain,
% 0.96/1.13 (r(s(s(z)), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[296, 1438])).
% 0.96/1.13 tff(1440,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[712, 28, 14, 18, 1439])).
% 0.96/1.13 tff(1441,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(1442,plain,
% 0.96/1.13 (~r(z, s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1441, 232, 15, 1260, 14, 1356, 13])).
% 0.96/1.13 tff(1443,plain,
% 0.96/1.13 (b(z, s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[64, 1442])).
% 0.96/1.13 tff(1444,plain,
% 0.96/1.13 (~r(s(s(z)), z)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[702, 299, 13])).
% 0.96/1.13 tff(1445,plain,
% 0.96/1.13 (b(s(s(z)), z)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[122, 1444])).
% 0.96/1.13 tff(1446,plain,
% 0.96/1.13 (~r(s(s(s(s(z)))), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1323, 1445, 1443, 1260, 14])).
% 0.96/1.13 tff(1447,plain,
% 0.96/1.13 (b(s(s(s(s(z)))), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[318, 1446])).
% 0.96/1.13 tff(1448,plain,
% 0.96/1.13 (~r(s(s(s(z))), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[881, 299, 14])).
% 0.96/1.13 tff(1449,plain,
% 0.96/1.13 (b(s(s(s(z))), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[818, 1448])).
% 0.96/1.13 tff(1450,plain,
% 0.96/1.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[327, 154, 1449, 232, 15, 1447])).
% 0.96/1.13 tff(1451,plain,
% 0.96/1.13 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[343, 1450])).
% 0.96/1.13 tff(1452,plain,
% 0.96/1.13 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[427, 299, 14, 1443, 13])).
% 0.96/1.13 tff(1453,plain,
% 0.96/1.13 (b(s(s(s(s(elem!1)))), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[441, 1452])).
% 0.96/1.13 tff(1454,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1455,plain,
% 0.96/1.13 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1456,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[1455])).
% 0.96/1.13 tff(1457,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.96/1.13 inference(transitivity,[status(thm)],[1456, 1454])).
% 0.96/1.13 tff(1458,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(1459,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 0.96/1.13 tff(1460,plain,
% 0.96/1.13 (~r(s(s(s(s(z)))), z)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1459, 28, 628, 604])).
% 0.96/1.13 tff(1461,plain,
% 0.96/1.13 (b(s(s(s(s(z)))), z)),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[206, 1460])).
% 0.96/1.13 tff(1462,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1463,plain,
% 0.96/1.13 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1464,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[1463])).
% 0.96/1.13 tff(1465,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[1464, 1462])).
% 0.96/1.13 tff(1466,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(1467,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 0.96/1.13 tff(1468,plain,
% 0.96/1.13 (~r(z, s(s(s(s(z)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1467, 28, 628, 604])).
% 0.96/1.13 tff(1469,plain,
% 0.96/1.13 (b(z, s(s(s(s(z)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[191, 1468])).
% 0.96/1.13 tff(1470,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1307, 1469, 1461, 1283, 142, 140])).
% 0.96/1.13 tff(1471,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(1472,plain,
% 0.96/1.13 (~r(z, s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1471, 1445, 1260, 1443, 1451])).
% 0.96/1.13 tff(1473,plain,
% 0.96/1.13 (b(z, s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[648, 1472])).
% 0.96/1.13 tff(1474,plain,
% 0.96/1.13 (~b(s(z), s(s(s(s(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[531, 12, 444, 15, 506, 1, 232])).
% 0.96/1.13 tff(1475,plain,
% 0.96/1.13 (r(s(z), s(s(s(s(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[467, 1474])).
% 0.96/1.13 tff(1476,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.96/1.13 tff(1477,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[474, 28, 535, 17, 1476])).
% 0.96/1.13 tff(1478,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(1479,plain,
% 0.96/1.13 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1478, 1475, 17])).
% 0.96/1.13 tff(1480,plain,
% 0.96/1.13 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[373, 60, 370, 1479])).
% 0.96/1.13 tff(1481,plain,
% 0.96/1.13 (~r(z, s(s(s(s(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[543, 1475, 14])).
% 0.96/1.13 tff(1482,plain,
% 0.96/1.13 (b(z, s(s(s(s(elem!1)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[548, 1481])).
% 0.96/1.13 tff(1483,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1484,plain,
% 0.96/1.13 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1485,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[1484])).
% 0.96/1.13 tff(1486,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[1485, 1483])).
% 0.96/1.13 tff(1487,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(1488,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 0.96/1.13 tff(1489,plain,
% 0.96/1.13 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1488, 154, 444, 1, 660])).
% 0.96/1.13 tff(1490,plain,
% 0.96/1.13 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1489, 1482])).
% 0.96/1.13 tff(1491,plain,
% 0.96/1.13 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[496, 1490])).
% 0.96/1.13 tff(1492,plain,
% 0.96/1.13 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[529, 28, 1491, 520])).
% 0.96/1.13 tff(1493,plain,
% 0.96/1.13 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[517, 60, 12, 1492])).
% 0.96/1.13 tff(1494,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1495,plain,
% 0.96/1.13 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1496,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[1495])).
% 0.96/1.13 tff(1497,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[1496, 1494])).
% 0.96/1.13 tff(1498,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(1499,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 0.96/1.13 tff(1500,plain,
% 0.96/1.13 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1499, 154, 444, 1283, 506])).
% 0.96/1.13 tff(1501,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1500, 1493, 1480])).
% 0.96/1.13 tff(1502,plain,((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(1503,plain,
% 0.96/1.13 (~r(s(z), s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1502, 1473, 1260, 12, 1449, 1453, 1447, 14, 15, 232])).
% 0.96/1.13 tff(1504,plain,
% 0.96/1.13 (b(s(z), s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[680, 1503])).
% 0.96/1.13 tff(1505,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1506,plain,
% 0.96/1.13 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1507,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[1506])).
% 0.96/1.13 tff(1508,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[1507, 1505])).
% 0.96/1.13 tff(1509,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(1510,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 0.96/1.13 tff(1511,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1510, 154, 144, 232, 143, 684, 142])).
% 0.96/1.13 tff(1512,plain,((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(1513,plain,
% 0.96/1.13 (~b(s(s(z)), s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1512, 1504, 232, 1356, 1445])).
% 0.96/1.13 tff(1514,plain,
% 0.96/1.13 (r(s(s(z)), s(s(s(z))))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[138, 1513])).
% 0.96/1.13 tff(1515,plain,
% 0.96/1.13 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1427, 28, 1514, 1451])).
% 0.96/1.13 tff(1516,plain,
% 0.96/1.13 (b(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[229, 1515])).
% 0.96/1.13 tff(1517,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1518,plain,
% 0.96/1.13 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.13 inference(rewrite,[status(thm)],[])).
% 0.96/1.13 tff(1519,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.96/1.13 inference(monotonicity,[status(thm)],[1518])).
% 0.96/1.13 tff(1520,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.13 inference(transitivity,[status(thm)],[1519, 1517])).
% 0.96/1.13 tff(1521,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
% 0.96/1.13 tff(1522,plain,
% 0.96/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.96/1.13 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 0.96/1.13 tff(1523,plain,
% 0.96/1.13 ($false),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1522, 154, 1260, 15, 1504, 1447, 1516])).
% 0.96/1.13 tff(1524,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.13 tff(1525,plain,
% 0.96/1.13 (~r(s(s(z)), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1524, 232, 15, 12, 14, 13])).
% 0.96/1.13 tff(1526,plain,
% 0.96/1.13 (b(s(s(z)), s(z))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[296, 1525])).
% 0.96/1.13 tff(1527,plain,
% 0.96/1.13 (~b(s(z), s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[1437, 1526, 15, 1260, 232, 1356, 13])).
% 0.96/1.13 tff(1528,plain,
% 0.96/1.13 (r(s(z), s(s(z)))),
% 0.96/1.13 inference(unit_resolution,[status(thm)],[680, 1527])).
% 0.96/1.13 tff(1529,plain,
% 0.96/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(1530,plain,
% 0.96/1.14 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(1531,plain,
% 0.96/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 0.96/1.14 inference(monotonicity,[status(thm)],[1530])).
% 0.96/1.14 tff(1532,plain,
% 0.96/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 0.96/1.14 inference(transitivity,[status(thm)],[1531, 1529])).
% 0.96/1.14 tff(1533,plain,
% 0.96/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
% 0.96/1.14 tff(1534,plain,
% 0.96/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 0.96/1.14 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 0.96/1.14 tff(1535,plain,
% 0.96/1.14 ($false),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[1534, 28, 13, 106, 17])).
% 0.96/1.14 tff(1536,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(1537,plain,
% 0.96/1.14 (~r(s(s(z)), z)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[1536, 1528, 13])).
% 0.96/1.14 tff(1538,plain,
% 0.96/1.14 (b(s(s(z)), z)),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[122, 1537])).
% 0.96/1.14 tff(1539,plain,
% 0.96/1.14 (~r(s(s(s(s(z)))), s(z))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[1323, 1538, 1443, 1260, 14])).
% 0.96/1.14 tff(1540,plain,
% 0.96/1.14 (b(s(s(s(s(z)))), s(z))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[318, 1539])).
% 0.96/1.14 tff(1541,plain,
% 0.96/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(1542,plain,
% 0.96/1.14 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(1543,plain,
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% 0.96/1.14 inference(monotonicity,[status(thm)],[1542])).
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% 0.96/1.14 inference(transitivity,[status(thm)],[1543, 1541])).
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% 0.96/1.14 inference(quant_inst,[status(thm)],[])).
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% 0.96/1.14 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.96/1.14 tff(1547,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1546, 154, 1260, 15, 1526, 1540])).
% 0.96/1.14 tff(1548,plain,
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% 0.96/1.14 tff(1550,plain,
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% 0.96/1.14 inference(monotonicity,[status(thm)],[1550])).
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% 0.96/1.14 inference(transitivity,[status(thm)],[1551, 1549])).
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% 0.96/1.14 tff(1555,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1554, 28, 820, 67, 17])).
% 0.96/1.14 tff(1556,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(1557,plain,
% 0.96/1.14 (~r(s(s(s(z))), s(s(z)))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[1556, 820, 17])).
% 0.96/1.14 tff(1558,plain,
% 0.96/1.14 (~b(s(s(s(z))), s(s(z)))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[1190, 820, 140, 231, 142, 143])).
% 0.96/1.14 tff(1559,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[104, 1558, 1557])).
% 0.96/1.14 tff(1560,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(1561,plain,
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% 0.96/1.14 tff(1562,plain,
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% 0.96/1.14 tff(1563,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1289, 154, 1562, 1260, 15, 1526])).
% 0.96/1.14 tff(1564,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[104, 1563])).
% 0.96/1.14 tff(1565,plain,
% 0.96/1.14 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[327, 154, 1562, 232, 15, 1540])).
% 0.96/1.14 tff(1566,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[343, 1565])).
% 0.96/1.14 tff(1567,plain,
% 0.96/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
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% 0.96/1.14 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.96/1.14 inference(rewrite,[status(thm)],[])).
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% 0.96/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
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% 0.96/1.14 inference(modus_ponens,[status(thm)],[1571, 1570])).
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1572, 28, 1566, 1564, 1548])).
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% 0.96/1.14 tff(1575,plain,
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% 0.96/1.14 tff(1579,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[931, 154, 1393, 683, 718, 1578])).
% 0.96/1.14 tff(1580,plain,
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% 0.96/1.14 inference(rewrite,[status(thm)],[])).
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% 0.96/1.14 inference(monotonicity,[status(thm)],[1582])).
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% 0.96/1.14 inference(modus_ponens,[status(thm)],[1585, 1584])).
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1586, 28, 273, 1580, 1403])).
% 0.96/1.14 tff(1588,plain,((~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(1589,plain,
% 0.96/1.14 (~b(s(s(z)), s(z))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[1588, 1358, 14, 13, 1283, 273, 15])).
% 0.96/1.14 tff(1590,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[296, 1589])).
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[712, 28, 14, 18, 1590])).
% 0.96/1.14 tff(1592,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(1593,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1592, 1283, 13, 14, 273, 15])).
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[64, 1593])).
% 0.96/1.14 tff(1595,plain,
% 0.96/1.14 (~r(s(s(s(s(z)))), s(z))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[1323, 1445, 1594, 1283, 14])).
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[318, 1595])).
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% 0.96/1.14 (~r(s(s(z)), s(s(s(z))))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[657, 299, 273])).
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[138, 1597])).
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[162, 1598, 683, 1594, 1445])).
% 0.96/1.14 tff(1600,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[104, 1599])).
% 0.96/1.14 tff(1601,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[597, 1600, 273])).
% 0.96/1.14 tff(1602,plain,
% 0.96/1.14 (b(s(z), s(s(z)))),
% 0.96/1.14 inference(unit_resolution,[status(thm)],[680, 1601])).
% 0.96/1.14 tff(1603,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.96/1.14 tff(1604,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1522, 154, 1283, 15, 684, 506, 1603])).
% 0.96/1.14 tff(1605,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.14 tff(1606,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[1605, 1602, 15, 1283, 1596])).
% 0.96/1.14 tff(1607,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[229, 1606])).
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% 0.96/1.14 inference(rewrite,[status(thm)],[])).
% 0.96/1.14 tff(1610,plain,
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% 0.96/1.14 inference(monotonicity,[status(thm)],[1609])).
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% 0.96/1.14 inference(transitivity,[status(thm)],[1610, 1608])).
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% 0.96/1.14 inference(modus_ponens,[status(thm)],[1612, 1611])).
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% 0.96/1.14 tff(1615,plain,
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% 0.96/1.15 tff(1624,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[64, 1639])).
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% 0.96/1.15 inference(rewrite,[status(thm)],[])).
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% 0.96/1.15 inference(rewrite,[status(thm)],[])).
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% 0.96/1.15 inference(monotonicity,[status(thm)],[1642])).
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% 0.96/1.15 inference(transitivity,[status(thm)],[1643, 1641])).
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% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
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% 0.96/1.15 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 0.96/1.15 tff(1647,plain,
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% 0.96/1.15 tff(1648,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(1649,plain,
% 0.96/1.15 (~b(s(s(s(z))), s(z))),
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% 0.96/1.15 tff(1650,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[818, 1649, 1634])).
% 0.96/1.15 tff(1651,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(1652,plain,
% 0.96/1.15 (~b(s(z), s(s(s(s(z)))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1651, 14, 13, 12])).
% 0.96/1.15 tff(1653,plain,
% 0.96/1.15 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1372, 1361])).
% 0.96/1.15 tff(1654,plain,
% 0.96/1.15 (r(s(z), s(s(s(s(z)))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1653, 1652])).
% 0.96/1.15 tff(1655,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.96/1.15 tff(1656,plain,
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% 0.96/1.15 inference(rewrite,[status(thm)],[])).
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% 0.96/1.15 inference(monotonicity,[status(thm)],[1657])).
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% 0.96/1.15 inference(transitivity,[status(thm)],[1658, 1656])).
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% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
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% 0.96/1.15 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 0.96/1.15 tff(1662,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[1661, 28, 14, 172, 1655])).
% 0.96/1.15 tff(1663,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(1664,plain,
% 0.96/1.15 (~r(z, s(s(s(s(z)))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1663, 1654, 14])).
% 0.96/1.15 tff(1665,plain,
% 0.96/1.15 (b(z, s(s(s(s(z)))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[191, 1664])).
% 0.96/1.15 tff(1666,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1667,plain,
% 0.96/1.15 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1668,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[1667])).
% 0.96/1.15 tff(1669,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[1668, 1666])).
% 0.96/1.15 tff(1670,plain,
% 0.96/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(1671,plain,
% 0.96/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 0.96/1.15 tff(1672,plain,
% 0.96/1.15 (~r(s(s(z)), s(z))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1671, 28, 13, 16, 1654])).
% 0.96/1.15 tff(1673,plain,
% 0.96/1.15 (b(s(s(z)), s(z))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[296, 1672])).
% 0.96/1.15 tff(1674,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1675,plain,
% 0.96/1.15 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1676,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[1675])).
% 0.96/1.15 tff(1677,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[1676, 1674])).
% 0.96/1.15 tff(1678,plain,
% 0.96/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(1679,plain,
% 0.96/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 0.96/1.15 tff(1680,plain,
% 0.96/1.15 ($false),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1679, 28, 16, 17, 1655])).
% 0.96/1.15 tff(1681,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(1682,plain,
% 0.96/1.15 (~r(s(z), s(s(z)))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1681, 16, 1654])).
% 0.96/1.15 tff(1683,plain,
% 0.96/1.15 (b(s(z), s(s(z)))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[680, 1682])).
% 0.96/1.15 tff(1684,plain,
% 0.96/1.15 (~r(s(z), s(s(s(z))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[281, 171, 13])).
% 0.96/1.15 tff(1685,plain,
% 0.96/1.15 (b(s(z), s(s(s(z))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[252, 1684])).
% 0.96/1.15 tff(1686,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1687,plain,
% 0.96/1.15 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1688,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[1687])).
% 0.96/1.15 tff(1689,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[1688, 1686])).
% 0.96/1.15 tff(1690,plain,
% 0.96/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(1691,plain,
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% 0.96/1.15 tff(1693,plain,
% 0.96/1.15 (r(s(s(s(z))), s(s(z)))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[104, 1692])).
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% 0.96/1.15 (~b(s(s(z)), s(s(s(z))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1419, 154, 1270, 1685, 1683, 1673])).
% 0.96/1.15 tff(1695,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[138, 1694])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[913, 16, 106])).
% 0.96/1.15 tff(1697,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[191, 1696])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[75, 16, 67])).
% 0.96/1.15 tff(1699,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[564, 1698])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[1280, 67, 106])).
% 0.96/1.15 tff(1701,plain,
% 0.96/1.15 (b(s(s(s(z))), z)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[169, 1700])).
% 0.96/1.15 tff(1702,plain,
% 0.96/1.15 (~r(s(s(s(s(z)))), z)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[923, 16, 106])).
% 0.96/1.15 tff(1703,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[206, 1702])).
% 0.96/1.15 tff(1704,plain,
% 0.96/1.15 ($false),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[740, 154, 1703, 1701, 660, 1699, 1697])).
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% 0.96/1.15 tff(1706,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[1705, 16, 660, 67])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[132, 16, 124])).
% 0.96/1.15 tff(1709,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[564, 1708])).
% 0.96/1.15 tff(1710,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[612, 16, 124])).
% 0.96/1.15 tff(1711,plain,
% 0.96/1.15 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[343, 1710])).
% 0.96/1.15 tff(1712,plain,
% 0.96/1.15 (~r(s(s(s(z))), z)),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1346, 18, 67])).
% 0.96/1.15 tff(1713,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[169, 1712])).
% 0.96/1.15 tff(1714,plain,
% 0.96/1.15 (~b(z, s(s(s(s(z)))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1218, 154, 1713, 1711, 660, 1709])).
% 0.96/1.15 tff(1715,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[191, 1714])).
% 0.96/1.15 tff(1716,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1717,plain,
% 0.96/1.15 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1718,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[1717])).
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% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.15 inference(transitivity,[status(thm)],[1718, 1716])).
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% 0.96/1.15 inference(quant_inst,[status(thm)],[])).
% 0.96/1.15 tff(1721,plain,
% 0.96/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.96/1.15 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 0.96/1.15 tff(1722,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[1721, 28, 124, 1715, 18, 16])).
% 0.96/1.15 tff(1723,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(1724,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[1723, 16, 124, 660, 67])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[64, 1724])).
% 0.96/1.15 tff(1726,assumption,(b(z, s(z))), introduced(assumption)).
% 0.96/1.15 tff(1727,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[1681, 1655, 16])).
% 0.96/1.15 tff(1728,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[680, 1727])).
% 0.96/1.15 tff(1729,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1730,plain,
% 0.96/1.15 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.15 inference(rewrite,[status(thm)],[])).
% 0.96/1.15 tff(1731,plain,
% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 0.96/1.15 inference(monotonicity,[status(thm)],[1730])).
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% 0.96/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[1731, 1729])).
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% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(1734,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 0.96/1.16 tff(1735,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1734, 154, 1726, 684, 231, 142, 140])).
% 0.96/1.16 tff(1736,plain,((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(1737,plain,
% 0.96/1.16 (~b(s(s(z)), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1736, 1728, 140, 142, 1726])).
% 0.96/1.16 tff(1738,plain,
% 0.96/1.16 (r(s(s(z)), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[296, 1737])).
% 0.96/1.16 tff(1739,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1740,plain,
% 0.96/1.16 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1741,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[1740])).
% 0.96/1.16 tff(1742,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[1741, 1739])).
% 0.96/1.16 tff(1743,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(1744,plain,
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% 0.96/1.16 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 0.96/1.16 tff(1745,plain,
% 0.96/1.16 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1744, 154, 1, 232, 1711])).
% 0.96/1.16 tff(1746,plain,
% 0.96/1.16 (~b(s(s(s(s(z)))), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1745, 1709])).
% 0.96/1.16 tff(1747,plain,
% 0.96/1.16 (r(s(s(s(s(z)))), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[317, 1746, 313])).
% 0.96/1.16 tff(1748,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[305, 28, 16, 299, 1747])).
% 0.96/1.16 tff(1749,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(1750,plain,
% 0.96/1.16 (~b(s(z), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1749, 1738, 1, 16, 124])).
% 0.96/1.16 tff(1751,plain,
% 0.96/1.16 (r(s(z), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[252, 1750])).
% 0.96/1.16 tff(1752,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1753,plain,
% 0.96/1.16 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1754,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[1753])).
% 0.96/1.16 tff(1755,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[1754, 1752])).
% 0.96/1.16 tff(1756,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(1757,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 0.96/1.16 tff(1758,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1757, 28, 124, 1751, 1738, 1655])).
% 0.96/1.16 tff(1759,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(1760,plain,
% 0.96/1.16 (~r(s(z), s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1759, 1726, 1, 16, 140, 142, 124])).
% 0.96/1.16 tff(1761,plain,
% 0.96/1.16 (b(s(z), s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1653, 1760])).
% 0.96/1.16 tff(1762,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1763,plain,
% 0.96/1.16 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1764,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[1763])).
% 0.96/1.16 tff(1765,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[1764, 1762])).
% 0.96/1.16 tff(1766,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(1767,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 0.96/1.16 tff(1768,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1767, 154, 1726, 1, 660, 1761, 1709])).
% 0.96/1.16 tff(1769,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(1770,plain,
% 0.96/1.16 (~b(z, s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1769, 16, 660, 1, 1725, 1707, 124])).
% 0.96/1.16 tff(1771,plain,
% 0.96/1.16 (r(z, s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1181, 1770])).
% 0.96/1.16 tff(1772,plain,
% 0.96/1.16 (~b(s(z), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[623, 15, 615, 1, 566])).
% 0.96/1.16 tff(1773,plain,
% 0.96/1.16 (r(s(z), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[252, 1772])).
% 0.96/1.16 tff(1774,plain,
% 0.96/1.16 (~r(s(s(z)), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[655, 28, 124, 1773])).
% 0.96/1.16 tff(1775,plain,
% 0.96/1.16 (b(s(s(z)), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[296, 1774])).
% 0.96/1.16 tff(1776,plain,
% 0.96/1.16 (~r(s(z), s(s(z)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[597, 1773, 67])).
% 0.96/1.16 tff(1777,plain,
% 0.96/1.16 (b(s(z), s(s(z)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[680, 1776])).
% 0.96/1.16 tff(1778,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1779,plain,
% 0.96/1.16 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1780,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[1779])).
% 0.96/1.16 tff(1781,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[1780, 1778])).
% 0.96/1.16 tff(1782,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(1783,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 0.96/1.16 tff(1784,plain,
% 0.96/1.16 ((~b(s(z), z)) | (~b(s(s(z)), s(z)))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1783, 154, 1777, 142, 140])).
% 0.96/1.16 tff(1785,plain,
% 0.96/1.16 (~b(s(z), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1784, 1775])).
% 0.96/1.16 tff(1786,plain,
% 0.96/1.16 (r(s(z), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[271, 1785])).
% 0.96/1.16 tff(1787,plain,
% 0.96/1.16 (~r(s(s(s(z))), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[281, 1786, 1773])).
% 0.96/1.16 tff(1788,plain,
% 0.96/1.16 (b(s(s(s(z))), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[169, 1787])).
% 0.96/1.16 tff(1789,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1790,plain,
% 0.96/1.16 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1791,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[1790])).
% 0.96/1.16 tff(1792,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[1791, 1789])).
% 0.96/1.16 tff(1793,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(1794,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[1793, 1792])).
% 0.96/1.16 tff(1795,plain,
% 0.96/1.16 (~b(s(s(s(s(z)))), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1794, 154, 1788, 615, 660, 566])).
% 0.96/1.16 tff(1796,plain,
% 0.96/1.16 (r(s(s(s(s(z)))), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[206, 1795])).
% 0.96/1.16 tff(1797,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1798,plain,
% 0.96/1.16 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(1799,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[1798])).
% 0.96/1.16 tff(1800,plain,
% 0.96/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.96/1.16 inference(transitivity,[status(thm)],[1799, 1797])).
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% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(1802,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 0.96/1.16 tff(1803,plain,
% 0.96/1.16 (~r(s(s(s(s(z)))), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1802, 28, 1773, 1786, 1796])).
% 0.96/1.16 tff(1804,plain,
% 0.96/1.16 (b(s(s(s(s(z)))), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[318, 1803])).
% 0.96/1.16 tff(1805,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[750, 154, 1, 615, 15, 1804, 566])).
% 0.96/1.16 tff(1806,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.17 tff(1807,plain,
% 0.96/1.17 (~b(s(z), s(s(s(s(z)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1806, 1711, 1, 1709, 660, 1707, 1725, 124, 67])).
% 0.96/1.17 tff(1808,plain,
% 0.96/1.17 (r(s(z), s(s(s(s(z)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1653, 1807])).
% 0.96/1.17 tff(1809,plain,
% 0.96/1.17 (~r(z, s(s(s(s(z)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1663, 1808, 1771])).
% 0.96/1.17 tff(1810,plain,
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% 0.96/1.17 inference(unit_resolution,[status(thm)],[191, 1809])).
% 0.96/1.17 tff(1811,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1812,plain,
% 0.96/1.17 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1813,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[1812])).
% 0.96/1.17 tff(1814,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[1813, 1811])).
% 0.96/1.17 tff(1815,plain,
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% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(1816,plain,
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% 0.96/1.17 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 0.96/1.17 tff(1817,plain,
% 0.96/1.17 (~b(s(s(s(s(z)))), z)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1816, 154, 1711, 660, 1709, 1810])).
% 0.96/1.17 tff(1818,plain,
% 0.96/1.17 (r(s(s(s(s(z)))), z)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[206, 1817])).
% 0.96/1.17 tff(1819,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1820,plain,
% 0.96/1.17 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1821,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[1820])).
% 0.96/1.17 tff(1822,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[1821, 1819])).
% 0.96/1.17 tff(1823,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(1824,plain,
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% 0.96/1.17 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 0.96/1.17 tff(1825,plain,
% 0.96/1.17 (~r(s(s(z)), s(z))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1824, 28, 16, 1808])).
% 0.96/1.17 tff(1826,plain,
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% 0.96/1.17 inference(unit_resolution,[status(thm)],[296, 1825])).
% 0.96/1.17 tff(1827,plain,
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% 0.96/1.17 inference(unit_resolution,[status(thm)],[1681, 1808, 16])).
% 0.96/1.17 tff(1828,plain,
% 0.96/1.17 (b(s(z), s(s(z)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[680, 1827])).
% 0.96/1.17 tff(1829,plain,
% 0.96/1.17 ((~b(s(z), z)) | (~b(s(s(z)), s(z)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1783, 154, 1828, 1707, 1725])).
% 0.96/1.17 tff(1830,plain,
% 0.96/1.17 (~b(s(z), z)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1829, 1826])).
% 0.96/1.17 tff(1831,plain,
% 0.96/1.17 (r(s(z), z)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[271, 1830])).
% 0.96/1.17 tff(1832,plain,
% 0.96/1.17 ($false),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1367, 28, 1831, 1808, 1818])).
% 0.96/1.17 tff(1833,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.17 tff(1834,plain,
% 0.96/1.17 (~b(z, s(s(s(z))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1833, 1695, 16, 1270, 1693])).
% 0.96/1.17 tff(1835,plain,
% 0.96/1.17 (r(z, s(s(s(z))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[648, 1834])).
% 0.96/1.17 tff(1836,plain,
% 0.96/1.17 (~r(z, s(s(z)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1346, 1693, 171])).
% 0.96/1.17 tff(1837,plain,
% 0.96/1.17 (b(z, s(s(z)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[64, 1836])).
% 0.96/1.17 tff(1838,plain,
% 0.96/1.17 ($false),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1367, 28, 13, 1655, 193])).
% 0.96/1.17 tff(1839,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.17 tff(1840,plain,
% 0.96/1.17 (~r(s(s(s(s(z)))), z)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1839, 1654, 13])).
% 0.96/1.17 tff(1841,plain,
% 0.96/1.17 (b(s(s(s(s(z)))), z)),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[206, 1840])).
% 0.96/1.17 tff(1842,plain,
% 0.96/1.17 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[804, 1685, 16, 1683, 1270])).
% 0.96/1.17 tff(1843,plain,
% 0.96/1.17 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[564, 1842])).
% 0.96/1.17 tff(1844,plain,
% 0.96/1.17 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[612, 1695, 16])).
% 0.96/1.17 tff(1845,plain,
% 0.96/1.17 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[343, 1844])).
% 0.96/1.17 tff(1846,plain,
% 0.96/1.17 (~b(s(s(s(s(z)))), s(z))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1744, 154, 1270, 1685, 1845, 1843])).
% 0.96/1.17 tff(1847,plain,
% 0.96/1.17 (r(s(s(s(s(z)))), s(z))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[318, 1846])).
% 0.96/1.17 tff(1848,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1849,plain,
% 0.96/1.17 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1850,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[1849])).
% 0.96/1.17 tff(1851,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[1850, 1848])).
% 0.96/1.17 tff(1852,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(1853,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 0.96/1.17 tff(1854,plain,
% 0.96/1.17 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1853, 28, 345, 298])).
% 0.96/1.17 tff(1855,plain,
% 0.96/1.17 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[963, 60, 934, 1854])).
% 0.96/1.17 tff(1856,plain,
% 0.96/1.17 (b(z, s(s(s(s(elem!1)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[548, 397])).
% 0.96/1.17 tff(1857,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1858,plain,
% 0.96/1.17 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1859,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[1858])).
% 0.96/1.17 tff(1860,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[1859, 1857])).
% 0.96/1.17 tff(1861,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(1862,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 0.96/1.17 tff(1863,plain,
% 0.96/1.17 ($false),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1862, 154, 419, 1856, 1299, 254, 1855])).
% 0.96/1.17 tff(1864,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.17 tff(1865,plain,
% 0.96/1.17 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1864, 1847, 1665, 845, 1841, 14, 13])).
% 0.96/1.17 tff(1866,plain,
% 0.96/1.17 (b(s(s(s(s(elem!1)))), s(z))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[441, 1865])).
% 0.96/1.17 tff(1867,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1868,plain,
% 0.96/1.17 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1869,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[1868])).
% 0.96/1.17 tff(1870,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[1869, 1867])).
% 0.96/1.17 tff(1871,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(1872,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 0.96/1.17 tff(1873,plain,
% 0.96/1.17 (~r(z, s(s(s(s(elem!1)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1872, 28, 780, 628])).
% 0.96/1.17 tff(1874,plain,
% 0.96/1.17 (b(z, s(s(s(s(elem!1)))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[548, 1873])).
% 0.96/1.17 tff(1875,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1876,plain,
% 0.96/1.17 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.96/1.17 inference(rewrite,[status(thm)],[])).
% 0.96/1.17 tff(1877,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 0.96/1.17 inference(monotonicity,[status(thm)],[1876])).
% 0.96/1.17 tff(1878,plain,
% 0.96/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 0.96/1.17 inference(transitivity,[status(thm)],[1877, 1875])).
% 0.96/1.17 tff(1879,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 0.96/1.17 inference(quant_inst,[status(thm)],[])).
% 0.96/1.17 tff(1880,plain,
% 0.96/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 0.96/1.17 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 0.96/1.17 tff(1881,plain,
% 0.96/1.17 ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1880, 154, 444, 231, 140])).
% 0.96/1.17 tff(1882,plain,
% 0.96/1.17 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 0.96/1.17 inference(unit_resolution,[status(thm)],[1881, 1874])).
% 0.96/1.17 tff(1883,plain,
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% 0.96/1.17 inference(unit_resolution,[status(thm)],[1051, 60, 1107, 1048, 1882])).
% 0.96/1.17 tff(1884,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1885,plain,
% 0.96/1.18 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
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% 0.96/1.18 tff(1886,plain,
% 0.96/1.18 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[496, 1885])).
% 0.96/1.18 tff(1887,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1888,plain,
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% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(1889,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 0.96/1.18 tff(1890,plain,
% 0.96/1.18 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1889, 154, 1866, 1270, 1845])).
% 0.96/1.18 tff(1891,plain,
% 0.96/1.18 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1890, 1886])).
% 0.96/1.18 tff(1892,plain,
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% 0.96/1.18 inference(unit_resolution,[status(thm)],[963, 60, 845, 1891])).
% 0.96/1.18 tff(1893,plain,
% 0.96/1.18 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[458, 154, 1866, 1270, 1685])).
% 0.96/1.18 tff(1894,plain,
% 0.96/1.18 (~b(s(z), s(s(s(s(elem!1)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1893, 1886])).
% 0.96/1.18 tff(1895,plain,
% 0.96/1.18 (r(s(z), s(s(s(s(elem!1)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[467, 1894])).
% 0.96/1.18 tff(1896,plain,
% 0.96/1.18 (~r(z, s(s(s(s(elem!1)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[543, 1895, 14])).
% 0.96/1.18 tff(1897,plain,
% 0.96/1.18 (b(z, s(s(s(s(elem!1)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[548, 1896])).
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% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1899,plain,
% 0.96/1.18 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1900,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[1899])).
% 0.96/1.18 tff(1901,plain,
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% 0.96/1.18 inference(transitivity,[status(thm)],[1900, 1898])).
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% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
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% 0.96/1.18 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 0.96/1.18 tff(1904,plain,
% 0.96/1.18 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1903, 154, 1897, 1886, 1845, 1665])).
% 0.96/1.18 tff(1905,plain,
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% 0.96/1.18 tff(1907,plain,
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% 0.96/1.18 inference(unit_resolution,[status(thm)],[1906, 1897])).
% 0.96/1.18 tff(1908,plain,
% 0.96/1.18 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1051, 60, 1048, 1907])).
% 0.96/1.18 tff(1909,plain,
% 0.96/1.18 (~r(s(s(z)), z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1280, 1693, 171])).
% 0.96/1.18 tff(1910,plain,
% 0.96/1.18 (b(s(s(z)), z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[122, 1909])).
% 0.96/1.18 tff(1911,plain,
% 0.96/1.18 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[213, 154, 1841, 1910, 1837, 1665])).
% 0.96/1.18 tff(1912,plain,
% 0.96/1.18 (r(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[229, 1911])).
% 0.96/1.18 tff(1913,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1914,plain,
% 0.96/1.18 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1915,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[1914])).
% 0.96/1.18 tff(1916,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[1915, 1913])).
% 0.96/1.18 tff(1917,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(1918,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[1917, 1916])).
% 0.96/1.18 tff(1919,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1918, 28, 1912, 1908, 1905, 1892])).
% 0.96/1.18 tff(1920,plain,((~r(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1921,plain,
% 0.96/1.18 (~r(s(s(s(z))), z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1920, 16, 14, 13, 12])).
% 0.96/1.18 tff(1922,plain,
% 0.96/1.18 (b(s(s(s(z))), z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[169, 1921])).
% 0.96/1.18 tff(1923,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1924,plain,
% 0.96/1.18 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1925,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[1924])).
% 0.96/1.18 tff(1926,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[1925, 1923])).
% 0.96/1.18 tff(1927,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(1928,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 0.96/1.18 tff(1929,plain,
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% 0.96/1.18 inference(unit_resolution,[status(thm)],[1928, 28, 820, 66, 1655])).
% 0.96/1.18 tff(1930,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1931,plain,
% 0.96/1.18 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1930, 820, 1655])).
% 0.96/1.18 tff(1932,plain,
% 0.96/1.18 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[564, 1931])).
% 0.96/1.18 tff(1933,plain,
% 0.96/1.18 (~r(z, s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1663, 1655, 14])).
% 0.96/1.18 tff(1934,plain,
% 0.96/1.18 (b(z, s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[191, 1933])).
% 0.96/1.18 tff(1935,plain,
% 0.96/1.18 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[740, 154, 1299, 143, 1934])).
% 0.96/1.18 tff(1936,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1935, 1932, 885])).
% 0.96/1.18 tff(1937,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1938,plain,
% 0.96/1.18 (~r(s(s(s(z))), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1937, 1922, 1841, 1654, 14])).
% 0.96/1.18 tff(1939,plain,
% 0.96/1.18 (b(s(s(s(z))), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[818, 1938])).
% 0.96/1.18 tff(1940,plain,
% 0.96/1.18 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[714, 1939, 14, 13, 16, 1683, 1922])).
% 0.96/1.18 tff(1941,plain,
% 0.96/1.18 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[564, 1940])).
% 0.96/1.18 tff(1942,plain,
% 0.96/1.18 (~r(s(s(z)), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1671, 28, 13, 16, 1655])).
% 0.96/1.18 tff(1943,plain,
% 0.96/1.18 (b(s(s(z)), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[296, 1942])).
% 0.96/1.18 tff(1944,plain,
% 0.96/1.18 (~r(s(z), s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1681, 16, 1655])).
% 0.96/1.18 tff(1945,plain,
% 0.96/1.18 (b(s(z), s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[680, 1944])).
% 0.96/1.18 tff(1946,plain,
% 0.96/1.18 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[714, 1, 14, 13, 16, 1945, 143])).
% 0.96/1.18 tff(1947,plain,
% 0.96/1.18 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[564, 1946])).
% 0.96/1.18 tff(1948,plain,
% 0.96/1.18 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1232, 1947, 143, 106, 16])).
% 0.96/1.18 tff(1949,plain,
% 0.96/1.18 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[343, 1948])).
% 0.96/1.18 tff(1950,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1951,plain,
% 0.96/1.18 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1952,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[1951])).
% 0.96/1.18 tff(1953,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[1952, 1950])).
% 0.96/1.18 tff(1954,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(1955,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 0.96/1.18 tff(1956,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1955, 28, 273, 604, 1655])).
% 0.96/1.18 tff(1957,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1958,plain,
% 0.96/1.18 (~r(s(z), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1957, 1949, 1655])).
% 0.96/1.18 tff(1959,plain,
% 0.96/1.18 (b(s(z), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[252, 1958])).
% 0.96/1.18 tff(1960,plain,
% 0.96/1.18 (~r(s(s(z)), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[612, 1949, 16])).
% 0.96/1.18 tff(1961,plain,
% 0.96/1.18 (b(s(s(z)), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[138, 1960])).
% 0.96/1.18 tff(1962,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1419, 154, 1961, 1, 1959, 1945, 1943])).
% 0.96/1.18 tff(1963,plain,((~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1964,plain,
% 0.96/1.18 (~r(s(s(z)), z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1963, 1939, 16, 1922, 1654, 14, 13])).
% 0.96/1.18 tff(1965,plain,
% 0.96/1.18 (b(s(s(z)), z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[122, 1964])).
% 0.96/1.18 tff(1966,plain,
% 0.96/1.18 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[740, 154, 1841, 1922, 1665])).
% 0.96/1.18 tff(1967,plain,
% 0.96/1.18 (~b(z, s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1966, 1941])).
% 0.96/1.18 tff(1968,plain,
% 0.96/1.18 (r(z, s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[648, 1967])).
% 0.96/1.18 tff(1969,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1970,plain,
% 0.96/1.18 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1971,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[1970])).
% 0.96/1.18 tff(1972,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 0.96/1.18 inference(transitivity,[status(thm)],[1971, 1969])).
% 0.96/1.18 tff(1973,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(1974,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[1973, 1972])).
% 0.96/1.18 tff(1975,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1974, 28, 273, 628, 13])).
% 0.96/1.18 tff(1976,plain,((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1977,plain,
% 0.96/1.18 (~r(s(z), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1976, 1968, 13])).
% 0.96/1.18 tff(1978,plain,
% 0.96/1.18 (b(s(z), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[252, 1977])).
% 0.96/1.18 tff(1979,plain,
% 0.96/1.18 (~b(s(s(z)), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1512, 1978, 1683, 1922, 1965])).
% 0.96/1.18 tff(1980,plain,
% 0.96/1.18 (r(s(s(z)), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[138, 1979])).
% 0.96/1.18 tff(1981,plain,
% 0.96/1.18 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[612, 1980, 16])).
% 0.96/1.18 tff(1982,plain,
% 0.96/1.18 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[343, 1981])).
% 0.96/1.18 tff(1983,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1230, 154, 1841, 1922, 1982, 1941, 1665])).
% 0.96/1.18 tff(1984,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1985,plain,
% 0.96/1.18 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1984, 14, 13, 12])).
% 0.96/1.18 tff(1986,plain,
% 0.96/1.18 (b(s(s(z)), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1259, 1985])).
% 0.96/1.18 tff(1987,plain,
% 0.96/1.18 (~b(z, s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1307, 1445, 1299, 254, 1283])).
% 0.96/1.18 tff(1988,plain,
% 0.96/1.18 (r(z, s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[64, 1987])).
% 0.96/1.18 tff(1989,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[712, 28, 14, 1988, 299])).
% 0.96/1.18 tff(1990,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(1991,plain,
% 0.96/1.18 (~r(s(s(z)), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[1990, 14, 1841, 1665, 1986, 13])).
% 0.96/1.18 tff(1992,plain,
% 0.96/1.18 (b(s(s(z)), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[296, 1991])).
% 0.96/1.18 tff(1993,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1994,plain,
% 0.96/1.18 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(1995,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[1994])).
% 0.96/1.18 tff(1996,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[1995, 1993])).
% 0.96/1.18 tff(1997,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(1998,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 0.96/1.19 tff(1999,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1998, 28, 17, 1243, 1655])).
% 0.96/1.19 tff(2000,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(2001,plain,
% 0.96/1.19 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2000, 17, 1655])).
% 0.96/1.19 tff(2002,plain,
% 0.96/1.19 (b(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[229, 2001])).
% 0.96/1.19 tff(2003,plain,
% 0.96/1.19 (~r(s(s(s(s(z)))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1839, 13, 1655])).
% 0.96/1.19 tff(2004,plain,
% 0.96/1.19 (b(s(s(s(s(z)))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[206, 2003])).
% 0.96/1.19 tff(2005,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2006,plain,
% 0.96/1.19 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2007,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[2006])).
% 0.96/1.19 tff(2008,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[2007, 2005])).
% 0.96/1.19 tff(2009,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(2010,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 0.96/1.19 tff(2011,plain,
% 0.96/1.19 ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2010, 154, 2004, 1283, 254])).
% 0.96/1.19 tff(2012,plain,
% 0.96/1.19 (~b(s(s(z)), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2011, 2002])).
% 0.96/1.19 tff(2013,plain,
% 0.96/1.19 (r(s(s(z)), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[122, 2012])).
% 0.96/1.19 tff(2014,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1534, 28, 13, 2013, 17])).
% 0.96/1.19 tff(2015,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(2016,plain,
% 0.96/1.19 (~r(s(z), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2015, 1986, 13, 1654, 1665])).
% 0.96/1.19 tff(2017,plain,
% 0.96/1.19 (b(s(z), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[680, 2016])).
% 0.96/1.19 tff(2018,plain,
% 0.96/1.19 (~b(s(s(s(z))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1691, 154, 1270, 1685, 684, 231])).
% 0.96/1.19 tff(2019,plain,
% 0.96/1.19 (r(s(s(s(z))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[104, 2018])).
% 0.96/1.19 tff(2020,plain,
% 0.96/1.19 (~r(s(s(z)), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1280, 2019, 171])).
% 0.96/1.19 tff(2021,plain,
% 0.96/1.19 (b(s(s(z)), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[122, 2020])).
% 0.96/1.19 tff(2022,plain,
% 0.96/1.19 (~r(z, s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1346, 2019, 171])).
% 0.96/1.19 tff(2023,plain,
% 0.96/1.19 (b(z, s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[64, 2022])).
% 0.96/1.19 tff(2024,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1307, 2023, 2021, 1299, 254, 1283])).
% 0.96/1.19 tff(2025,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(2026,plain,
% 0.96/1.19 (~r(s(s(s(z))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2025, 1841, 1665, 1986, 2017, 1992, 13])).
% 0.96/1.19 tff(2027,plain,
% 0.96/1.19 (b(s(s(s(z))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[169, 2026])).
% 0.96/1.19 tff(2028,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2029,plain,
% 0.96/1.19 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2030,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[2029])).
% 0.96/1.19 tff(2031,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[2030, 2028])).
% 0.96/1.19 tff(2032,plain,
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% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
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% 0.96/1.19 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 0.96/1.19 tff(2034,plain,
% 0.96/1.19 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2033, 154, 143, 1283, 254])).
% 0.96/1.19 tff(2035,plain,
% 0.96/1.19 (~b(s(s(s(z))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2034, 142])).
% 0.96/1.19 tff(2036,plain,
% 0.96/1.19 (r(s(s(s(z))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[104, 2035])).
% 0.96/1.19 tff(2037,plain,
% 0.96/1.19 (~b(z, s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1307, 142, 1299, 254, 1283])).
% 0.96/1.19 tff(2038,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[64, 2037])).
% 0.96/1.19 tff(2039,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2040,plain,
% 0.96/1.19 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2041,plain,
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% 0.96/1.19 inference(monotonicity,[status(thm)],[2040])).
% 0.96/1.19 tff(2042,plain,
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% 0.96/1.19 inference(transitivity,[status(thm)],[2041, 2039])).
% 0.96/1.19 tff(2043,plain,
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% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(2044,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 0.96/1.19 tff(2045,plain,
% 0.96/1.19 (~r(z, s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2044, 28, 2038, 2036])).
% 0.96/1.19 tff(2046,plain,
% 0.96/1.19 (b(z, s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[648, 2045])).
% 0.96/1.19 tff(2047,plain,
% 0.96/1.19 ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2010, 154, 1299, 1283, 254])).
% 0.96/1.19 tff(2048,plain,
% 0.96/1.19 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2047, 142])).
% 0.96/1.19 tff(2049,plain,
% 0.96/1.19 (r(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[229, 2048])).
% 0.96/1.19 tff(2050,plain,
% 0.96/1.19 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1621, 28, 2036, 2049])).
% 0.96/1.19 tff(2051,plain,
% 0.96/1.19 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[564, 2050])).
% 0.96/1.19 tff(2052,plain,
% 0.96/1.19 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[740, 154, 1299, 143, 254])).
% 0.96/1.19 tff(2053,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2052, 2051, 2046])).
% 0.96/1.19 tff(2054,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(2055,plain,
% 0.96/1.19 (~b(s(s(z)), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2054, 1841, 2027, 1665, 1986])).
% 0.96/1.19 tff(2056,plain,
% 0.96/1.19 (r(s(s(z)), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[122, 2055])).
% 0.96/1.19 tff(2057,plain,
% 0.96/1.19 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1935, 718])).
% 0.96/1.19 tff(2058,plain,
% 0.96/1.19 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[564, 2057])).
% 0.96/1.19 tff(2059,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2060,plain,
% 0.96/1.19 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2061,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[2060])).
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% 0.96/1.19 inference(transitivity,[status(thm)],[2061, 2059])).
% 0.96/1.19 tff(2063,plain,
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% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(2064,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 0.96/1.19 tff(2065,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[2064, 28, 273, 2058, 1655])).
% 0.96/1.19 tff(2066,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(2067,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[2066, 1654, 1841, 2027, 14])).
% 0.96/1.19 tff(2068,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[252, 2067])).
% 0.96/1.19 tff(2069,plain,
% 0.96/1.19 (~r(s(s(s(z))), s(z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1937, 2027, 1841, 1654, 14])).
% 0.96/1.19 tff(2070,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[818, 2069])).
% 0.96/1.19 tff(2071,plain,
% 0.96/1.19 (~b(s(s(z)), s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1419, 154, 2070, 2068, 2017, 1992])).
% 0.96/1.19 tff(2072,plain,
% 0.96/1.19 (r(s(s(z)), s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[138, 2071])).
% 0.96/1.19 tff(2073,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2074,plain,
% 0.96/1.19 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
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% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[2074])).
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% 0.96/1.19 inference(transitivity,[status(thm)],[2075, 2073])).
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% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
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% 0.96/1.19 inference(modus_ponens,[status(thm)],[2077, 2076])).
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[2078, 28, 124, 628, 106])).
% 0.96/1.19 tff(2080,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(2081,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[648, 2081])).
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[931, 154, 1841, 2027, 2082, 1665])).
% 0.96/1.19 tff(2084,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[343, 2083])).
% 0.96/1.19 tff(2085,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[1427, 28, 2072, 2084])).
% 0.96/1.19 tff(2086,plain,
% 0.96/1.19 (b(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[229, 2085])).
% 0.96/1.19 tff(2087,plain,
% 0.96/1.19 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1691, 154, 2070, 2017, 1992])).
% 0.96/1.19 tff(2088,plain,
% 0.96/1.19 (~b(s(s(s(z))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2087, 232])).
% 0.96/1.19 tff(2089,plain,
% 0.96/1.19 (r(s(s(s(z))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[104, 2088])).
% 0.96/1.19 tff(2090,plain,
% 0.96/1.19 (~r(z, s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2044, 28, 18, 2089])).
% 0.96/1.19 tff(2091,plain,
% 0.96/1.19 (b(z, s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[648, 2090])).
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% 0.96/1.19 tff(2093,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[343, 2092])).
% 0.96/1.19 tff(2094,plain,
% 0.96/1.19 (~b(s(s(z)), s(s(s(z))))),
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% 0.96/1.19 tff(2095,plain,
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% 0.96/1.19 inference(unit_resolution,[status(thm)],[138, 2094])).
% 0.96/1.19 tff(2096,plain,
% 0.96/1.19 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1427, 28, 2095, 2093])).
% 0.96/1.19 tff(2097,plain,
% 0.96/1.19 (b(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[229, 2096])).
% 0.96/1.19 tff(2098,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2099,plain,
% 0.96/1.19 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(2100,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[2099])).
% 0.96/1.19 tff(2101,plain,
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% 0.96/1.19 inference(transitivity,[status(thm)],[2100, 2098])).
% 0.96/1.19 tff(2102,plain,
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% 0.96/1.19 tff(2103,plain,
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% 0.96/1.19 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 0.96/1.19 tff(2104,plain,
% 0.96/1.19 (~b(s(s(s(s(z)))), s(z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2103, 154, 1986, 2017, 1992, 2097])).
% 0.96/1.19 tff(2105,plain,
% 0.96/1.19 (r(s(s(s(s(z)))), s(z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[318, 2104])).
% 0.96/1.19 tff(2106,plain,
% 0.96/1.19 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1864, 2105, 1665, 845, 1841, 14, 13])).
% 0.96/1.19 tff(2107,plain,
% 0.96/1.19 (b(s(s(s(s(elem!1)))), s(z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[441, 2106])).
% 0.96/1.19 tff(2108,plain,
% 0.96/1.19 (~b(s(z), s(s(s(s(elem!1)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[521, 443])).
% 0.96/1.19 tff(2109,plain,
% 0.96/1.19 (r(s(z), s(s(s(s(elem!1)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[467, 2108])).
% 0.96/1.19 tff(2110,plain,
% 0.96/1.19 (~b(z, s(s(s(s(elem!1)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[1489, 443])).
% 0.96/1.19 tff(2111,plain,
% 0.96/1.19 (r(z, s(s(s(s(elem!1)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[548, 2110])).
% 0.96/1.19 tff(2112,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[543, 2111, 2109, 14])).
% 0.96/1.19 tff(2113,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(2114,plain,
% 0.96/1.19 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[2113, 2107, 14, 2070, 2091, 232])).
% 0.96/1.19 tff(2115,plain,
% 0.96/1.19 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[496, 2114])).
% 0.96/1.19 tff(2116,plain,
% 0.96/1.19 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[959, 28, 2115, 2093])).
% 0.96/1.20 tff(2117,plain,
% 0.96/1.20 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[963, 60, 845, 2116])).
% 0.96/1.20 tff(2118,plain,
% 0.96/1.20 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[529, 28, 2115, 2093])).
% 0.96/1.20 tff(2119,plain,
% 0.96/1.20 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[517, 60, 12, 2118])).
% 0.96/1.20 tff(2120,plain,
% 0.96/1.20 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[1427, 28, 124, 604])).
% 0.96/1.20 tff(2121,plain,
% 0.96/1.20 (b(s(s(s(s(z)))), s(s(z)))),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[229, 2120])).
% 0.96/1.20 tff(2122,assumption,(b(s(s(s(s(z)))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.96/1.20 tff(2123,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 0.96/1.20 tff(2124,plain,
% 0.96/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(2125,plain,
% 0.96/1.20 (((~b(s(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(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(2126,plain,
% 0.96/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[2125])).
% 0.96/1.20 tff(2127,plain,
% 0.96/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[2126, 2124])).
% 0.96/1.20 tff(2128,plain,
% 0.96/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.96/1.20 inference(quant_inst,[status(thm)],[])).
% 0.96/1.20 tff(2129,plain,
% 0.96/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 0.96/1.20 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.96/1.20 tff(2130,plain,
% 0.96/1.20 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2129, 154, 1283, 2123, 2122])).
% 1.03/1.20 tff(2131,plain,
% 1.03/1.20 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2130, 2121])).
% 1.03/1.20 tff(2132,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[373, 60, 370, 2131, 1116])).
% 1.03/1.20 tff(2133,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2134,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2133, 2119, 2117, 2095, 2093, 2115, 1986])).
% 1.03/1.20 tff(2135,plain,((~b(s(z), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2136,plain,
% 1.03/1.20 (~r(z, s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2135, 2068, 14, 13, 12])).
% 1.03/1.20 tff(2137,plain,
% 1.03/1.20 (b(z, s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[64, 2136])).
% 1.03/1.20 tff(2138,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2139,plain,
% 1.03/1.20 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2140,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2139])).
% 1.03/1.20 tff(2141,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2140, 2138])).
% 1.03/1.20 tff(2142,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2143,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 1.03/1.20 tff(2144,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2143, 154, 1841, 1986, 2137, 2086, 1665])).
% 1.03/1.20 tff(2145,plain,((~r(z, s(z))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2146,plain,
% 1.03/1.20 (~r(z, s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2145, 13, 12])).
% 1.03/1.20 tff(2147,plain,
% 1.03/1.20 (b(z, s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1181, 2146])).
% 1.03/1.20 tff(2148,plain,
% 1.03/1.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[180, 172, 171])).
% 1.03/1.20 tff(2149,plain,
% 1.03/1.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[564, 2148])).
% 1.03/1.20 tff(2150,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2151,plain,
% 1.03/1.20 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2152,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2151])).
% 1.03/1.20 tff(2153,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2152, 2150])).
% 1.03/1.20 tff(2154,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2155,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 1.03/1.20 tff(2156,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2155, 28, 172, 13, 1655])).
% 1.03/1.20 tff(2157,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2158,plain,
% 1.03/1.20 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2157, 172, 13])).
% 1.03/1.20 tff(2159,plain,
% 1.03/1.20 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1653, 2158])).
% 1.03/1.20 tff(2160,plain,
% 1.03/1.20 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[623, 2159, 2149, 1270, 1685])).
% 1.03/1.20 tff(2161,plain,
% 1.03/1.20 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[343, 2160])).
% 1.03/1.20 tff(2162,plain,
% 1.03/1.20 (~b(z, s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1767, 154, 1726, 1270, 2159, 2149])).
% 1.03/1.20 tff(2163,plain,
% 1.03/1.20 (r(z, s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[648, 2162])).
% 1.03/1.20 tff(2164,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1467, 28, 2163, 172, 2161])).
% 1.03/1.20 tff(2165,plain,((~r(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2166,plain,
% 1.03/1.20 (~r(z, s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2165, 171, 13, 1726])).
% 1.03/1.20 tff(2167,plain,
% 1.03/1.20 (b(z, s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[191, 2166])).
% 1.03/1.20 tff(2168,plain,
% 1.03/1.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[201, 193, 171])).
% 1.03/1.20 tff(2169,plain,
% 1.03/1.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[564, 2168])).
% 1.03/1.20 tff(2170,plain,
% 1.03/1.20 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1839, 193, 13])).
% 1.03/1.20 tff(2171,plain,
% 1.03/1.20 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1653, 2170])).
% 1.03/1.20 tff(2172,plain,
% 1.03/1.20 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[623, 2171, 2169, 1270, 1685])).
% 1.03/1.20 tff(2173,plain,
% 1.03/1.20 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[343, 2172])).
% 1.03/1.20 tff(2174,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2175,plain,
% 1.03/1.20 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2176,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2175])).
% 1.03/1.20 tff(2177,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2176, 2174])).
% 1.03/1.20 tff(2178,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2179,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 1.03/1.20 tff(2180,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2179, 28, 2173, 171, 193])).
% 1.03/1.20 tff(2181,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2182,plain,
% 1.03/1.20 (~r(s(s(s(s(z)))), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2181, 171, 13])).
% 1.03/1.20 tff(2183,plain,
% 1.03/1.20 (b(s(s(s(s(z)))), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[206, 2182])).
% 1.03/1.20 tff(2184,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2185,plain,
% 1.03/1.20 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2186,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2185])).
% 1.03/1.20 tff(2187,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.03/1.20 tff(2188,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2189,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.03/1.20 tff(2190,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2189, 154, 1726, 1299, 15, 506, 254])).
% 1.03/1.20 tff(2191,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2192,plain,
% 1.03/1.20 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2191, 15, 2183, 1726, 2167])).
% 1.03/1.20 tff(2193,plain,
% 1.03/1.20 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[318, 2192])).
% 1.03/1.20 tff(2194,plain,
% 1.03/1.20 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[75, 16, 66])).
% 1.03/1.20 tff(2195,plain,
% 1.03/1.20 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[104, 2194])).
% 1.03/1.20 tff(2196,plain,
% 1.03/1.20 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[132, 16, 66])).
% 1.03/1.20 tff(2197,plain,
% 1.03/1.20 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[138, 2196])).
% 1.03/1.20 tff(2198,plain,
% 1.03/1.20 (~r(s(s(z)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[307, 16, 298])).
% 1.03/1.20 tff(2199,plain,
% 1.03/1.20 (b(s(s(z)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[296, 2198])).
% 1.03/1.20 tff(2200,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[240, 2199, 2197, 2195, 232, 1])).
% 1.03/1.20 tff(2201,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2202,plain,
% 1.03/1.20 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2201, 2193, 1270, 1685, 66])).
% 1.03/1.20 tff(2203,plain,
% 1.03/1.20 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1259, 2202])).
% 1.03/1.20 tff(2204,plain,
% 1.03/1.20 (~r(s(s(z)), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1536, 17, 13])).
% 1.03/1.20 tff(2205,plain,
% 1.03/1.20 (b(s(s(z)), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[122, 2204])).
% 1.03/1.20 tff(2206,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1309, 2205, 65, 171, 66, 1283])).
% 1.03/1.20 tff(2207,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2208,plain,
% 1.03/1.20 (~r(s(z), s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2207, 2203, 66, 171, 13])).
% 1.03/1.20 tff(2209,plain,
% 1.03/1.20 (b(s(z), s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[680, 2208])).
% 1.03/1.20 tff(2210,plain,
% 1.03/1.20 (~b(s(s(z)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2025, 2209, 171, 2183, 2167, 2203, 13])).
% 1.03/1.20 tff(2211,plain,
% 1.03/1.20 (r(s(s(z)), s(z))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[296, 2210])).
% 1.03/1.20 tff(2212,plain,
% 1.03/1.20 (~r(s(s(z)), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[702, 2211, 13])).
% 1.03/1.20 tff(2213,plain,
% 1.03/1.20 (b(s(s(z)), z)),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[122, 2212])).
% 1.03/1.20 tff(2214,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2215,plain,
% 1.03/1.20 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2216,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[2215])).
% 1.03/1.20 tff(2217,plain,
% 1.03/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.20 inference(transitivity,[status(thm)],[2216, 2214])).
% 1.03/1.20 tff(2218,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.03/1.20 inference(quant_inst,[status(thm)],[])).
% 1.03/1.20 tff(2219,plain,
% 1.03/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[2218, 2217])).
% 1.03/1.20 tff(2220,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2219, 154, 2183, 2203, 15, 2209, 2213])).
% 1.03/1.20 tff(2221,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2222,plain,
% 1.03/1.20 (~b(s(z), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2221, 66, 171, 13, 1726])).
% 1.03/1.20 tff(2223,plain,
% 1.03/1.20 (r(s(z), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1653, 2222])).
% 1.03/1.20 tff(2224,plain,
% 1.03/1.20 (~b(s(z), s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[804, 16, 232, 66, 1])).
% 1.03/1.20 tff(2225,plain,
% 1.03/1.20 ($false),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[680, 2224, 1944])).
% 1.03/1.20 tff(2226,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.20 tff(2227,plain,
% 1.03/1.20 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2226, 2223, 66, 1270, 1685])).
% 1.03/1.20 tff(2228,plain,
% 1.03/1.20 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[1259, 2227])).
% 1.03/1.20 tff(2229,plain,
% 1.03/1.20 (~r(s(z), s(s(z)))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[2015, 2228, 13, 2167, 2223])).
% 1.03/1.20 tff(2230,plain,
% 1.03/1.20 (b(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[680, 2229])).
% 1.03/1.21 tff(2231,plain,
% 1.03/1.21 (~b(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2025, 2230, 171, 2183, 2167, 2228, 13])).
% 1.03/1.21 tff(2232,plain,
% 1.03/1.21 (r(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[296, 2231])).
% 1.03/1.21 tff(2233,plain,
% 1.03/1.21 (~r(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[702, 2232, 13])).
% 1.03/1.21 tff(2234,plain,
% 1.03/1.21 (b(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[122, 2233])).
% 1.03/1.21 tff(2235,plain,
% 1.03/1.21 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2010, 154, 2183, 2228, 2234, 2167])).
% 1.03/1.21 tff(2236,plain,
% 1.03/1.21 (r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[229, 2235])).
% 1.03/1.21 tff(2237,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2238,plain,
% 1.03/1.21 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2239,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2238])).
% 1.03/1.21 tff(2240,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.03/1.21 tff(2241,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2242,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.03/1.21 tff(2243,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2242, 154, 1726, 1299, 1283, 506, 142])).
% 1.03/1.21 tff(2244,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2245,plain,
% 1.03/1.21 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2244, 2228, 2183, 1726, 2234])).
% 1.03/1.21 tff(2246,plain,
% 1.03/1.21 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[318, 2245])).
% 1.03/1.21 tff(2247,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2248,plain,
% 1.03/1.21 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2249,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2248])).
% 1.03/1.21 tff(2250,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2249, 2247])).
% 1.03/1.21 tff(2251,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2252,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 1.03/1.21 tff(2253,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2252, 28, 2232, 2246, 2236])).
% 1.03/1.21 tff(2254,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2255,plain,
% 1.03/1.21 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2254, 171, 13, 1726])).
% 1.03/1.21 tff(2256,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[564, 2255])).
% 1.03/1.21 tff(2257,plain,
% 1.03/1.21 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1681, 16, 17])).
% 1.03/1.21 tff(2258,plain,
% 1.03/1.21 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1653, 2257])).
% 1.03/1.21 tff(2259,plain,
% 1.03/1.21 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[623, 2258, 566, 1, 232])).
% 1.03/1.21 tff(2260,plain,
% 1.03/1.21 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[343, 2259])).
% 1.03/1.21 tff(2261,plain,
% 1.03/1.21 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[601, 2258, 13, 17, 1, 566, 16])).
% 1.03/1.21 tff(2262,plain,
% 1.03/1.21 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[138, 2261])).
% 1.03/1.21 tff(2263,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[612, 2262, 2260, 16])).
% 1.03/1.21 tff(2264,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2265,plain,
% 1.03/1.21 (~r(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2264, 16, 13, 1270, 2256, 1685])).
% 1.03/1.21 tff(2266,plain,
% 1.03/1.21 (b(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[680, 2265])).
% 1.03/1.21 tff(2267,plain,
% 1.03/1.21 (~r(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[702, 106, 13])).
% 1.03/1.21 tff(2268,plain,
% 1.03/1.21 (b(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[296, 2267])).
% 1.03/1.21 tff(2269,plain,
% 1.03/1.21 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[692, 2268, 684, 1282, 1270])).
% 1.03/1.21 tff(2270,plain,
% 1.03/1.21 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[138, 2269])).
% 1.03/1.21 tff(2271,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2272,plain,
% 1.03/1.21 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2273,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2272])).
% 1.03/1.21 tff(2274,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2273, 2271])).
% 1.03/1.21 tff(2275,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2276,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 1.03/1.21 tff(2277,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2276, 28, 2270, 106, 171])).
% 1.03/1.21 tff(2278,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2279,plain,
% 1.03/1.21 (~r(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2278, 2266, 171, 13])).
% 1.03/1.21 tff(2280,plain,
% 1.03/1.21 (b(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[122, 2279])).
% 1.03/1.21 tff(2281,plain,
% 1.03/1.21 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[307, 299, 16])).
% 1.03/1.21 tff(2282,plain,
% 1.03/1.21 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[318, 2281])).
% 1.03/1.21 tff(2283,plain,
% 1.03/1.21 (~b(s(z), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2191, 2282, 1299, 1726, 254])).
% 1.03/1.21 tff(2284,plain,
% 1.03/1.21 (r(s(z), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1653, 2283])).
% 1.03/1.21 tff(2285,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1824, 28, 16, 299, 2284])).
% 1.03/1.21 tff(2286,plain,((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2287,plain,
% 1.03/1.21 (~r(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2286, 16, 2183, 1726, 2167])).
% 1.03/1.21 tff(2288,plain,
% 1.03/1.21 (b(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[296, 2287])).
% 1.03/1.21 tff(2289,plain,
% 1.03/1.21 (~b(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1736, 2288, 1726, 2266, 2280])).
% 1.03/1.21 tff(2290,plain,
% 1.03/1.21 (r(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[64, 2289])).
% 1.03/1.21 tff(2291,plain,
% 1.03/1.21 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1346, 2290, 171])).
% 1.03/1.21 tff(2292,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[104, 2291])).
% 1.03/1.21 tff(2293,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1691, 154, 1270, 1685, 2266, 2288, 2292])).
% 1.03/1.21 tff(2294,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2295,plain,
% 1.03/1.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2294, 171, 1726, 13])).
% 1.03/1.21 tff(2296,plain,
% 1.03/1.21 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1259, 2295])).
% 1.03/1.21 tff(2297,plain,
% 1.03/1.21 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1346, 18, 171])).
% 1.03/1.21 tff(2298,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[104, 2297])).
% 1.03/1.21 tff(2299,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2300,plain,
% 1.03/1.21 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2301,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2300])).
% 1.03/1.21 tff(2302,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2301, 2299])).
% 1.03/1.21 tff(2303,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2304,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 1.03/1.21 tff(2305,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2304, 154, 232, 1283, 684, 141, 566])).
% 1.03/1.21 tff(2306,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2307,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2306, 2298, 1358, 566, 1685, 1283])).
% 1.03/1.21 tff(2308,plain,((~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2309,plain,
% 1.03/1.21 (~r(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2308, 2256, 2296, 171, 13])).
% 1.03/1.21 tff(2310,plain,
% 1.03/1.21 (b(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[64, 2309])).
% 1.03/1.21 tff(2311,plain,
% 1.03/1.21 (~b(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1307, 2310, 2183, 2167, 2296])).
% 1.03/1.21 tff(2312,plain,
% 1.03/1.21 (r(s(s(z)), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[122, 2311])).
% 1.03/1.21 tff(2313,plain,
% 1.03/1.21 (~r(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1536, 2312, 13])).
% 1.03/1.21 tff(2314,plain,
% 1.03/1.21 (~b(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2278, 2312, 171, 13])).
% 1.03/1.21 tff(2315,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[680, 2314, 2313])).
% 1.03/1.21 tff(2316,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2317,plain,
% 1.03/1.21 (~r(s(s(s(z))), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2316, 13, 2147])).
% 1.03/1.21 tff(2318,plain,
% 1.03/1.21 (b(s(s(s(z))), z)),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[169, 2317])).
% 1.03/1.21 tff(2319,plain,
% 1.03/1.21 (~b(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1560, 2205, 820, 65, 143, 17])).
% 1.03/1.21 tff(2320,plain,
% 1.03/1.21 (r(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[296, 2319])).
% 1.03/1.21 tff(2321,plain,
% 1.03/1.21 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1556, 17, 820])).
% 1.03/1.21 tff(2322,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[104, 2321])).
% 1.03/1.21 tff(2323,plain,
% 1.03/1.21 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[162, 2322, 143, 65, 2205])).
% 1.03/1.21 tff(2324,plain,
% 1.03/1.21 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[138, 2323])).
% 1.03/1.21 tff(2325,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1125, 2324, 2320, 820])).
% 1.03/1.21 tff(2326,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2327,plain,
% 1.03/1.21 (~r(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2326, 820, 2318, 13])).
% 1.03/1.21 tff(2328,plain,
% 1.03/1.21 (b(s(z), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[680, 2327])).
% 1.03/1.21 tff(2329,plain,
% 1.03/1.21 (~b(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1736, 140, 1726, 684, 142])).
% 1.03/1.21 tff(2330,plain,
% 1.03/1.21 (r(s(s(z)), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[296, 2329])).
% 1.03/1.21 tff(2331,plain,
% 1.03/1.21 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1125, 2330, 820])).
% 1.03/1.21 tff(2332,plain,
% 1.03/1.21 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[138, 2331])).
% 1.03/1.21 tff(2333,plain,
% 1.03/1.21 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[865, 2330, 820])).
% 1.03/1.21 tff(2334,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[104, 2333])).
% 1.03/1.21 tff(2335,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[162, 2334, 2332, 143, 140, 142])).
% 1.03/1.21 tff(2336,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2337,plain,
% 1.03/1.21 (~b(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2336, 142, 2318, 820, 2147, 2328])).
% 1.03/1.21 tff(2338,plain,
% 1.03/1.21 (r(z, s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[64, 2337])).
% 1.03/1.21 tff(2339,plain,
% 1.03/1.21 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[865, 299, 820])).
% 1.03/1.21 tff(2340,plain,
% 1.03/1.21 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[104, 2339])).
% 1.03/1.21 tff(2341,plain,
% 1.03/1.21 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1802, 28, 273, 13, 193])).
% 1.03/1.21 tff(2342,plain,
% 1.03/1.21 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[318, 2341])).
% 1.03/1.21 tff(2343,plain,
% 1.03/1.21 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1125, 299, 820])).
% 1.03/1.21 tff(2344,plain,
% 1.03/1.21 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[138, 2343])).
% 1.03/1.21 tff(2345,plain,
% 1.03/1.21 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[942, 345, 820])).
% 1.03/1.21 tff(2346,plain,
% 1.03/1.21 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[496, 2345])).
% 1.03/1.21 tff(2347,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2348,plain,
% 1.03/1.21 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(2349,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.03/1.21 inference(monotonicity,[status(thm)],[2348])).
% 1.03/1.21 tff(2350,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[2349, 2347])).
% 1.03/1.21 tff(2351,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.03/1.21 inference(quant_inst,[status(thm)],[])).
% 1.03/1.21 tff(2352,plain,
% 1.03/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 1.03/1.21 tff(2353,plain,
% 1.03/1.21 ($false),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2352, 154, 144, 990, 2346, 141, 374])).
% 1.03/1.21 tff(2354,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.21 tff(2355,plain,
% 1.03/1.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2354, 2344, 820, 299, 2340])).
% 1.03/1.21 tff(2356,plain,
% 1.03/1.21 (b(s(s(s(s(elem!1)))), s(z))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[441, 2355])).
% 1.03/1.21 tff(2357,plain,
% 1.03/1.21 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[1016, 402, 13])).
% 1.03/1.21 tff(2358,plain,
% 1.03/1.21 (b(s(z), s(s(s(s(elem!1)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[467, 2357])).
% 1.03/1.21 tff(2359,plain,
% 1.03/1.21 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[512, 154, 444, 2171, 506])).
% 1.03/1.21 tff(2360,plain,
% 1.03/1.21 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[2359, 2358])).
% 1.03/1.21 tff(2361,plain,
% 1.03/1.21 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.03/1.21 inference(unit_resolution,[status(thm)],[517, 60, 2360, 12])).
% 1.03/1.21 tff(2362,plain,
% 1.03/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2363,plain,
% 1.03/1.22 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2364,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2363])).
% 1.03/1.22 tff(2365,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2364, 2362])).
% 1.03/1.22 tff(2366,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2367,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2366, 2365])).
% 1.03/1.22 tff(2368,plain,
% 1.03/1.22 ($false),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2367, 28, 402, 193, 2361])).
% 1.03/1.22 tff(2369,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.22 tff(2370,plain,
% 1.03/1.22 (~r(s(s(s(s(elem!1)))), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2369, 2356, 12, 193, 2342, 13])).
% 1.03/1.22 tff(2371,plain,
% 1.03/1.22 (b(s(s(s(s(elem!1)))), z)),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[418, 2370])).
% 1.03/1.22 tff(2372,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2373,plain,
% 1.03/1.22 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~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(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2374,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2373])).
% 1.03/1.22 tff(2375,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2374, 2372])).
% 1.03/1.22 tff(2376,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2377,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2376, 2375])).
% 1.03/1.22 tff(2378,plain,
% 1.03/1.22 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2377, 154, 2147, 2356, 2318])).
% 1.03/1.22 tff(2379,plain,
% 1.03/1.22 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2378, 2371])).
% 1.03/1.22 tff(2380,plain,
% 1.03/1.22 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[989, 2379])).
% 1.03/1.22 tff(2381,plain,
% 1.03/1.22 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1027, 2380, 273])).
% 1.03/1.22 tff(2382,plain,
% 1.03/1.22 (b(s(z), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[467, 2381])).
% 1.03/1.22 tff(2383,plain,
% 1.03/1.22 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[952, 154, 2382, 2356, 2171, 2342])).
% 1.03/1.22 tff(2384,plain,
% 1.03/1.22 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[963, 60, 845, 2383])).
% 1.03/1.22 tff(2385,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2386,plain,
% 1.03/1.22 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2387,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2386])).
% 1.03/1.22 tff(2388,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2387, 2385])).
% 1.03/1.22 tff(2389,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2390,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 1.03/1.22 tff(2391,plain,
% 1.03/1.22 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2390, 154, 2147, 2356, 142])).
% 1.03/1.22 tff(2392,plain,
% 1.03/1.22 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2391, 2371])).
% 1.03/1.22 tff(2393,plain,
% 1.03/1.22 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[373, 60, 370, 2392])).
% 1.03/1.22 tff(2394,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2395,plain,
% 1.03/1.22 (((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2396,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2395])).
% 1.03/1.22 tff(2397,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2396, 2394])).
% 1.03/1.22 tff(2398,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2399,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 1.03/1.22 tff(2400,plain,
% 1.03/1.22 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2399, 28, 2393, 2384])).
% 1.03/1.22 tff(2401,plain,
% 1.03/1.22 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[1259, 2400])).
% 1.03/1.22 tff(2402,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2403,plain,
% 1.03/1.22 (((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2404,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2403])).
% 1.03/1.22 tff(2405,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2404, 2402])).
% 1.03/1.22 tff(2406,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2407,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.03/1.22 tff(2408,plain,
% 1.03/1.22 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2407, 28, 2380, 2384])).
% 1.03/1.22 tff(2409,plain,
% 1.03/1.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[564, 2408])).
% 1.03/1.22 tff(2410,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2411,plain,
% 1.03/1.22 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2412,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2411])).
% 1.03/1.22 tff(2413,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2412, 2410])).
% 1.03/1.22 tff(2414,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.22 inference(quant_inst,[status(thm)],[])).
% 1.03/1.22 tff(2415,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.03/1.22 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.03/1.22 tff(2416,plain,
% 1.03/1.22 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[2415, 28, 2380, 2384])).
% 1.03/1.22 tff(2417,plain,
% 1.03/1.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.22 inference(unit_resolution,[status(thm)],[343, 2416])).
% 1.03/1.22 tff(2418,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2419,plain,
% 1.03/1.22 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(2420,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.22 inference(monotonicity,[status(thm)],[2419])).
% 1.03/1.22 tff(2421,plain,
% 1.03/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.22 inference(transitivity,[status(thm)],[2420, 2418])).
% 1.03/1.22 tff(2422,plain,
% 1.03/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(2423,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.03/1.23 tff(2424,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2423, 154, 144, 615, 1283, 141, 566])).
% 1.03/1.23 tff(2425,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2426,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2425, 2417, 2409, 2344, 2401, 2340])).
% 1.03/1.23 tff(2427,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2428,plain,
% 1.03/1.23 (~r(s(s(z)), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2427, 193, 142, 12, 273, 13, 820])).
% 1.03/1.23 tff(2429,plain,
% 1.03/1.23 (b(s(s(z)), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[296, 2428])).
% 1.03/1.23 tff(2430,plain,
% 1.03/1.23 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1391, 2429, 13, 2328, 193])).
% 1.03/1.23 tff(2431,plain,
% 1.03/1.23 (r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1259, 2430])).
% 1.03/1.23 tff(2432,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2433,plain,
% 1.03/1.23 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2434,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[2433])).
% 1.03/1.23 tff(2435,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[2434, 2432])).
% 1.03/1.23 tff(2436,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(2437,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.03/1.23 tff(2438,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2437, 28, 172, 18, 16])).
% 1.03/1.23 tff(2439,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2440,plain,
% 1.03/1.23 (~r(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2439, 2431, 2338])).
% 1.03/1.23 tff(2441,plain,
% 1.03/1.23 (b(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[191, 2440])).
% 1.03/1.23 tff(2442,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2443,plain,
% 1.03/1.23 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2444,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[2443])).
% 1.03/1.23 tff(2445,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[2444, 2442])).
% 1.03/1.23 tff(2446,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(2447,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 1.03/1.23 tff(2448,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2447, 154, 2147, 2171, 2429, 142, 2441])).
% 1.03/1.23 tff(2449,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2450,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2449, 142, 13, 12, 273, 820])).
% 1.03/1.23 tff(2451,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[206, 2450])).
% 1.03/1.23 tff(2452,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1251, 172, 18])).
% 1.03/1.23 tff(2453,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[229, 2452])).
% 1.03/1.23 tff(2454,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2455,plain,
% 1.03/1.23 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2456,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[2455])).
% 1.03/1.23 tff(2457,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[2456, 2454])).
% 1.03/1.23 tff(2458,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(2459,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 1.03/1.23 tff(2460,plain,
% 1.03/1.23 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2459, 154, 1299, 684, 142])).
% 1.03/1.23 tff(2461,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2460, 2453, 2159])).
% 1.03/1.23 tff(2462,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2463,plain,
% 1.03/1.23 (~r(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2462, 2451, 2328, 142, 2338, 13])).
% 1.03/1.23 tff(2464,plain,
% 1.03/1.23 (b(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[191, 2463])).
% 1.03/1.23 tff(2465,plain,
% 1.03/1.23 (~r(z, s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1976, 13, 273])).
% 1.03/1.23 tff(2466,plain,
% 1.03/1.23 (b(z, s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[648, 2465])).
% 1.03/1.23 tff(2467,plain,
% 1.03/1.23 (~r(s(s(s(z))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1268, 13, 820])).
% 1.03/1.23 tff(2468,plain,
% 1.03/1.23 (b(s(s(s(z))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[169, 2467])).
% 1.03/1.23 tff(2469,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[740, 154, 1299, 2468, 2466, 566, 254])).
% 1.03/1.23 tff(2470,plain,((~r(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2471,plain,
% 1.03/1.23 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2470, 2464, 13, 820, 273, 2451])).
% 1.03/1.23 tff(2472,plain,
% 1.03/1.23 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[564, 2471])).
% 1.03/1.23 tff(2473,plain,
% 1.03/1.23 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1930, 2472, 820])).
% 1.03/1.23 tff(2474,plain,
% 1.03/1.23 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1653, 2473])).
% 1.03/1.23 tff(2475,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[853, 2472, 820])).
% 1.03/1.23 tff(2476,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[318, 2475])).
% 1.03/1.23 tff(2477,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2191, 2476, 2474, 2451, 2147, 2464])).
% 1.03/1.23 tff(2478,plain,((~b(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2479,plain,
% 1.03/1.23 (~b(s(s(z)), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2478, 273, 13, 820, 12])).
% 1.03/1.23 tff(2480,plain,
% 1.03/1.23 (r(s(s(z)), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[122, 2479])).
% 1.03/1.23 tff(2481,plain,
% 1.03/1.23 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1391, 193, 13, 684, 2268])).
% 1.03/1.23 tff(2482,plain,
% 1.03/1.23 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[923, 193, 106])).
% 1.03/1.23 tff(2483,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1259, 2482, 2481])).
% 1.03/1.23 tff(2484,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2485,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2484, 2480, 13, 2328])).
% 1.03/1.23 tff(2486,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[206, 2485])).
% 1.03/1.23 tff(2487,plain,
% 1.03/1.23 (~r(s(s(z)), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[702, 2480, 13])).
% 1.03/1.23 tff(2488,plain,
% 1.03/1.23 (b(s(s(z)), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[296, 2487])).
% 1.03/1.23 tff(2489,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1839, 1655, 13])).
% 1.03/1.23 tff(2490,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[206, 2489])).
% 1.03/1.23 tff(2491,plain,
% 1.03/1.23 (~r(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2157, 1655, 13])).
% 1.03/1.23 tff(2492,plain,
% 1.03/1.23 (b(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[191, 2491])).
% 1.03/1.23 tff(2493,plain,
% 1.03/1.23 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1930, 1655, 820])).
% 1.03/1.23 tff(2494,plain,
% 1.03/1.23 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[564, 2493])).
% 1.03/1.23 tff(2495,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2470, 2494, 2492, 13, 820, 273, 2490])).
% 1.03/1.23 tff(2496,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2497,plain,
% 1.03/1.23 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2496, 273, 820, 13])).
% 1.03/1.23 tff(2498,plain,
% 1.03/1.23 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1653, 2497])).
% 1.03/1.23 tff(2499,plain,
% 1.03/1.23 (~r(s(s(s(z))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2316, 13, 1726])).
% 1.03/1.23 tff(2500,plain,
% 1.03/1.23 (b(s(s(s(z))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[169, 2499])).
% 1.03/1.23 tff(2501,plain,
% 1.03/1.23 (~r(s(z), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2326, 820, 2500, 13])).
% 1.03/1.23 tff(2502,plain,
% 1.03/1.23 (b(s(z), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[680, 2501])).
% 1.03/1.23 tff(2503,plain,
% 1.03/1.23 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1389, 1283, 2502, 231, 2498])).
% 1.03/1.23 tff(2504,plain,
% 1.03/1.23 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[318, 2503])).
% 1.03/1.23 tff(2505,plain,
% 1.03/1.23 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[853, 2504, 820])).
% 1.03/1.23 tff(2506,plain,
% 1.03/1.23 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[564, 2505])).
% 1.03/1.23 tff(2507,plain,
% 1.03/1.23 (~b(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2470, 2506, 13, 820, 273, 1299])).
% 1.03/1.23 tff(2508,plain,
% 1.03/1.23 (r(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[191, 2507])).
% 1.03/1.23 tff(2509,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2510,plain,
% 1.03/1.23 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2511,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[2510])).
% 1.03/1.23 tff(2512,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[2511, 2509])).
% 1.03/1.23 tff(2513,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(2514,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.23 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 1.03/1.23 tff(2515,plain,
% 1.03/1.23 (~b(z, s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2514, 154, 1726, 1283, 2498, 231])).
% 1.03/1.23 tff(2516,plain,
% 1.03/1.23 (r(z, s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[64, 2515])).
% 1.03/1.23 tff(2517,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1251, 2516, 2508])).
% 1.03/1.23 tff(2518,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[229, 2517])).
% 1.03/1.23 tff(2519,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1435, 154, 1283, 2498, 2502, 231, 2518])).
% 1.03/1.23 tff(2520,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2521,plain,
% 1.03/1.23 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2520, 2488, 2147, 13, 820, 273, 2486])).
% 1.03/1.23 tff(2522,plain,
% 1.03/1.23 (r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1259, 2521])).
% 1.03/1.23 tff(2523,plain,
% 1.03/1.23 (~r(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[913, 2522, 2480])).
% 1.03/1.23 tff(2524,plain,
% 1.03/1.23 (b(z, s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[191, 2523])).
% 1.03/1.23 tff(2525,plain,
% 1.03/1.23 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2470, 2524, 13, 820, 273, 2486])).
% 1.03/1.23 tff(2526,plain,
% 1.03/1.23 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[564, 2525])).
% 1.03/1.23 tff(2527,plain,
% 1.03/1.23 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2191, 2524, 2498, 2147, 2486])).
% 1.03/1.23 tff(2528,plain,
% 1.03/1.23 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[318, 2527])).
% 1.03/1.23 tff(2529,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[853, 2528, 2526, 820])).
% 1.03/1.23 tff(2530,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2531,plain,
% 1.03/1.23 (~r(s(z), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2530, 820, 13, 12])).
% 1.03/1.23 tff(2532,plain,
% 1.03/1.23 (b(s(z), s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[252, 2531])).
% 1.03/1.23 tff(2533,plain,
% 1.03/1.23 (~r(s(z), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2326, 820, 143, 13])).
% 1.03/1.23 tff(2534,plain,
% 1.03/1.23 (b(s(z), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[680, 2533])).
% 1.03/1.23 tff(2535,plain,
% 1.03/1.23 (~r(z, s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1976, 273, 13])).
% 1.03/1.23 tff(2536,plain,
% 1.03/1.23 (b(z, s(s(s(z))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[648, 2535])).
% 1.03/1.23 tff(2537,plain,
% 1.03/1.23 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1705, 2536, 67, 106])).
% 1.03/1.23 tff(2538,plain,
% 1.03/1.23 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1259, 2537])).
% 1.03/1.23 tff(2539,plain,
% 1.03/1.23 (~r(s(z), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1556, 67, 820])).
% 1.03/1.23 tff(2540,plain,
% 1.03/1.23 (b(s(z), s(s(z)))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[680, 2539])).
% 1.03/1.23 tff(2541,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[317, 2341, 313])).
% 1.03/1.23 tff(2542,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[1389, 2541, 1373, 231, 684, 1283])).
% 1.03/1.23 tff(2543,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.23 tff(2544,plain,
% 1.03/1.23 (~r(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[2543, 2538, 2540, 231, 273, 13])).
% 1.03/1.23 tff(2545,plain,
% 1.03/1.23 (b(s(s(s(s(z)))), z)),
% 1.03/1.23 inference(unit_resolution,[status(thm)],[206, 2544])).
% 1.03/1.23 tff(2546,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2547,plain,
% 1.03/1.23 (((~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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(rewrite,[status(thm)],[])).
% 1.03/1.23 tff(2548,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.23 inference(monotonicity,[status(thm)],[2547])).
% 1.03/1.23 tff(2549,plain,
% 1.03/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.23 inference(transitivity,[status(thm)],[2548, 2546])).
% 1.03/1.23 tff(2550,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.23 inference(quant_inst,[status(thm)],[])).
% 1.03/1.23 tff(2551,plain,
% 1.03/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 1.03/1.24 tff(2552,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2551, 154, 144, 1299, 143, 1283, 566])).
% 1.03/1.24 tff(2553,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(2554,plain,
% 1.03/1.24 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2553, 2545, 144, 1701, 2538])).
% 1.03/1.24 tff(2555,plain,
% 1.03/1.24 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[564, 2554])).
% 1.03/1.24 tff(2556,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[853, 2555, 820])).
% 1.03/1.24 tff(2557,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[317, 2556, 313])).
% 1.03/1.24 tff(2558,plain,
% 1.03/1.24 (~b(s(z), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1389, 2557, 231, 2540, 2538])).
% 1.03/1.24 tff(2559,plain,
% 1.03/1.24 (r(s(z), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1372, 2558, 1361])).
% 1.03/1.24 tff(2560,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2064, 28, 273, 2555, 2559])).
% 1.03/1.24 tff(2561,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(2562,plain,
% 1.03/1.24 (~r(s(z), s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2561, 13, 820, 144, 231, 67, 106])).
% 1.03/1.24 tff(2563,plain,
% 1.03/1.24 (b(s(z), s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[252, 2562])).
% 1.03/1.24 tff(2564,plain,
% 1.03/1.24 (~r(z, s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[838, 628, 820])).
% 1.03/1.24 tff(2565,plain,
% 1.03/1.24 (b(z, s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1181, 2564])).
% 1.03/1.24 tff(2566,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2567,plain,
% 1.03/1.24 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2568,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2567])).
% 1.03/1.24 tff(2569,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[2568, 2566])).
% 1.03/1.24 tff(2570,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(2571,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 1.03/1.24 tff(2572,plain,
% 1.03/1.24 (~b(z, s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2571, 154, 144, 2565, 232, 231])).
% 1.03/1.24 tff(2573,plain,
% 1.03/1.24 (r(z, s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[64, 2572])).
% 1.03/1.24 tff(2574,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2575,plain,
% 1.03/1.24 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2576,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2575])).
% 1.03/1.24 tff(2577,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.03/1.24 tff(2578,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(2579,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.03/1.24 tff(2580,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2579, 28, 820, 628, 2573, 67])).
% 1.03/1.24 tff(2581,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(2582,plain,
% 1.03/1.24 (~r(z, s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2581, 2563, 67, 144, 820, 231])).
% 1.03/1.24 tff(2583,plain,
% 1.03/1.24 (b(z, s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[648, 2582])).
% 1.03/1.24 tff(2584,plain,
% 1.03/1.24 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1705, 2583, 67, 106])).
% 1.03/1.24 tff(2585,plain,
% 1.03/1.24 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1259, 2584])).
% 1.03/1.24 tff(2586,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), z)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1391, 2585, 2540, 231, 13])).
% 1.03/1.24 tff(2587,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), z)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[206, 2586])).
% 1.03/1.24 tff(2588,plain,
% 1.03/1.24 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2553, 2587, 144, 1701, 2585])).
% 1.03/1.24 tff(2589,plain,
% 1.03/1.24 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[564, 2588])).
% 1.03/1.24 tff(2590,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[853, 2589, 820])).
% 1.03/1.24 tff(2591,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[317, 2590, 313])).
% 1.03/1.24 tff(2592,plain,
% 1.03/1.24 (~b(s(z), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1389, 2591, 231, 2540, 2585])).
% 1.03/1.24 tff(2593,plain,
% 1.03/1.24 (r(s(z), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1372, 2592, 1361])).
% 1.03/1.24 tff(2594,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2595,plain,
% 1.03/1.24 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2596,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2595])).
% 1.03/1.24 tff(2597,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[2596, 2594])).
% 1.03/1.24 tff(2598,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(2599,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 1.03/1.24 tff(2600,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2599, 28, 820, 2589, 13, 2593])).
% 1.03/1.24 tff(2601,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(2602,plain,
% 1.03/1.24 (~r(s(z), z)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2601, 67, 231, 144, 820, 106])).
% 1.03/1.24 tff(2603,plain,
% 1.03/1.24 (b(s(z), z)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[271, 2602])).
% 1.03/1.24 tff(2604,assumption,(b(s(z), z)), introduced(assumption)).
% 1.03/1.24 tff(2605,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2606,plain,
% 1.03/1.24 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2607,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2606])).
% 1.03/1.24 tff(2608,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[2607, 2605])).
% 1.03/1.24 tff(2609,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(2610,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 1.03/1.24 tff(2611,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2610, 154, 1726, 2604, 684, 231, 140])).
% 1.03/1.24 tff(2612,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(2613,plain,
% 1.03/1.24 (~b(z, s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2612, 2565, 231, 2540, 2604])).
% 1.03/1.24 tff(2614,plain,
% 1.03/1.24 (r(z, s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[64, 2613])).
% 1.03/1.24 tff(2615,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2579, 28, 820, 628, 2614, 67])).
% 1.03/1.24 tff(2616,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(2617,plain,
% 1.03/1.24 (~r(z, s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2616, 67, 820, 231, 2603])).
% 1.03/1.24 tff(2618,plain,
% 1.03/1.24 (b(z, s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[648, 2617])).
% 1.03/1.24 tff(2619,plain,
% 1.03/1.24 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1705, 2618, 67, 106])).
% 1.03/1.24 tff(2620,plain,
% 1.03/1.24 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1259, 2619])).
% 1.03/1.24 tff(2621,plain,
% 1.03/1.24 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2553, 1299, 144, 143, 1283])).
% 1.03/1.24 tff(2622,plain,
% 1.03/1.24 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[564, 2621])).
% 1.03/1.24 tff(2623,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[853, 2622, 820])).
% 1.03/1.24 tff(2624,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[317, 2623, 313])).
% 1.03/1.24 tff(2625,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2626,plain,
% 1.03/1.24 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2627,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2626])).
% 1.03/1.24 tff(2628,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[2627, 2625])).
% 1.03/1.24 tff(2629,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(2630,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 1.03/1.24 tff(2631,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2630, 154, 2604, 1299, 1283, 231, 2624])).
% 1.03/1.24 tff(2632,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.24 tff(2633,plain,
% 1.03/1.24 (~b(s(s(s(s(z)))), z)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2632, 2603, 2620, 231, 820, 144, 1701])).
% 1.03/1.24 tff(2634,plain,
% 1.03/1.24 (r(s(s(s(s(z)))), z)),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[206, 2633])).
% 1.03/1.24 tff(2635,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2636,plain,
% 1.03/1.24 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2637,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2636])).
% 1.03/1.24 tff(2638,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[2637, 2635])).
% 1.03/1.24 tff(2639,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(2640,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2639, 2638])).
% 1.03/1.24 tff(2641,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2640, 28, 106, 2634])).
% 1.03/1.24 tff(2642,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[229, 2641])).
% 1.03/1.24 tff(2643,plain,
% 1.03/1.24 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2103, 154, 2620, 2540, 231, 2642])).
% 1.03/1.24 tff(2644,plain,
% 1.03/1.24 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[317, 2643, 313])).
% 1.03/1.24 tff(2645,plain,
% 1.03/1.24 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[853, 2644, 820])).
% 1.03/1.24 tff(2646,plain,
% 1.03/1.24 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[564, 2645])).
% 1.03/1.24 tff(2647,plain,
% 1.03/1.24 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[1409, 28, 820, 2644])).
% 1.03/1.24 tff(2648,plain,
% 1.03/1.24 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[343, 2647])).
% 1.03/1.24 tff(2649,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2650,plain,
% 1.03/1.24 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.24 inference(rewrite,[status(thm)],[])).
% 1.03/1.24 tff(2651,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.24 inference(monotonicity,[status(thm)],[2650])).
% 1.03/1.24 tff(2652,plain,
% 1.03/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.24 inference(transitivity,[status(thm)],[2651, 2649])).
% 1.03/1.24 tff(2653,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.24 inference(quant_inst,[status(thm)],[])).
% 1.03/1.24 tff(2654,plain,
% 1.03/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.24 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 1.03/1.24 tff(2655,plain,
% 1.03/1.24 ($false),
% 1.03/1.24 inference(unit_resolution,[status(thm)],[2654, 154, 144, 2648, 2620, 2642, 2646])).
% 1.03/1.24 tff(2656,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(2657,plain,
% 1.03/1.25 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2656, 144, 820, 106, 231])).
% 1.03/1.25 tff(2658,plain,
% 1.03/1.25 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[104, 2657])).
% 1.03/1.25 tff(2659,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[903, 154, 144, 232, 684, 231, 2658])).
% 1.03/1.25 tff(2660,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(2661,plain,
% 1.03/1.25 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2660, 2268, 2534, 232, 820, 106])).
% 1.03/1.25 tff(2662,plain,
% 1.03/1.25 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[138, 2661])).
% 1.03/1.25 tff(2663,plain,
% 1.03/1.25 (~r(z, s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2080, 2662, 106])).
% 1.03/1.25 tff(2664,plain,
% 1.03/1.25 (b(z, s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[648, 2663])).
% 1.03/1.25 tff(2665,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2484, 106, 13, 2534])).
% 1.03/1.25 tff(2666,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[206, 2665])).
% 1.03/1.25 tff(2667,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[740, 154, 1299, 143, 660, 2494, 2492])).
% 1.03/1.25 tff(2668,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(2669,plain,
% 1.03/1.25 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2668, 2666, 143, 2664, 820, 13])).
% 1.03/1.25 tff(2670,plain,
% 1.03/1.25 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1653, 2669])).
% 1.03/1.25 tff(2671,plain,
% 1.03/1.25 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1437, 2670, 2534, 232, 2268, 143, 13])).
% 1.03/1.25 tff(2672,plain,
% 1.03/1.25 (r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1259, 2671])).
% 1.03/1.25 tff(2673,plain,
% 1.03/1.25 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1399, 154, 232, 2666, 143])).
% 1.03/1.25 tff(2674,plain,
% 1.03/1.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2673, 2670])).
% 1.03/1.25 tff(2675,plain,
% 1.03/1.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[343, 2674])).
% 1.03/1.25 tff(2676,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[612, 2675, 2672, 2662])).
% 1.03/1.25 tff(2677,plain,((~r(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(2678,plain,
% 1.03/1.25 (~r(s(s(z)), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2677, 2532, 2318, 13, 820])).
% 1.03/1.25 tff(2679,plain,
% 1.03/1.25 (b(s(s(z)), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[122, 2678])).
% 1.03/1.25 tff(2680,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2681,plain,
% 1.03/1.25 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2682,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[2681])).
% 1.03/1.25 tff(2683,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.03/1.25 tff(2684,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(2685,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.03/1.25 tff(2686,plain,
% 1.03/1.25 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2685, 154, 2532, 2318, 2328, 2679])).
% 1.03/1.25 tff(2687,plain,
% 1.03/1.25 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[104, 2686])).
% 1.03/1.25 tff(2688,plain,
% 1.03/1.25 (~b(z, s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2336, 2679, 2318, 820, 2147, 2328])).
% 1.03/1.25 tff(2689,plain,
% 1.03/1.25 (r(z, s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[64, 2688])).
% 1.03/1.25 tff(2690,plain,
% 1.03/1.25 (~r(z, s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2044, 28, 2689, 2687])).
% 1.03/1.25 tff(2691,plain,
% 1.03/1.25 (b(z, s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[648, 2690])).
% 1.03/1.25 tff(2692,plain,
% 1.03/1.25 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1512, 2679, 2318, 2328, 2532])).
% 1.03/1.25 tff(2693,plain,
% 1.03/1.25 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[138, 2692])).
% 1.03/1.25 tff(2694,plain,
% 1.03/1.25 (~r(s(s(z)), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1125, 2693, 820])).
% 1.03/1.25 tff(2695,plain,
% 1.03/1.25 (b(s(s(z)), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[296, 2694])).
% 1.03/1.25 tff(2696,plain,
% 1.03/1.25 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1723, 2691, 2693, 2689, 2687])).
% 1.03/1.25 tff(2697,plain,
% 1.03/1.25 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1259, 2696])).
% 1.03/1.25 tff(2698,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1391, 2697, 13, 2328, 2695])).
% 1.03/1.25 tff(2699,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[206, 2698])).
% 1.03/1.25 tff(2700,plain,
% 1.03/1.25 (~b(s(z), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1437, 2697, 2328, 2532, 2695, 2318, 13])).
% 1.03/1.25 tff(2701,plain,
% 1.03/1.25 (r(s(z), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1653, 2700])).
% 1.03/1.25 tff(2702,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2668, 2701, 2699, 2318, 2691, 820, 13])).
% 1.03/1.25 tff(2703,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(2704,plain,
% 1.03/1.25 (~r(s(s(s(z))), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2703, 13, 12])).
% 1.03/1.25 tff(2705,plain,
% 1.03/1.25 (b(s(s(s(z))), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[818, 2704])).
% 1.03/1.25 tff(2706,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[318, 1380])).
% 1.03/1.25 tff(2707,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2708,plain,
% 1.03/1.25 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2709,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[2708])).
% 1.03/1.25 tff(2710,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[2709, 2707])).
% 1.03/1.25 tff(2711,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(2712,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 1.03/1.25 tff(2713,plain,
% 1.03/1.25 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2712, 154, 1726, 1, 143, 142])).
% 1.03/1.25 tff(2714,plain,
% 1.03/1.25 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[138, 2713])).
% 1.03/1.25 tff(2715,plain,
% 1.03/1.25 (~r(s(z), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[657, 299, 2714])).
% 1.03/1.25 tff(2716,plain,
% 1.03/1.25 (b(s(z), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[252, 2715])).
% 1.03/1.25 tff(2717,plain,
% 1.03/1.25 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1749, 2716, 2714, 1, 299])).
% 1.03/1.25 tff(2718,plain,
% 1.03/1.25 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1259, 2717])).
% 1.03/1.25 tff(2719,plain,
% 1.03/1.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[327, 154, 1, 2716, 15, 506])).
% 1.03/1.25 tff(2720,plain,
% 1.03/1.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[343, 2719])).
% 1.03/1.25 tff(2721,plain,
% 1.03/1.25 (~r(z, s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1471, 2720, 140, 2718, 142])).
% 1.03/1.25 tff(2722,plain,
% 1.03/1.25 (b(z, s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[648, 2721])).
% 1.03/1.25 tff(2723,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2724,plain,
% 1.03/1.25 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2725,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[2724])).
% 1.03/1.25 tff(2726,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[2725, 2723])).
% 1.03/1.25 tff(2727,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(2728,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 1.03/1.25 tff(2729,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2728, 154, 1726, 1, 2716, 143, 2722])).
% 1.03/1.25 tff(2730,plain,((~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(2731,plain,
% 1.03/1.25 (~r(s(s(z)), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2730, 2171, 1, 2500, 65, 2205, 1726, 2706])).
% 1.03/1.25 tff(2732,plain,
% 1.03/1.25 (b(s(s(z)), s(z))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[296, 2731])).
% 1.03/1.25 tff(2733,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2734,plain,
% 1.03/1.25 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2735,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[2734])).
% 1.03/1.25 tff(2736,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[2735, 2733])).
% 1.03/1.25 tff(2737,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(2738,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[2737, 2736])).
% 1.03/1.25 tff(2739,plain,
% 1.03/1.25 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2738, 154, 1726, 2500, 2732, 2205])).
% 1.03/1.25 tff(2740,plain,
% 1.03/1.25 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[104, 2739])).
% 1.03/1.25 tff(2741,plain,
% 1.03/1.25 (~r(s(z), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[597, 2740, 17])).
% 1.03/1.25 tff(2742,plain,
% 1.03/1.25 (b(s(z), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[252, 2741])).
% 1.03/1.25 tff(2743,plain,
% 1.03/1.25 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[583, 154, 1, 2171, 2706])).
% 1.03/1.25 tff(2744,plain,
% 1.03/1.25 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2743, 2742])).
% 1.03/1.25 tff(2745,plain,
% 1.03/1.25 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[564, 2744])).
% 1.03/1.25 tff(2746,plain,
% 1.03/1.25 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[75, 2745, 2740])).
% 1.03/1.25 tff(2747,plain,
% 1.03/1.25 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1259, 2746])).
% 1.03/1.25 tff(2748,plain,
% 1.03/1.25 ($false),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2514, 154, 1726, 2747, 2171, 2732, 65])).
% 1.03/1.25 tff(2749,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.25 tff(2750,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2749, 17, 1, 1726, 13])).
% 1.03/1.25 tff(2751,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), z)),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[206, 2750])).
% 1.03/1.25 tff(2752,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2753,plain,
% 1.03/1.25 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2754,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[2753])).
% 1.03/1.25 tff(2755,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[2754, 2752])).
% 1.03/1.25 tff(2756,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(2757,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.03/1.25 inference(modus_ponens,[status(thm)],[2756, 2755])).
% 1.03/1.25 tff(2758,plain,
% 1.03/1.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2757, 154, 1726, 1, 2751, 2500])).
% 1.03/1.25 tff(2759,plain,
% 1.03/1.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[343, 2758])).
% 1.03/1.25 tff(2760,plain,
% 1.03/1.25 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[2712, 154, 1726, 1, 2500, 2205])).
% 1.03/1.25 tff(2761,plain,
% 1.03/1.25 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[138, 2760])).
% 1.03/1.25 tff(2762,plain,
% 1.03/1.25 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1427, 28, 2761, 2759])).
% 1.03/1.25 tff(2763,plain,
% 1.03/1.25 (b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[229, 2762])).
% 1.03/1.25 tff(2764,plain,
% 1.03/1.25 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[612, 2759, 2761])).
% 1.03/1.25 tff(2765,plain,
% 1.03/1.25 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.25 inference(unit_resolution,[status(thm)],[1259, 2764])).
% 1.03/1.25 tff(2766,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2767,plain,
% 1.03/1.25 (((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.25 inference(rewrite,[status(thm)],[])).
% 1.03/1.25 tff(2768,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.25 inference(monotonicity,[status(thm)],[2767])).
% 1.03/1.25 tff(2769,plain,
% 1.03/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.25 inference(transitivity,[status(thm)],[2768, 2766])).
% 1.03/1.25 tff(2770,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.25 inference(quant_inst,[status(thm)],[])).
% 1.03/1.25 tff(2771,plain,
% 1.03/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.03/1.26 tff(2772,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2771, 154, 2751, 2765, 2205, 65, 2763])).
% 1.03/1.26 tff(2773,plain,((~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2774,plain,
% 1.03/1.26 (~r(s(z), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2773, 1726, 1, 13])).
% 1.03/1.26 tff(2775,plain,
% 1.03/1.26 (b(s(z), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[680, 2774])).
% 1.03/1.26 tff(2776,plain,
% 1.03/1.26 (~r(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2484, 106, 13, 2775])).
% 1.03/1.26 tff(2777,plain,
% 1.03/1.26 (b(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[206, 2776])).
% 1.03/1.26 tff(2778,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2757, 154, 1726, 1, 2777, 2500])).
% 1.03/1.26 tff(2779,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[343, 2778])).
% 1.03/1.26 tff(2780,plain,
% 1.03/1.26 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[612, 2779, 16])).
% 1.03/1.26 tff(2781,plain,
% 1.03/1.26 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[138, 2780])).
% 1.03/1.26 tff(2782,plain,
% 1.03/1.26 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[692, 2781, 1, 2775, 2268])).
% 1.03/1.26 tff(2783,plain,
% 1.03/1.26 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[104, 2782])).
% 1.03/1.26 tff(2784,plain,
% 1.03/1.26 (~b(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1705, 2783, 16, 106])).
% 1.03/1.26 tff(2785,plain,
% 1.03/1.26 (r(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[648, 2784])).
% 1.03/1.26 tff(2786,plain,
% 1.03/1.26 (~r(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1976, 2785, 13])).
% 1.03/1.26 tff(2787,plain,
% 1.03/1.26 (b(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[252, 2786])).
% 1.03/1.26 tff(2788,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1419, 154, 2781, 1, 2787, 2775, 2268])).
% 1.03/1.26 tff(2789,plain,((~r(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2790,plain,
% 1.03/1.26 (~r(s(s(z)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2789, 16, 13, 1, 1726])).
% 1.03/1.26 tff(2791,plain,
% 1.03/1.26 (b(s(s(z)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[122, 2790])).
% 1.03/1.26 tff(2792,plain,
% 1.03/1.26 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2712, 154, 1726, 1, 2500, 2791])).
% 1.03/1.26 tff(2793,plain,
% 1.03/1.26 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[138, 2792])).
% 1.03/1.26 tff(2794,plain,
% 1.03/1.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[612, 2793, 16])).
% 1.03/1.26 tff(2795,plain,
% 1.03/1.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[343, 2794])).
% 1.03/1.26 tff(2796,plain,
% 1.03/1.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[132, 2793, 16])).
% 1.03/1.26 tff(2797,plain,
% 1.03/1.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[564, 2796])).
% 1.03/1.26 tff(2798,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[752, 2171, 1, 566, 615])).
% 1.03/1.26 tff(2799,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[318, 2798])).
% 1.03/1.26 tff(2800,plain,
% 1.03/1.26 (~b(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[623, 2171, 1, 566, 615])).
% 1.03/1.26 tff(2801,plain,
% 1.03/1.26 (r(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[252, 2800])).
% 1.03/1.26 tff(2802,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1802, 28, 2801, 13, 2799, 193])).
% 1.03/1.26 tff(2803,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), 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(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2804,plain,
% 1.03/1.26 (~r(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2803, 2797, 1, 13, 2795])).
% 1.03/1.26 tff(2805,plain,
% 1.03/1.26 (b(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[206, 2804])).
% 1.03/1.26 tff(2806,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2807,plain,
% 1.03/1.26 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2808,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[2807])).
% 1.03/1.26 tff(2809,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[2808, 2806])).
% 1.03/1.26 tff(2810,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(2811,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.03/1.26 tff(2812,plain,
% 1.03/1.26 ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2811, 154, 1726, 1, 2795])).
% 1.03/1.26 tff(2813,plain,
% 1.03/1.26 (~b(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2812, 2805])).
% 1.03/1.26 tff(2814,plain,
% 1.03/1.26 (r(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[648, 2813])).
% 1.03/1.26 tff(2815,plain,
% 1.03/1.26 (~r(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1976, 2814, 13])).
% 1.03/1.26 tff(2816,plain,
% 1.03/1.26 (b(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[252, 2815])).
% 1.03/1.26 tff(2817,plain,
% 1.03/1.26 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2685, 154, 2500, 2775, 2791])).
% 1.03/1.26 tff(2818,plain,
% 1.03/1.26 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2817, 2816])).
% 1.03/1.26 tff(2819,plain,
% 1.03/1.26 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[104, 2818])).
% 1.03/1.26 tff(2820,plain,
% 1.03/1.26 (~r(s(s(z)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1749, 2816, 16, 1, 2793])).
% 1.03/1.26 tff(2821,plain,
% 1.03/1.26 (b(s(s(z)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[296, 2820])).
% 1.03/1.26 tff(2822,plain,
% 1.03/1.26 (~b(z, s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1736, 2821, 1726, 2775, 2791])).
% 1.03/1.26 tff(2823,plain,
% 1.03/1.26 (r(z, s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[64, 2822])).
% 1.03/1.26 tff(2824,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2044, 28, 2814, 2823, 2819])).
% 1.03/1.26 tff(2825,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2826,plain,
% 1.03/1.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2825, 1726, 1, 13])).
% 1.03/1.26 tff(2827,plain,
% 1.03/1.26 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1259, 2826])).
% 1.03/1.26 tff(2828,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1605, 2706, 2775, 2171, 2827])).
% 1.03/1.26 tff(2829,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[229, 2828])).
% 1.03/1.26 tff(2830,plain,
% 1.03/1.26 (~r(s(s(z)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2484, 193, 13, 2775])).
% 1.03/1.26 tff(2831,plain,
% 1.03/1.26 (b(s(s(z)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[122, 2830])).
% 1.03/1.26 tff(2832,plain,
% 1.03/1.26 (~b(s(s(z)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1391, 193, 13, 2775, 2827])).
% 1.03/1.26 tff(2833,plain,
% 1.03/1.26 (r(s(s(z)), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[296, 2832])).
% 1.03/1.26 tff(2834,plain,
% 1.03/1.26 (~b(z, s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2730, 2706, 1, 2500, 2833, 2831, 1726, 2171])).
% 1.03/1.26 tff(2835,plain,
% 1.03/1.26 (r(z, s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[64, 2834])).
% 1.03/1.26 tff(2836,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2837,plain,
% 1.03/1.26 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2838,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[2837])).
% 1.03/1.26 tff(2839,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[2838, 2836])).
% 1.03/1.26 tff(2840,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(2841,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[2840, 2839])).
% 1.03/1.26 tff(2842,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2841, 28, 2835, 2829, 193])).
% 1.03/1.26 tff(2843,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2844,plain,
% 1.03/1.26 (~r(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2843, 1, 1726, 13])).
% 1.03/1.26 tff(2845,plain,
% 1.03/1.26 (b(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[206, 2844])).
% 1.03/1.26 tff(2846,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2757, 154, 1726, 1, 2845, 2500])).
% 1.03/1.26 tff(2847,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[343, 2846])).
% 1.03/1.26 tff(2848,plain,
% 1.03/1.26 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1419, 154, 1, 232, 684, 231])).
% 1.03/1.26 tff(2849,plain,
% 1.03/1.26 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[138, 2848])).
% 1.03/1.26 tff(2850,plain,
% 1.03/1.26 (~r(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2080, 2849, 106])).
% 1.03/1.26 tff(2851,plain,
% 1.03/1.26 (b(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[648, 2850])).
% 1.03/1.26 tff(2852,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2728, 154, 1726, 1, 232, 143, 2851])).
% 1.03/1.26 tff(2853,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2854,plain,
% 1.03/1.26 (~b(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2853, 106, 1, 2500, 1726, 2775, 2268])).
% 1.03/1.26 tff(2855,plain,
% 1.03/1.26 (r(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[252, 2854])).
% 1.03/1.26 tff(2856,plain,
% 1.03/1.26 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1957, 2855, 2847])).
% 1.03/1.26 tff(2857,plain,
% 1.03/1.26 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1653, 2856])).
% 1.03/1.26 tff(2858,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1389, 2857, 2775, 2268, 2827])).
% 1.03/1.26 tff(2859,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[318, 2858])).
% 1.03/1.26 tff(2860,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1586, 28, 2855, 2847, 2859])).
% 1.03/1.26 tff(2861,plain,((~r(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2862,plain,
% 1.03/1.26 (~r(s(s(z)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2861, 2705, 2147, 13])).
% 1.03/1.26 tff(2863,plain,
% 1.03/1.26 (b(s(s(z)), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[122, 2862])).
% 1.03/1.26 tff(2864,plain,
% 1.03/1.26 (~r(s(z), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2773, 2147, 2705, 13])).
% 1.03/1.26 tff(2865,plain,
% 1.03/1.26 (b(s(z), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[680, 2864])).
% 1.03/1.26 tff(2866,plain,
% 1.03/1.26 (~r(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2843, 2705, 2147, 13])).
% 1.03/1.26 tff(2867,plain,
% 1.03/1.26 (b(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[206, 2866])).
% 1.03/1.26 tff(2868,plain,
% 1.03/1.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2825, 2147, 2705, 13])).
% 1.03/1.26 tff(2869,plain,
% 1.03/1.26 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1259, 2868])).
% 1.03/1.26 tff(2870,plain,
% 1.03/1.26 (~b(z, s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2054, 2863, 2318, 2869, 2867])).
% 1.03/1.26 tff(2871,plain,
% 1.03/1.26 (r(z, s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[191, 2870])).
% 1.03/1.26 tff(2872,plain,
% 1.03/1.26 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2157, 2871, 13])).
% 1.03/1.26 tff(2873,plain,
% 1.03/1.26 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1653, 2872])).
% 1.03/1.26 tff(2874,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2219, 154, 2867, 2869, 2873, 2865, 2863])).
% 1.03/1.26 tff(2875,plain,((~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2876,plain,
% 1.03/1.26 (~r(s(z), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2875, 12])).
% 1.03/1.26 tff(2877,plain,
% 1.03/1.26 (b(s(z), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[271, 2876])).
% 1.03/1.26 tff(2878,plain,
% 1.03/1.26 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2000, 1655, 17])).
% 1.03/1.26 tff(2879,plain,
% 1.03/1.26 (b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[229, 2878])).
% 1.03/1.26 tff(2880,plain,
% 1.03/1.26 (~r(s(s(s(z))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1556, 67, 17])).
% 1.03/1.26 tff(2881,plain,
% 1.03/1.26 (b(s(s(s(z))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[818, 2880])).
% 1.03/1.26 tff(2882,plain,
% 1.03/1.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1681, 1655, 17])).
% 1.03/1.26 tff(2883,plain,
% 1.03/1.26 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1259, 2882])).
% 1.03/1.26 tff(2884,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2885,plain,
% 1.03/1.26 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2886,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[2885])).
% 1.03/1.26 tff(2887,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[2886, 2884])).
% 1.03/1.26 tff(2888,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(2889,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[2888, 2887])).
% 1.03/1.26 tff(2890,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2889, 154, 2883, 142, 140, 2879, 1934])).
% 1.03/1.26 tff(2891,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2892,plain,
% 1.03/1.26 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2891, 857, 142, 17, 14])).
% 1.03/1.26 tff(2893,plain,
% 1.03/1.26 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[1653, 2892])).
% 1.03/1.26 tff(2894,plain,
% 1.03/1.26 (~r(s(s(s(z))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[828, 171, 14])).
% 1.03/1.26 tff(2895,plain,
% 1.03/1.26 (b(s(s(s(z))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[818, 2894])).
% 1.03/1.26 tff(2896,plain,
% 1.03/1.26 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[307, 16, 299])).
% 1.03/1.26 tff(2897,plain,
% 1.03/1.26 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[318, 2896])).
% 1.03/1.26 tff(2898,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2899,plain,
% 1.03/1.26 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2900,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[2899])).
% 1.03/1.26 tff(2901,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[2900, 2898])).
% 1.03/1.26 tff(2902,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(2903,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 1.03/1.26 tff(2904,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2903, 154, 2604, 1299, 15, 506, 254])).
% 1.03/1.26 tff(2905,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2906,plain,
% 1.03/1.26 (~b(z, s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2905, 1299, 2604, 15, 506])).
% 1.03/1.26 tff(2907,plain,
% 1.03/1.26 (r(z, s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[191, 2906])).
% 1.03/1.26 tff(2908,plain,
% 1.03/1.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[180, 2907, 171])).
% 1.03/1.26 tff(2909,plain,
% 1.03/1.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[564, 2908])).
% 1.03/1.26 tff(2910,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2911,plain,
% 1.03/1.26 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2912,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.03/1.26 inference(monotonicity,[status(thm)],[2911])).
% 1.03/1.26 tff(2913,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.26 inference(transitivity,[status(thm)],[2912, 2910])).
% 1.03/1.26 tff(2914,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.03/1.26 inference(quant_inst,[status(thm)],[])).
% 1.03/1.26 tff(2915,plain,
% 1.03/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.03/1.26 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 1.03/1.26 tff(2916,plain,
% 1.03/1.26 ($false),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2915, 154, 2604, 1, 1299, 506, 2909])).
% 1.03/1.26 tff(2917,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.26 tff(2918,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2917, 2897, 2895, 2604, 171, 2893])).
% 1.03/1.26 tff(2919,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), z)),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[206, 2918])).
% 1.03/1.26 tff(2920,plain,
% 1.03/1.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[201, 2919, 171])).
% 1.03/1.26 tff(2921,plain,
% 1.03/1.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[564, 2920])).
% 1.03/1.26 tff(2922,plain,
% 1.03/1.26 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[583, 154, 2895, 2893, 2897])).
% 1.03/1.26 tff(2923,plain,
% 1.03/1.26 (~b(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[2922, 2921])).
% 1.03/1.26 tff(2924,plain,
% 1.03/1.26 (r(s(z), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[252, 2923])).
% 1.03/1.26 tff(2925,plain,
% 1.03/1.26 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[597, 2924, 17])).
% 1.03/1.26 tff(2926,plain,
% 1.03/1.26 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[104, 2925])).
% 1.03/1.26 tff(2927,plain,
% 1.03/1.26 (~r(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[636, 2924, 14])).
% 1.03/1.26 tff(2928,plain,
% 1.03/1.26 (b(z, s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[648, 2927])).
% 1.03/1.26 tff(2929,plain,
% 1.03/1.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[752, 2921, 2895, 2893, 2897])).
% 1.03/1.26 tff(2930,plain,
% 1.03/1.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[343, 2929])).
% 1.03/1.26 tff(2931,plain,
% 1.03/1.26 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[612, 2930, 16])).
% 1.03/1.26 tff(2932,plain,
% 1.03/1.26 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.26 inference(unit_resolution,[status(thm)],[138, 2931])).
% 1.03/1.26 tff(2933,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2934,plain,
% 1.03/1.26 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.03/1.26 inference(rewrite,[status(thm)],[])).
% 1.03/1.26 tff(2935,plain,
% 1.03/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[2934])).
% 1.03/1.27 tff(2936,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[2935, 2933])).
% 1.03/1.27 tff(2937,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(2938,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.03/1.27 tff(2939,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2938, 154, 2932, 2928, 142, 2926, 857])).
% 1.03/1.27 tff(2940,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(2941,plain,
% 1.03/1.27 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2940, 299, 14, 17, 171, 2604, 142])).
% 1.03/1.27 tff(2942,plain,
% 1.03/1.27 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1259, 2941])).
% 1.03/1.27 tff(2943,plain,
% 1.03/1.27 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1323, 2942, 14, 142, 857])).
% 1.03/1.27 tff(2944,plain,
% 1.03/1.27 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[318, 2943])).
% 1.03/1.27 tff(2945,plain,
% 1.03/1.27 (~b(s(s(s(s(z)))), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2917, 2944, 2895, 2604, 171, 2893])).
% 1.03/1.27 tff(2946,plain,
% 1.03/1.27 (r(s(s(s(s(z)))), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[206, 2945])).
% 1.03/1.27 tff(2947,plain,
% 1.03/1.27 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1309, 2942, 171, 142, 857])).
% 1.03/1.27 tff(2948,plain,
% 1.03/1.27 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[564, 2947])).
% 1.03/1.27 tff(2949,plain,
% 1.03/1.27 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[752, 2948, 2895, 2893, 2944])).
% 1.03/1.27 tff(2950,plain,
% 1.03/1.27 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[343, 2949])).
% 1.03/1.27 tff(2951,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2179, 28, 2950, 171, 2946])).
% 1.03/1.27 tff(2952,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(2953,plain,
% 1.03/1.27 (~r(s(s(z)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2952, 142, 2604, 14, 171, 17])).
% 1.03/1.27 tff(2954,plain,
% 1.03/1.27 (b(s(s(z)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[296, 2953])).
% 1.03/1.27 tff(2955,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(2956,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(2957,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[2956, 2955])).
% 1.03/1.27 tff(2958,plain,
% 1.03/1.27 ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2957, 154, 2604, 2895, 142])).
% 1.03/1.27 tff(2959,plain,
% 1.03/1.27 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2958, 2954])).
% 1.03/1.27 tff(2960,plain,
% 1.03/1.27 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[104, 2959])).
% 1.03/1.27 tff(2961,plain,
% 1.03/1.27 (~r(z, s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1346, 2960, 171])).
% 1.03/1.27 tff(2962,plain,
% 1.03/1.27 (b(z, s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[64, 2961])).
% 1.03/1.27 tff(2963,plain,
% 1.03/1.27 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2891, 2962, 142, 17, 14])).
% 1.03/1.27 tff(2964,plain,
% 1.03/1.27 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1653, 2963])).
% 1.03/1.27 tff(2965,plain,
% 1.03/1.27 (~r(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[597, 2960, 17])).
% 1.03/1.27 tff(2966,plain,
% 1.03/1.27 (b(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[252, 2965])).
% 1.03/1.27 tff(2967,plain,
% 1.03/1.27 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1309, 1283, 171, 142, 140])).
% 1.03/1.27 tff(2968,plain,
% 1.03/1.27 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[564, 2967])).
% 1.03/1.27 tff(2969,plain,
% 1.03/1.27 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1323, 1283, 14, 142, 140])).
% 1.03/1.27 tff(2970,plain,
% 1.03/1.27 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[318, 2969])).
% 1.03/1.27 tff(2971,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[583, 154, 2895, 232, 15, 2970, 2968])).
% 1.03/1.27 tff(2972,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(2973,plain,
% 1.03/1.27 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2972, 2966, 2964, 14, 142, 2962, 171])).
% 1.03/1.27 tff(2974,plain,
% 1.03/1.27 (r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1259, 2973])).
% 1.03/1.27 tff(2975,plain,
% 1.03/1.27 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[75, 2974, 2960])).
% 1.03/1.27 tff(2976,plain,
% 1.03/1.27 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[564, 2975])).
% 1.03/1.27 tff(2977,plain,
% 1.03/1.27 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[623, 2976, 2895, 2964, 2966])).
% 1.03/1.27 tff(2978,plain,
% 1.03/1.27 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[343, 2977])).
% 1.03/1.27 tff(2979,plain,
% 1.03/1.27 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[764, 2976, 2895, 2954, 2964])).
% 1.03/1.27 tff(2980,plain,
% 1.03/1.27 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[138, 2979])).
% 1.03/1.27 tff(2981,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[612, 2980, 2978, 2974])).
% 1.03/1.27 tff(2982,plain,((~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(2983,plain,
% 1.03/1.27 (~b(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2982, 171, 14, 17, 2604])).
% 1.03/1.27 tff(2984,plain,
% 1.03/1.27 (r(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[122, 2983])).
% 1.03/1.27 tff(2985,plain,
% 1.03/1.27 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1280, 2984, 171])).
% 1.03/1.27 tff(2986,plain,
% 1.03/1.27 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[104, 2985])).
% 1.03/1.27 tff(2987,plain,
% 1.03/1.27 (~r(s(s(z)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[382, 2984, 14])).
% 1.03/1.27 tff(2988,plain,
% 1.03/1.27 (b(s(s(z)), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[296, 2987])).
% 1.03/1.27 tff(2989,plain,
% 1.03/1.27 (~r(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1648, 2986, 17, 14, 2895, 2988])).
% 1.03/1.27 tff(2990,plain,
% 1.03/1.27 (b(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[252, 2989])).
% 1.03/1.27 tff(2991,plain,
% 1.03/1.27 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[240, 2990, 2895, 2988, 2986])).
% 1.03/1.27 tff(2992,plain,
% 1.03/1.27 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[138, 2991])).
% 1.03/1.27 tff(2993,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2276, 28, 2992, 2984, 171])).
% 1.03/1.27 tff(2994,plain,((~r(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(2995,plain,
% 1.03/1.27 (~r(s(s(s(z))), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2994, 14, 17, 2604])).
% 1.03/1.27 tff(2996,plain,
% 1.03/1.27 (b(s(s(s(z))), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[169, 2995])).
% 1.03/1.27 tff(2997,plain,
% 1.03/1.27 (~b(z, s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1560, 142, 820, 883, 2996, 17])).
% 1.03/1.27 tff(2998,plain,
% 1.03/1.27 (r(z, s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[64, 2997])).
% 1.03/1.27 tff(2999,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1646, 28, 14, 273, 18, 17])).
% 1.03/1.27 tff(3000,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3001,plain,
% 1.03/1.27 (~r(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3000, 2998, 14, 17])).
% 1.03/1.27 tff(3002,plain,
% 1.03/1.27 (b(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[252, 3001])).
% 1.03/1.27 tff(3003,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3004,plain,
% 1.03/1.27 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3005,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3004])).
% 1.03/1.27 tff(3006,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3005, 3003])).
% 1.03/1.27 tff(3007,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3008,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 1.03/1.27 tff(3009,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3008, 154, 2604, 3002, 885, 883, 142])).
% 1.03/1.27 tff(3010,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3011,plain,
% 1.03/1.27 (~b(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3010, 820, 14, 17, 2604])).
% 1.03/1.27 tff(3012,plain,
% 1.03/1.27 (r(s(s(z)), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[122, 3011])).
% 1.03/1.27 tff(3013,plain,
% 1.03/1.27 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[853, 298, 820])).
% 1.03/1.27 tff(3014,plain,
% 1.03/1.27 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[742, 298, 14, 143, 885])).
% 1.03/1.27 tff(3015,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[564, 3014, 3013])).
% 1.03/1.27 tff(3016,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3017,plain,
% 1.03/1.27 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3016, 820, 2996, 14])).
% 1.03/1.27 tff(3018,plain,
% 1.03/1.27 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[318, 3017])).
% 1.03/1.27 tff(3019,plain,
% 1.03/1.27 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[104, 1557])).
% 1.03/1.27 tff(3020,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3021,plain,
% 1.03/1.27 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3022,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3021])).
% 1.03/1.27 tff(3023,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3022, 3020])).
% 1.03/1.27 tff(3024,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3025,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3024, 3023])).
% 1.03/1.27 tff(3026,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3025, 154, 143, 1283, 141, 140, 254])).
% 1.03/1.27 tff(3027,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3028,plain,
% 1.03/1.27 (~b(z, s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3027, 2883, 143, 141, 1934])).
% 1.03/1.27 tff(3029,plain,
% 1.03/1.27 (r(z, s(s(z)))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[64, 3028])).
% 1.03/1.27 tff(3030,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3031,plain,
% 1.03/1.27 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3032,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3031])).
% 1.03/1.27 tff(3033,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3032, 3030])).
% 1.03/1.27 tff(3034,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3035,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3034, 3033])).
% 1.03/1.27 tff(3036,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3035, 28, 14, 3029, 17, 1655])).
% 1.03/1.27 tff(3037,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3038,plain,
% 1.03/1.27 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3037, 3019, 17, 2996, 14])).
% 1.03/1.27 tff(3039,plain,
% 1.03/1.27 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1653, 3038])).
% 1.03/1.27 tff(3040,plain,
% 1.03/1.27 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[853, 820, 298])).
% 1.03/1.27 tff(3041,plain,
% 1.03/1.27 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[564, 3040])).
% 1.03/1.27 tff(3042,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2052, 3041, 885])).
% 1.03/1.27 tff(3043,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3044,plain,
% 1.03/1.27 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3043, 1703, 14, 143, 820, 1697])).
% 1.03/1.27 tff(3045,plain,
% 1.03/1.27 (~b(s(s(s(s(z)))), s(z))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2905, 1697, 2604, 15, 1703])).
% 1.03/1.27 tff(3046,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[318, 3045, 3044])).
% 1.03/1.27 tff(3047,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3048,plain,
% 1.03/1.27 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3047, 3012, 3039, 14, 2996, 820, 2604])).
% 1.03/1.27 tff(3049,plain,
% 1.03/1.27 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1259, 3048])).
% 1.03/1.27 tff(3050,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3051,plain,
% 1.03/1.27 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.27 inference(rewrite,[status(thm)],[])).
% 1.03/1.27 tff(3052,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.03/1.27 inference(monotonicity,[status(thm)],[3051])).
% 1.03/1.27 tff(3053,plain,
% 1.03/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.27 inference(transitivity,[status(thm)],[3052, 3050])).
% 1.03/1.27 tff(3054,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.27 inference(quant_inst,[status(thm)],[])).
% 1.03/1.27 tff(3055,plain,
% 1.03/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.03/1.27 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 1.03/1.27 tff(3056,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3055, 154, 2604, 232, 1299, 660, 506])).
% 1.03/1.27 tff(3057,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3058,plain,
% 1.03/1.27 (~b(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3057, 1299, 2604, 506, 660])).
% 1.03/1.27 tff(3059,plain,
% 1.03/1.27 (r(s(z), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[252, 3058])).
% 1.03/1.27 tff(3060,plain,
% 1.03/1.27 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[2632, 1299, 2604, 820, 1283, 231, 143])).
% 1.03/1.27 tff(3061,plain,
% 1.03/1.27 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[138, 3060])).
% 1.03/1.27 tff(3062,plain,
% 1.03/1.27 ($false),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[1094, 28, 3061, 3059, 17])).
% 1.03/1.27 tff(3063,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.27 tff(3064,plain,
% 1.03/1.27 (~b(s(s(s(s(z)))), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[3063, 3049, 2604, 3018, 885, 820, 17, 883, 2996])).
% 1.03/1.27 tff(3065,plain,
% 1.03/1.27 (r(s(s(s(s(z)))), z)),
% 1.03/1.27 inference(unit_resolution,[status(thm)],[206, 3064])).
% 1.03/1.28 tff(3066,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2640, 28, 106, 1243, 193])).
% 1.03/1.28 tff(3067,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3068,plain,
% 1.03/1.28 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3067, 3065, 3012])).
% 1.03/1.28 tff(3069,plain,
% 1.03/1.28 (b(s(s(s(s(z)))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[229, 3068])).
% 1.03/1.28 tff(3070,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1546, 154, 3049, 3039, 883, 3018, 3069])).
% 1.03/1.28 tff(3071,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3072,plain,
% 1.03/1.28 (~r(s(s(s(z))), s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3071, 14, 17, 2604])).
% 1.03/1.28 tff(3073,plain,
% 1.03/1.28 (b(s(s(s(z))), s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[818, 3072])).
% 1.03/1.28 tff(3074,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3075,plain,
% 1.03/1.28 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3076,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3075])).
% 1.03/1.28 tff(3077,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3076, 3074])).
% 1.03/1.28 tff(3078,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3079,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 1.03/1.28 tff(3080,plain,
% 1.03/1.28 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3079, 154, 2604, 3073, 2996, 1272])).
% 1.03/1.28 tff(3081,plain,
% 1.03/1.28 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[138, 3080])).
% 1.03/1.28 tff(3082,plain,
% 1.03/1.28 (~r(z, s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2080, 3081, 106])).
% 1.03/1.28 tff(3083,plain,
% 1.03/1.28 (b(z, s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[648, 3082])).
% 1.03/1.28 tff(3084,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3085,plain,
% 1.03/1.28 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3086,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3085])).
% 1.03/1.28 tff(3087,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3086, 3084])).
% 1.03/1.28 tff(3088,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3089,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 1.03/1.28 tff(3090,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3089, 154, 2604, 1, 232, 143, 660])).
% 1.03/1.28 tff(3091,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3092,plain,
% 1.03/1.28 (~b(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3091, 3083, 2604, 2996, 3073])).
% 1.03/1.28 tff(3093,plain,
% 1.03/1.28 (r(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[252, 3092])).
% 1.03/1.28 tff(3094,plain,
% 1.03/1.28 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[597, 3093, 17])).
% 1.03/1.28 tff(3095,plain,
% 1.03/1.28 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1648, 3093, 17, 14, 3073, 1272])).
% 1.03/1.28 tff(3096,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[104, 3095, 3094])).
% 1.03/1.28 tff(3097,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3098,plain,
% 1.03/1.28 (~r(s(s(z)), z)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3097, 14, 17, 2604])).
% 1.03/1.28 tff(3099,plain,
% 1.03/1.28 (b(s(s(z)), z)),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[122, 3098])).
% 1.03/1.28 tff(3100,plain,
% 1.03/1.28 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2891, 857, 3099, 17, 14])).
% 1.03/1.28 tff(3101,plain,
% 1.03/1.28 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1653, 3100])).
% 1.03/1.28 tff(3102,plain,
% 1.03/1.28 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[597, 273, 17])).
% 1.03/1.28 tff(3103,plain,
% 1.03/1.28 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[104, 3102])).
% 1.03/1.28 tff(3104,plain,
% 1.03/1.28 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[657, 273, 299])).
% 1.03/1.28 tff(3105,plain,
% 1.03/1.28 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[138, 3104])).
% 1.03/1.28 tff(3106,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[162, 3105, 3103, 143, 140, 142])).
% 1.03/1.28 tff(3107,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3108,plain,
% 1.03/1.28 (~r(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3107, 857, 2996, 3099, 299, 17])).
% 1.03/1.28 tff(3109,plain,
% 1.03/1.28 (b(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[252, 3108])).
% 1.03/1.28 tff(3110,plain,
% 1.03/1.28 (~r(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1749, 16, 299, 1, 232])).
% 1.03/1.28 tff(3111,plain,
% 1.03/1.28 (b(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[138, 3110])).
% 1.03/1.28 tff(3112,plain,
% 1.03/1.28 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[585, 3111, 232, 15, 1, 16])).
% 1.03/1.28 tff(3113,plain,
% 1.03/1.28 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[564, 3112])).
% 1.03/1.28 tff(3114,plain,
% 1.03/1.28 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[162, 3111, 143, 140, 142])).
% 1.03/1.28 tff(3115,plain,
% 1.03/1.28 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[104, 3114])).
% 1.03/1.28 tff(3116,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[75, 3115, 3113, 16])).
% 1.03/1.28 tff(3117,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3118,plain,
% 1.03/1.28 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3117, 857, 2996, 3099, 3109, 3101, 3073, 299])).
% 1.03/1.28 tff(3119,plain,
% 1.03/1.28 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1259, 3118])).
% 1.03/1.28 tff(3120,plain,
% 1.03/1.28 (~r(s(s(s(s(z)))), s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1323, 3119, 14, 3099, 857])).
% 1.03/1.28 tff(3121,plain,
% 1.03/1.28 (b(s(s(s(s(z)))), s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[318, 3120])).
% 1.03/1.28 tff(3122,plain,
% 1.03/1.28 (~b(z, s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3091, 3109, 2604, 2996, 3073])).
% 1.03/1.28 tff(3123,plain,
% 1.03/1.28 (r(z, s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[648, 3122])).
% 1.03/1.28 tff(3124,plain,
% 1.03/1.28 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1471, 3119, 857, 3123, 3099])).
% 1.03/1.28 tff(3125,plain,
% 1.03/1.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[343, 3124])).
% 1.03/1.28 tff(3126,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3127,plain,
% 1.03/1.28 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3128,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3127])).
% 1.03/1.28 tff(3129,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3128, 3126])).
% 1.03/1.28 tff(3130,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3131,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 1.03/1.28 tff(3132,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3131, 154, 2604, 3109, 2996, 3125, 3121])).
% 1.03/1.28 tff(3133,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3134,plain,
% 1.03/1.28 (~r(s(s(z)), s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3133, 14, 2604, 17])).
% 1.03/1.28 tff(3135,plain,
% 1.03/1.28 (b(s(s(z)), s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[296, 3134])).
% 1.03/1.28 tff(3136,plain,
% 1.03/1.28 ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2957, 154, 2604, 3073, 3099])).
% 1.03/1.28 tff(3137,plain,
% 1.03/1.28 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3136, 3135])).
% 1.03/1.28 tff(3138,plain,
% 1.03/1.28 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[104, 3137])).
% 1.03/1.28 tff(3139,plain,
% 1.03/1.28 (~r(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[597, 3138, 17])).
% 1.03/1.28 tff(3140,plain,
% 1.03/1.28 (b(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[252, 3139])).
% 1.03/1.28 tff(3141,plain,
% 1.03/1.28 (~b(z, s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2891, 1655, 142, 17, 14])).
% 1.03/1.28 tff(3142,plain,
% 1.03/1.28 (r(z, s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[64, 3141])).
% 1.03/1.28 tff(3143,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3035, 28, 14, 3142, 17, 1655])).
% 1.03/1.28 tff(3144,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3145,plain,
% 1.03/1.28 (~r(s(z), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3144, 14, 17, 3099])).
% 1.03/1.28 tff(3146,plain,
% 1.03/1.28 (b(s(z), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1653, 3145])).
% 1.03/1.28 tff(3147,plain,
% 1.03/1.28 (~b(z, s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3091, 3140, 2604, 2996, 3073])).
% 1.03/1.28 tff(3148,plain,
% 1.03/1.28 (r(z, s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[648, 3147])).
% 1.03/1.28 tff(3149,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[2044, 28, 628, 18, 67])).
% 1.03/1.28 tff(3150,plain,((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3151,plain,
% 1.03/1.28 (~r(z, s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3150, 3148, 3138])).
% 1.03/1.28 tff(3152,plain,
% 1.03/1.28 (b(z, s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[64, 3151])).
% 1.03/1.28 tff(3153,plain,
% 1.03/1.28 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1471, 1283, 140, 628, 142])).
% 1.03/1.28 tff(3154,plain,
% 1.03/1.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[343, 3153])).
% 1.03/1.28 tff(3155,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3156,plain,
% 1.03/1.28 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3157,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3156])).
% 1.03/1.28 tff(3158,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3157, 3155])).
% 1.03/1.28 tff(3159,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3160,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3159, 3158])).
% 1.03/1.28 tff(3161,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3160, 154, 232, 3154, 1283, 15, 231])).
% 1.03/1.28 tff(3162,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3163,plain,
% 1.03/1.28 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3162, 3140, 3146, 3135, 3152, 3148, 3099])).
% 1.03/1.28 tff(3164,plain,
% 1.03/1.28 (r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1259, 3163])).
% 1.03/1.28 tff(3165,plain,
% 1.03/1.28 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[75, 3164, 3138])).
% 1.03/1.28 tff(3166,plain,
% 1.03/1.28 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[564, 3165])).
% 1.03/1.28 tff(3167,plain,
% 1.03/1.28 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3079, 154, 2604, 3073, 2996, 3135])).
% 1.03/1.28 tff(3168,plain,
% 1.03/1.28 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[138, 3167])).
% 1.03/1.28 tff(3169,plain,
% 1.03/1.28 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[612, 3164, 3168])).
% 1.03/1.28 tff(3170,plain,
% 1.03/1.28 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[343, 3169])).
% 1.03/1.28 tff(3171,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[623, 3170, 3166, 3073, 3146, 3140])).
% 1.03/1.28 tff(3172,plain,((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3173,plain,
% 1.03/1.28 (~r(z, s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3172, 17, 2604])).
% 1.03/1.28 tff(3174,plain,
% 1.03/1.28 (b(z, s(z))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[1181, 3173])).
% 1.03/1.28 tff(3175,plain,
% 1.03/1.28 (~r(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[597, 67, 17])).
% 1.03/1.28 tff(3176,plain,
% 1.03/1.28 (b(s(z), s(s(s(z))))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[252, 3175])).
% 1.03/1.28 tff(3177,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3178,plain,
% 1.03/1.28 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3179,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.03/1.28 inference(monotonicity,[status(thm)],[3178])).
% 1.03/1.28 tff(3180,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.28 inference(transitivity,[status(thm)],[3179, 3177])).
% 1.03/1.28 tff(3181,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.28 inference(quant_inst,[status(thm)],[])).
% 1.03/1.28 tff(3182,plain,
% 1.03/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 1.03/1.28 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 1.03/1.28 tff(3183,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3182, 154, 1726, 2604, 1, 232, 143])).
% 1.03/1.28 tff(3184,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3185,plain,
% 1.03/1.28 ($false),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3184, 3176, 1701, 2604, 3174, 2881])).
% 1.03/1.28 tff(3186,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.28 tff(3187,plain,
% 1.03/1.28 (~r(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[3186, 106, 17, 2877])).
% 1.03/1.28 tff(3188,plain,
% 1.03/1.28 (b(s(s(s(z))), s(s(z)))),
% 1.03/1.28 inference(unit_resolution,[status(thm)],[104, 3187])).
% 1.03/1.28 tff(3189,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3190,plain,
% 1.03/1.28 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.28 inference(rewrite,[status(thm)],[])).
% 1.03/1.28 tff(3191,plain,
% 1.03/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3190])).
% 1.03/1.29 tff(3192,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3191, 3189])).
% 1.03/1.29 tff(3193,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3194,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3193, 3192])).
% 1.03/1.29 tff(3195,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3194, 154, 1726, 2604, 1224, 15, 1222])).
% 1.03/1.29 tff(3196,plain,((~r(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3197,plain,
% 1.03/1.29 (~b(s(z), s(s(s(s(z)))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3196, 16, 2604, 3174, 106])).
% 1.03/1.29 tff(3198,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1653, 3197, 2257])).
% 1.03/1.29 tff(3199,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3200,plain,
% 1.03/1.29 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3199, 106, 2877, 17])).
% 1.03/1.29 tff(3201,plain,
% 1.03/1.29 (b(s(s(z)), s(s(s(s(z)))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1259, 3200])).
% 1.03/1.29 tff(3202,plain,
% 1.03/1.29 (~r(s(z), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2155, 28, 172, 1655])).
% 1.03/1.29 tff(3203,plain,
% 1.03/1.29 (b(s(z), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[271, 3202])).
% 1.03/1.29 tff(3204,plain,
% 1.03/1.29 (~r(s(s(s(z))), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[180, 66, 172])).
% 1.03/1.29 tff(3205,plain,
% 1.03/1.29 (b(s(s(s(z))), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[169, 3204])).
% 1.03/1.29 tff(3206,plain,
% 1.03/1.29 (~r(z, s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1663, 172, 1655])).
% 1.03/1.29 tff(3207,plain,
% 1.03/1.29 (b(z, s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1181, 3206])).
% 1.03/1.29 tff(3208,plain,
% 1.03/1.29 (~r(s(s(s(z))), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1930, 66, 1655])).
% 1.03/1.29 tff(3209,plain,
% 1.03/1.29 (b(s(s(s(z))), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[818, 3208])).
% 1.03/1.29 tff(3210,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3211,plain,
% 1.03/1.29 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3212,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3211])).
% 1.03/1.29 tff(3213,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3212, 3210])).
% 1.03/1.29 tff(3214,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3215,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3214, 3213])).
% 1.03/1.29 tff(3216,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3215, 154, 1726, 2604, 1, 143, 660])).
% 1.03/1.29 tff(3217,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3218,plain,
% 1.03/1.29 (~b(z, s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3217, 3209, 3207, 3203, 3205])).
% 1.03/1.29 tff(3219,plain,
% 1.03/1.29 (r(z, s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[648, 3218])).
% 1.03/1.29 tff(3220,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3221,plain,
% 1.03/1.29 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3222,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3221])).
% 1.03/1.29 tff(3223,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3222, 3220])).
% 1.03/1.29 tff(3224,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3225,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 1.03/1.29 tff(3226,plain,
% 1.03/1.29 ($false),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3225, 28, 3219, 172, 66])).
% 1.03/1.29 tff(3227,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.03/1.29 tff(3228,plain,
% 1.03/1.29 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3227, 172, 1655])).
% 1.03/1.29 tff(3229,plain,
% 1.03/1.29 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[564, 3228])).
% 1.03/1.29 tff(3230,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3231,plain,
% 1.03/1.29 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3232,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3231])).
% 1.03/1.29 tff(3233,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3232, 3230])).
% 1.03/1.29 tff(3234,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3235,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3234, 3233])).
% 1.03/1.29 tff(3236,plain,
% 1.03/1.29 (~b(s(s(s(z))), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3235, 154, 615, 1283, 1603, 566])).
% 1.03/1.29 tff(3237,plain,
% 1.03/1.29 (r(s(s(s(z))), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[104, 3236])).
% 1.03/1.29 tff(3238,plain,
% 1.03/1.29 (~r(s(z), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[597, 273, 3237])).
% 1.03/1.29 tff(3239,plain,
% 1.03/1.29 (b(s(z), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[680, 3238])).
% 1.03/1.29 tff(3240,plain,
% 1.03/1.29 (~b(s(s(z)), s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2654, 154, 615, 1283, 1603, 566])).
% 1.03/1.29 tff(3241,plain,
% 1.03/1.29 (r(s(s(z)), s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[138, 3240])).
% 1.03/1.29 tff(3242,plain,
% 1.03/1.29 (~r(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[655, 28, 3241, 273])).
% 1.03/1.29 tff(3243,plain,
% 1.03/1.29 (b(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[296, 3242])).
% 1.03/1.29 tff(3244,plain,
% 1.03/1.29 (~b(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2612, 3243, 3207, 3239, 3203])).
% 1.03/1.29 tff(3245,plain,
% 1.03/1.29 (r(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[64, 3244])).
% 1.03/1.29 tff(3246,plain,
% 1.03/1.29 (~r(z, s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[2044, 28, 3245, 3237])).
% 1.03/1.29 tff(3247,plain,
% 1.03/1.29 (b(z, s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[648, 3246])).
% 1.03/1.29 tff(3248,plain,
% 1.03/1.29 (~r(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1346, 171, 3237])).
% 1.03/1.29 tff(3249,plain,
% 1.03/1.29 (b(z, s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[64, 3248])).
% 1.03/1.29 tff(3250,plain,
% 1.03/1.29 (~r(s(s(z)), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1280, 171, 3237])).
% 1.03/1.29 tff(3251,plain,
% 1.03/1.29 (b(s(s(z)), z)),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[122, 3250])).
% 1.03/1.29 tff(3252,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3253,plain,
% 1.03/1.29 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3254,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3253])).
% 1.03/1.29 tff(3255,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3254, 3252])).
% 1.03/1.29 tff(3256,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3257,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3256, 3255])).
% 1.03/1.29 tff(3258,plain,
% 1.03/1.29 (~b(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3257, 154, 1726, 2604, 3251, 3249])).
% 1.03/1.29 tff(3259,plain,
% 1.03/1.29 (r(s(s(z)), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[296, 3258])).
% 1.03/1.29 tff(3260,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3261,plain,
% 1.03/1.29 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3262,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3261])).
% 1.03/1.29 tff(3263,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3262, 3260])).
% 1.03/1.29 tff(3264,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3265,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3264, 3263])).
% 1.03/1.29 tff(3266,plain,
% 1.03/1.29 (~b(s(z), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3265, 154, 1726, 2604, 3251, 3249])).
% 1.03/1.29 tff(3267,plain,
% 1.03/1.29 (r(s(z), s(s(z)))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[680, 3266])).
% 1.03/1.29 tff(3268,plain,
% 1.03/1.29 (~r(s(z), s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[597, 3267, 3237])).
% 1.03/1.29 tff(3269,plain,
% 1.03/1.29 (b(s(z), s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[252, 3268])).
% 1.03/1.29 tff(3270,plain,
% 1.03/1.29 (~r(s(s(s(z))), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[1556, 3267, 3237])).
% 1.03/1.29 tff(3271,plain,
% 1.03/1.29 (b(s(s(s(z))), s(z))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[818, 3270])).
% 1.03/1.29 tff(3272,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3273,plain,
% 1.03/1.29 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.29 inference(rewrite,[status(thm)],[])).
% 1.03/1.29 tff(3274,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.03/1.29 inference(monotonicity,[status(thm)],[3273])).
% 1.03/1.29 tff(3275,plain,
% 1.03/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.03/1.29 inference(transitivity,[status(thm)],[3274, 3272])).
% 1.03/1.29 tff(3276,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.03/1.29 inference(quant_inst,[status(thm)],[])).
% 1.03/1.29 tff(3277,plain,
% 1.03/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.03/1.29 inference(modus_ponens,[status(thm)],[3276, 3275])).
% 1.03/1.29 tff(3278,plain,
% 1.03/1.29 (~b(z, s(s(s(z))))),
% 1.03/1.29 inference(unit_resolution,[status(thm)],[3277, 154, 1726, 2604, 1, 232])).
% 1.03/1.30 tff(3279,plain,
% 1.03/1.30 (r(z, s(s(s(z))))),
% 1.03/1.30 inference(unit_resolution,[status(thm)],[648, 3278])).
% 1.03/1.30 tff(3280,plain,
% 1.03/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.30 inference(rewrite,[status(thm)],[])).
% 1.03/1.30 tff(3281,plain,
% 1.03/1.30 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.30 inference(rewrite,[status(thm)],[])).
% 1.03/1.30 tff(3282,plain,
% 1.03/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.03/1.30 inference(monotonicity,[status(thm)],[3281])).
% 1.03/1.30 tff(3283,plain,
% 1.03/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.03/1.30 inference(transitivity,[status(thm)],[3282, 3280])).
% 1.03/1.30 tff(3284,plain,
% 1.03/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.03/1.30 inference(quant_inst,[status(thm)],[])).
% 1.03/1.30 tff(3285,plain,
% 1.03/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))),
% 1.03/1.30 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 1.03/1.30 tff(3286,plain,
% 1.03/1.30 (~b(z, s(s(s(s(elem!1)))))),
% 1.03/1.30 inference(unit_resolution,[status(thm)],[3285, 154, 1726, 444, 443, 232])).
% 1.13/1.30 tff(3287,plain,
% 1.13/1.30 (r(z, s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[548, 3286])).
% 1.13/1.30 tff(3288,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3289,plain,
% 1.13/1.30 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3290,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3289])).
% 1.13/1.30 tff(3291,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3290, 3288])).
% 1.13/1.30 tff(3292,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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)))))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3293,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 1.13/1.30 tff(3294,plain,
% 1.13/1.30 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3293, 154, 444, 1, 443, 232])).
% 1.13/1.30 tff(3295,plain,
% 1.13/1.30 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[989, 3294])).
% 1.13/1.30 tff(3296,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3297,plain,
% 1.13/1.30 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3298,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3297])).
% 1.13/1.30 tff(3299,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3298, 3296])).
% 1.13/1.30 tff(3300,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3301,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.13/1.30 tff(3302,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3301, 28, 3295, 3287, 171])).
% 1.13/1.30 tff(3303,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(3304,plain,
% 1.13/1.30 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3303, 444, 171, 1, 232, 1726])).
% 1.13/1.30 tff(3305,plain,
% 1.13/1.30 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[496, 3304])).
% 1.13/1.30 tff(3306,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3307,plain,
% 1.13/1.30 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3308,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3307])).
% 1.13/1.30 tff(3309,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3308, 3306])).
% 1.13/1.30 tff(3310,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3311,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 1.13/1.30 tff(3312,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3311, 28, 780, 628, 402])).
% 1.13/1.30 tff(3313,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(3314,plain,
% 1.13/1.30 (~r(s(s(s(s(elem!1)))), z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3313, 3305, 3279])).
% 1.13/1.30 tff(3315,plain,
% 1.13/1.30 (b(s(s(s(s(elem!1)))), z)),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[418, 3314])).
% 1.13/1.30 tff(3316,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3317,plain,
% 1.13/1.30 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3318,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3317])).
% 1.13/1.30 tff(3319,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3318, 3316])).
% 1.13/1.30 tff(3320,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3321,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3320, 3319])).
% 1.13/1.30 tff(3322,plain,
% 1.13/1.30 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3321, 154, 1726, 2604, 444])).
% 1.13/1.30 tff(3323,plain,
% 1.13/1.30 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3322, 3315])).
% 1.13/1.30 tff(3324,plain,
% 1.13/1.30 (r(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[467, 3323])).
% 1.13/1.30 tff(3325,plain,
% 1.13/1.30 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1478, 3324, 17])).
% 1.13/1.30 tff(3326,plain,
% 1.13/1.30 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[2390, 154, 1726, 444, 142])).
% 1.13/1.30 tff(3327,plain,
% 1.13/1.30 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3326, 3315])).
% 1.13/1.30 tff(3328,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[373, 60, 370, 3327, 3325])).
% 1.13/1.30 tff(3329,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(3330,plain,
% 1.13/1.30 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3329, 3267, 1726, 3251, 2604, 171, 3271, 3269])).
% 1.13/1.30 tff(3331,plain,
% 1.13/1.30 (r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[441, 3330])).
% 1.13/1.30 tff(3332,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3333,plain,
% 1.13/1.30 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3334,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3333])).
% 1.13/1.30 tff(3335,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3334, 3332])).
% 1.13/1.30 tff(3336,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3337,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3336, 3335])).
% 1.13/1.30 tff(3338,plain,
% 1.13/1.30 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3337, 28, 3241, 3331, 3259])).
% 1.13/1.30 tff(3339,plain,
% 1.13/1.30 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1051, 60, 3338, 1048])).
% 1.13/1.30 tff(3340,plain,
% 1.13/1.30 (~b(s(s(s(s(z)))), s(z))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[1744, 154, 3271, 3269, 615, 566])).
% 1.13/1.30 tff(3341,plain,
% 1.13/1.30 (r(s(s(s(s(z)))), s(z))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[318, 3340])).
% 1.13/1.30 tff(3342,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3343,plain,
% 1.13/1.30 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3344,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[3343])).
% 1.13/1.30 tff(3345,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[3344, 3342])).
% 1.13/1.30 tff(3346,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(3347,plain,
% 1.13/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 1.13/1.30 tff(3348,plain,
% 1.13/1.30 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[3347, 28, 3331, 3341])).
% 1.13/1.30 tff(3349,plain,
% 1.13/1.30 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[517, 60, 12, 3348])).
% 1.13/1.30 tff(3350,plain,
% 1.13/1.30 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[351, 28, 3331, 3259])).
% 1.13/1.30 tff(3351,plain,
% 1.13/1.30 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[373, 60, 370, 3350])).
% 1.13/1.30 tff(3352,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3353,plain,
% 1.13/1.30 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(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(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(3354,plain,
% 1.13/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(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(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3353])).
% 1.13/1.31 tff(3355,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(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(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3354, 3352])).
% 1.13/1.31 tff(3356,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(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(s(elem!1)))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3357,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3356, 3355])).
% 1.13/1.31 tff(3358,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3357, 154, 1283, 1603, 3351, 3349, 3339])).
% 1.13/1.31 tff(3359,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3360,plain,
% 1.13/1.31 (~r(s(s(s(z))), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3359, 566, 1603, 12, 3207, 3203, 615, 1283])).
% 1.13/1.31 tff(3361,plain,
% 1.13/1.31 (b(s(s(s(z))), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[169, 3360])).
% 1.13/1.31 tff(3362,plain,
% 1.13/1.31 (~b(s(s(s(z))), s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3217, 3247, 3207, 3203, 3361])).
% 1.13/1.31 tff(3363,plain,
% 1.13/1.31 (r(s(s(s(z))), s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[818, 3362])).
% 1.13/1.31 tff(3364,plain,
% 1.13/1.31 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1135, 3363, 3241, 3239])).
% 1.13/1.31 tff(3365,plain,
% 1.13/1.31 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[496, 3364])).
% 1.13/1.31 tff(3366,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.31 tff(3367,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3368,plain,
% 1.13/1.31 (((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3369,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3368])).
% 1.13/1.31 tff(3370,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3369, 3367])).
% 1.13/1.31 tff(3371,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3372,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3371, 3370])).
% 1.13/1.31 tff(3373,plain,
% 1.13/1.31 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3372, 28, 1655, 3366])).
% 1.13/1.31 tff(3374,plain,
% 1.13/1.31 (b(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[467, 3373])).
% 1.13/1.31 tff(3375,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3376,plain,
% 1.13/1.31 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3377,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3376])).
% 1.13/1.31 tff(3378,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3377, 3375])).
% 1.13/1.31 tff(3379,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3380,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3379, 3378])).
% 1.13/1.31 tff(3381,plain,
% 1.13/1.31 (~r(s(s(s(s(elem!1)))), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3380, 28, 172, 3366])).
% 1.13/1.31 tff(3382,plain,
% 1.13/1.31 (b(s(s(s(s(elem!1)))), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[418, 3381])).
% 1.13/1.31 tff(3383,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3384,plain,
% 1.13/1.31 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3385,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3384])).
% 1.13/1.31 tff(3386,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3385, 3383])).
% 1.13/1.31 tff(3387,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3388,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3387, 3386])).
% 1.13/1.31 tff(3389,plain,
% 1.13/1.31 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3388, 154, 3203, 443, 660])).
% 1.13/1.31 tff(3390,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3389, 3382, 3374])).
% 1.13/1.31 tff(3391,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3392,plain,
% 1.13/1.31 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3391, 3365, 3247, 172, 1655])).
% 1.13/1.31 tff(3393,plain,
% 1.13/1.31 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[517, 60, 12, 3392])).
% 1.13/1.31 tff(3394,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3395,plain,
% 1.13/1.31 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(s(elem!1))))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3396,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3395])).
% 1.13/1.31 tff(3397,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3396, 3394])).
% 1.13/1.31 tff(3398,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(s(elem!1)))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3399,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 1.13/1.31 tff(3400,plain,
% 1.13/1.31 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3399, 154, 3365, 615, 1283])).
% 1.13/1.31 tff(3401,plain,
% 1.13/1.31 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3400, 3393])).
% 1.13/1.31 tff(3402,plain,
% 1.13/1.31 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[373, 60, 370, 3401])).
% 1.13/1.31 tff(3403,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3404,plain,
% 1.13/1.31 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3405,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3404])).
% 1.13/1.31 tff(3406,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3405, 3403])).
% 1.13/1.31 tff(3407,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3408,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 1.13/1.31 tff(3409,plain,
% 1.13/1.31 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3408, 154, 3365, 615, 566])).
% 1.13/1.31 tff(3410,plain,
% 1.13/1.31 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3409, 3393])).
% 1.13/1.31 tff(3411,plain,
% 1.13/1.31 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[989, 3410])).
% 1.13/1.31 tff(3412,plain,
% 1.13/1.31 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1027, 3411, 273])).
% 1.13/1.31 tff(3413,plain,
% 1.13/1.31 (b(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[467, 3412])).
% 1.13/1.31 tff(3414,plain,
% 1.13/1.31 (~b(s(s(s(s(z)))), s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[2103, 154, 1283, 3239, 3243, 1603])).
% 1.13/1.31 tff(3415,plain,
% 1.13/1.31 (r(s(s(s(s(z)))), s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[318, 3414])).
% 1.13/1.31 tff(3416,plain,
% 1.13/1.31 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3347, 28, 345, 298])).
% 1.13/1.31 tff(3417,plain,
% 1.13/1.31 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3408, 154, 443, 615, 566])).
% 1.13/1.31 tff(3418,plain,
% 1.13/1.31 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3417, 990])).
% 1.13/1.31 tff(3419,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[517, 60, 3418, 12, 3416])).
% 1.13/1.31 tff(3420,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3421,plain,
% 1.13/1.31 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3420, 3365, 12, 615, 566, 3415, 3363])).
% 1.13/1.31 tff(3422,plain,
% 1.13/1.31 (b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[441, 3421])).
% 1.13/1.31 tff(3423,plain,
% 1.13/1.31 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1155, 154, 3422, 3239, 3243])).
% 1.13/1.31 tff(3424,plain,
% 1.13/1.31 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3423, 3413])).
% 1.13/1.31 tff(3425,plain,
% 1.13/1.31 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[1051, 60, 1048, 3424])).
% 1.13/1.31 tff(3426,plain,
% 1.13/1.31 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3388, 154, 3203, 3365, 3247])).
% 1.13/1.31 tff(3427,plain,
% 1.13/1.31 (~b(s(s(s(s(elem!1)))), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3426, 3413])).
% 1.13/1.31 tff(3428,plain,
% 1.13/1.31 (r(s(s(s(s(elem!1)))), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[418, 3427])).
% 1.13/1.31 tff(3429,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3430,plain,
% 1.13/1.31 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3431,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.13/1.31 inference(monotonicity,[status(thm)],[3430])).
% 1.13/1.31 tff(3432,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[3431, 3429])).
% 1.13/1.31 tff(3433,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(3434,plain,
% 1.13/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[3433, 3432])).
% 1.13/1.31 tff(3435,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3434, 154, 1726, 2604, 684, 231, 142])).
% 1.13/1.31 tff(3436,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(3437,plain,
% 1.13/1.31 (~b(s(s(z)), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[3436, 3243, 3203, 3207, 3239])).
% 1.13/1.31 tff(3438,plain,
% 1.13/1.31 (r(s(s(z)), z)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[122, 3437])).
% 1.13/1.31 tff(3439,plain,
% 1.13/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(3440,plain,
% 1.13/1.31 (((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3441,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3440])).
% 1.13/1.32 tff(3442,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3441, 3439])).
% 1.13/1.32 tff(3443,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(3444,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3443, 3442])).
% 1.13/1.32 tff(3445,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3444, 28, 3438, 3428, 3425, 3402])).
% 1.13/1.32 tff(3446,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3447,plain,
% 1.13/1.32 (~r(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3446, 566, 615, 1283, 12, 172, 1655, 1603])).
% 1.13/1.32 tff(3448,plain,
% 1.13/1.32 (b(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[252, 3447])).
% 1.13/1.32 tff(3449,plain,
% 1.13/1.32 (~b(s(s(s(z))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3184, 3448, 3203, 3361, 3207])).
% 1.13/1.32 tff(3450,plain,
% 1.13/1.32 (r(s(s(s(z))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[818, 3449])).
% 1.13/1.32 tff(3451,plain,
% 1.13/1.32 (~r(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1556, 3450, 3237])).
% 1.13/1.32 tff(3452,plain,
% 1.13/1.32 (b(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[680, 3451])).
% 1.13/1.32 tff(3453,plain,
% 1.13/1.32 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1135, 3452, 3241, 3450])).
% 1.13/1.32 tff(3454,plain,
% 1.13/1.32 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[496, 3453])).
% 1.13/1.32 tff(3455,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3456,plain,
% 1.13/1.32 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3457,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3456])).
% 1.13/1.32 tff(3458,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3457, 3455])).
% 1.13/1.32 tff(3459,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(3460,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3459, 3458])).
% 1.13/1.32 tff(3461,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3460, 154, 2604, 444, 443, 232, 143])).
% 1.13/1.32 tff(3462,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3463,plain,
% 1.13/1.32 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3462, 3454, 3203, 3361, 3448])).
% 1.13/1.32 tff(3464,plain,
% 1.13/1.32 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3131, 154, 3203, 3361, 615])).
% 1.13/1.32 tff(3465,plain,
% 1.13/1.32 (~b(s(s(s(s(z)))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3464, 3448])).
% 1.13/1.32 tff(3466,plain,
% 1.13/1.32 (r(s(s(s(s(z)))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[318, 3465])).
% 1.13/1.32 tff(3467,plain,
% 1.13/1.32 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3420, 3454, 12, 615, 566, 3466, 3450])).
% 1.13/1.32 tff(3468,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[441, 3467, 3463])).
% 1.13/1.32 tff(3469,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3470,plain,
% 1.13/1.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3469, 615, 12, 1283, 172, 1655, 3229])).
% 1.13/1.32 tff(3471,plain,
% 1.13/1.32 (r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[229, 3470])).
% 1.13/1.32 tff(3472,plain,
% 1.13/1.32 (~r(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2000, 3471, 1655])).
% 1.13/1.32 tff(3473,plain,
% 1.13/1.32 (b(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[680, 3472])).
% 1.13/1.32 tff(3474,plain,
% 1.13/1.32 (~b(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2423, 154, 144, 615, 1283, 566])).
% 1.13/1.32 tff(3475,plain,
% 1.13/1.32 (r(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[104, 3474])).
% 1.13/1.32 tff(3476,plain,
% 1.13/1.32 (~r(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[865, 3475, 820])).
% 1.13/1.32 tff(3477,plain,
% 1.13/1.32 (b(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[296, 3476])).
% 1.13/1.32 tff(3478,plain,
% 1.13/1.32 (~b(s(s(z)), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3436, 3477, 2604, 1726, 684])).
% 1.13/1.32 tff(3479,plain,
% 1.13/1.32 (~r(s(s(z)), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2656, 3477, 820, 144, 3475])).
% 1.13/1.32 tff(3480,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[122, 3479, 3478])).
% 1.13/1.32 tff(3481,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3482,plain,
% 1.13/1.32 (~b(s(s(z)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3481, 3473, 3203, 3207, 820, 615, 1283, 3229])).
% 1.13/1.32 tff(3483,plain,
% 1.13/1.32 (r(s(s(z)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[138, 3482])).
% 1.13/1.32 tff(3484,plain,
% 1.13/1.32 (~r(z, s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1251, 3471, 172])).
% 1.13/1.32 tff(3485,plain,
% 1.13/1.32 (b(z, s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[64, 3484])).
% 1.13/1.32 tff(3486,plain,
% 1.13/1.32 (~b(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2612, 3473, 3207, 3485, 3203])).
% 1.13/1.32 tff(3487,plain,
% 1.13/1.32 (r(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[296, 3486])).
% 1.13/1.32 tff(3488,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1125, 3487, 3483, 820])).
% 1.13/1.32 tff(3489,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3490,plain,
% 1.13/1.32 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3489, 820, 1283, 1655, 172, 12])).
% 1.13/1.32 tff(3491,plain,
% 1.13/1.32 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[343, 3490])).
% 1.13/1.32 tff(3492,plain,
% 1.13/1.32 (~r(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1957, 3491, 1655])).
% 1.13/1.32 tff(3493,plain,
% 1.13/1.32 (b(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[252, 3492])).
% 1.13/1.32 tff(3494,plain,
% 1.13/1.32 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1411, 820, 3491])).
% 1.13/1.32 tff(3495,plain,
% 1.13/1.32 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[318, 3494])).
% 1.13/1.32 tff(3496,plain,
% 1.13/1.32 (~b(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2306, 684, 1283, 566, 232])).
% 1.13/1.32 tff(3497,plain,
% 1.13/1.32 (r(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[104, 3496])).
% 1.13/1.32 tff(3498,plain,
% 1.13/1.32 (~r(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[865, 3497, 820])).
% 1.13/1.32 tff(3499,plain,
% 1.13/1.32 (b(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[296, 3498])).
% 1.13/1.32 tff(3500,plain,
% 1.13/1.32 (~b(z, s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2612, 3499, 1726, 684, 2604])).
% 1.13/1.32 tff(3501,plain,
% 1.13/1.32 (r(z, s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[64, 3500])).
% 1.13/1.32 tff(3502,plain,
% 1.13/1.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1251, 3501, 172])).
% 1.13/1.32 tff(3503,plain,
% 1.13/1.32 (b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[229, 3502])).
% 1.13/1.32 tff(3504,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2103, 154, 1283, 684, 3499, 506, 3503])).
% 1.13/1.32 tff(3505,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3506,plain,
% 1.13/1.32 (~b(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3505, 3495, 1283, 172, 3207, 3203, 820, 3229, 3493])).
% 1.13/1.32 tff(3507,plain,
% 1.13/1.32 (r(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[680, 3506])).
% 1.13/1.32 tff(3508,plain,
% 1.13/1.32 (~r(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1556, 3507, 820])).
% 1.13/1.32 tff(3509,plain,
% 1.13/1.32 (b(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[104, 3508])).
% 1.13/1.32 tff(3510,plain,
% 1.13/1.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2000, 3507, 1655])).
% 1.13/1.32 tff(3511,plain,
% 1.13/1.32 (b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[229, 3510])).
% 1.13/1.32 tff(3512,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3513,plain,
% 1.13/1.32 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3514,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3513])).
% 1.13/1.32 tff(3515,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3514, 3512])).
% 1.13/1.32 tff(3516,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(3517,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3516, 3515])).
% 1.13/1.32 tff(3518,plain,
% 1.13/1.32 (~b(s(s(z)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3517, 154, 1283, 3509, 3511, 3229])).
% 1.13/1.32 tff(3519,plain,
% 1.13/1.32 (r(s(s(z)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[138, 3518])).
% 1.13/1.32 tff(3520,plain,
% 1.13/1.32 (~r(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1125, 3519, 820])).
% 1.13/1.32 tff(3521,plain,
% 1.13/1.32 (b(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[296, 3520])).
% 1.13/1.32 tff(3522,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3523,plain,
% 1.13/1.32 (((~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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3524,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3523])).
% 1.13/1.32 tff(3525,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3524, 3522])).
% 1.13/1.32 tff(3526,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(3527,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 1.13/1.32 tff(3528,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3527, 154, 1283, 3521, 3495, 3509, 3229])).
% 1.13/1.32 tff(3529,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3530,plain,
% 1.13/1.32 (~r(s(s(s(z))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3529, 172, 1655, 1283, 12])).
% 1.13/1.32 tff(3531,plain,
% 1.13/1.32 (b(s(s(s(z))), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[818, 3530])).
% 1.13/1.32 tff(3532,plain,
% 1.13/1.32 (~r(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1957, 604, 1655])).
% 1.13/1.32 tff(3533,plain,
% 1.13/1.32 (b(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[252, 3532])).
% 1.13/1.32 tff(3534,plain,
% 1.13/1.32 (~b(z, s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3277, 154, 3207, 3203, 1, 3533])).
% 1.13/1.32 tff(3535,plain,
% 1.13/1.32 (r(z, s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[648, 3534])).
% 1.13/1.32 tff(3536,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1467, 28, 3535, 172, 604])).
% 1.13/1.32 tff(3537,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3538,plain,
% 1.13/1.32 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3537, 172, 3531, 1655])).
% 1.13/1.32 tff(3539,plain,
% 1.13/1.32 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[343, 3538])).
% 1.13/1.32 tff(3540,plain,
% 1.13/1.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3469, 3539, 12, 1283, 172, 1655, 3229])).
% 1.13/1.32 tff(3541,plain,
% 1.13/1.32 (r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[229, 3540])).
% 1.13/1.32 tff(3542,plain,
% 1.13/1.32 (~r(z, s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1251, 3541, 172])).
% 1.13/1.32 tff(3543,plain,
% 1.13/1.32 (b(z, s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[64, 3542])).
% 1.13/1.32 tff(3544,plain,
% 1.13/1.32 (~r(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2000, 3541, 1655])).
% 1.13/1.32 tff(3545,plain,
% 1.13/1.32 (b(s(z), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[680, 3544])).
% 1.13/1.32 tff(3546,plain,
% 1.13/1.32 (~b(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2612, 3545, 3207, 3543, 3203])).
% 1.13/1.32 tff(3547,plain,
% 1.13/1.32 (r(s(s(z)), s(z))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[296, 3546])).
% 1.13/1.32 tff(3548,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3549,plain,
% 1.13/1.32 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.13/1.32 inference(rewrite,[status(thm)],[])).
% 1.13/1.32 tff(3550,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.13/1.32 inference(monotonicity,[status(thm)],[3549])).
% 1.13/1.32 tff(3551,plain,
% 1.13/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.13/1.32 inference(transitivity,[status(thm)],[3550, 3548])).
% 1.13/1.32 tff(3552,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.13/1.32 inference(quant_inst,[status(thm)],[])).
% 1.13/1.32 tff(3553,plain,
% 1.13/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.13/1.32 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 1.13/1.32 tff(3554,plain,
% 1.13/1.32 (~b(s(s(s(z))), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3553, 154, 3207, 3531, 3545, 3543])).
% 1.13/1.32 tff(3555,plain,
% 1.13/1.32 (r(s(s(s(z))), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[169, 3554])).
% 1.13/1.32 tff(3556,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3265, 154, 1726, 2604, 684, 142, 140])).
% 1.13/1.32 tff(3557,plain,((~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.32 tff(3558,plain,
% 1.13/1.32 (~b(s(s(z)), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[3557, 3207, 3203, 3545, 3543])).
% 1.13/1.32 tff(3559,plain,
% 1.13/1.32 (r(s(s(z)), z)),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[122, 3558])).
% 1.13/1.32 tff(3560,plain,
% 1.13/1.32 (~r(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[1280, 3559, 3555])).
% 1.13/1.32 tff(3561,plain,
% 1.13/1.32 (b(s(s(s(z))), s(s(z)))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[104, 3560])).
% 1.13/1.32 tff(3562,plain,
% 1.13/1.32 (~b(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2306, 3561, 1283, 3229, 3545])).
% 1.13/1.32 tff(3563,plain,
% 1.13/1.32 (r(s(z), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[252, 3562])).
% 1.13/1.32 tff(3564,plain,
% 1.13/1.32 (~b(s(s(z)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[2425, 3561, 1283, 3539, 3229])).
% 1.13/1.32 tff(3565,plain,
% 1.13/1.32 (r(s(s(z)), s(s(s(z))))),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[138, 3564])).
% 1.13/1.32 tff(3566,plain,
% 1.13/1.32 ($false),
% 1.13/1.32 inference(unit_resolution,[status(thm)],[657, 3565, 3563, 3547])).
% 1.13/1.33 tff(3567,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3568,plain,
% 1.13/1.33 (~r(z, s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3567, 1655, 3201, 12])).
% 1.13/1.33 tff(3569,plain,
% 1.13/1.33 (b(z, s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[191, 3568])).
% 1.13/1.33 tff(3570,plain,
% 1.13/1.33 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3517, 154, 1283, 141, 1603])).
% 1.13/1.33 tff(3571,plain,
% 1.13/1.33 (~b(s(s(z)), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3570, 566])).
% 1.13/1.33 tff(3572,plain,
% 1.13/1.33 (r(s(s(z)), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[138, 3571])).
% 1.13/1.33 tff(3573,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3574,plain,
% 1.13/1.33 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3575,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[3574])).
% 1.13/1.33 tff(3576,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[3575, 3573])).
% 1.13/1.33 tff(3577,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(3578,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 1.13/1.33 tff(3579,plain,
% 1.13/1.33 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3578, 154, 141, 1603, 254])).
% 1.13/1.33 tff(3580,plain,
% 1.13/1.33 (~b(z, s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3579, 566])).
% 1.13/1.33 tff(3581,plain,
% 1.13/1.33 (r(z, s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[648, 3580])).
% 1.13/1.33 tff(3582,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2080, 3581, 3572, 106])).
% 1.13/1.33 tff(3583,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3584,plain,
% 1.13/1.33 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3583, 2879, 3188, 106, 3569, 3201])).
% 1.13/1.33 tff(3585,plain,
% 1.13/1.33 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[564, 3584])).
% 1.13/1.33 tff(3586,plain,
% 1.13/1.33 (~r(s(s(s(z))), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1930, 3585, 1655])).
% 1.13/1.33 tff(3587,plain,
% 1.13/1.33 (b(s(s(s(z))), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[818, 3586])).
% 1.13/1.33 tff(3588,plain,
% 1.13/1.33 (~r(z, s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3172, 17, 2877])).
% 1.13/1.33 tff(3589,plain,
% 1.13/1.33 (b(z, s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1181, 3588])).
% 1.13/1.33 tff(3590,plain,
% 1.13/1.33 (~r(s(z), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2064, 28, 3585, 1655])).
% 1.13/1.33 tff(3591,plain,
% 1.13/1.33 (b(s(z), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[252, 3590])).
% 1.13/1.33 tff(3592,plain,
% 1.13/1.33 (~b(s(s(s(z))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3184, 3591, 2877, 3589, 3587])).
% 1.13/1.33 tff(3593,plain,
% 1.13/1.33 (r(s(s(s(z))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[169, 3592])).
% 1.13/1.33 tff(3594,plain,
% 1.13/1.33 (~r(s(s(z)), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2276, 28, 106, 3593])).
% 1.13/1.33 tff(3595,plain,
% 1.13/1.33 (b(s(s(z)), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[138, 3594])).
% 1.13/1.33 tff(3596,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3597,plain,
% 1.13/1.33 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3598,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[3597])).
% 1.13/1.33 tff(3599,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[3598, 3596])).
% 1.13/1.33 tff(3600,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(3601,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[3600, 3599])).
% 1.13/1.33 tff(3602,plain,
% 1.13/1.33 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3601, 154, 3595, 3201, 3188, 2879])).
% 1.13/1.33 tff(3603,plain,
% 1.13/1.33 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[343, 3602])).
% 1.13/1.33 tff(3604,plain,
% 1.13/1.33 (~b(s(s(z)), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[240, 3595, 3188, 3587, 3591])).
% 1.13/1.33 tff(3605,plain,
% 1.13/1.33 (r(s(s(z)), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[296, 3604])).
% 1.13/1.33 tff(3606,plain,
% 1.13/1.33 (~b(s(z), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[802, 154, 144, 1, 232, 141])).
% 1.13/1.33 tff(3607,plain,
% 1.13/1.33 (r(s(z), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[680, 3606])).
% 1.13/1.33 tff(3608,plain,
% 1.13/1.33 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[476, 443, 1, 3607, 232, 144])).
% 1.13/1.33 tff(3609,plain,
% 1.13/1.33 (r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[441, 3608])).
% 1.13/1.33 tff(3610,plain,
% 1.13/1.33 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[351, 28, 3609, 299])).
% 1.13/1.33 tff(3611,plain,
% 1.13/1.33 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[373, 60, 370, 3610])).
% 1.13/1.33 tff(3612,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3613,plain,
% 1.13/1.33 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3614,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[3613])).
% 1.13/1.33 tff(3615,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[3614, 3612])).
% 1.13/1.33 tff(3616,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(3617,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 1.13/1.33 tff(3618,plain,
% 1.13/1.33 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3617, 28, 3609, 106, 299])).
% 1.13/1.33 tff(3619,plain,
% 1.13/1.33 ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1051, 60, 3618])).
% 1.13/1.33 tff(3620,plain,
% 1.13/1.33 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3619, 1100])).
% 1.13/1.33 tff(3621,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3622,plain,
% 1.13/1.33 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3623,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[3622])).
% 1.13/1.33 tff(3624,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[3623, 3621])).
% 1.13/1.33 tff(3625,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(3626,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[3625, 3624])).
% 1.13/1.33 tff(3627,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3626, 154, 144, 443, 141, 3620, 3611])).
% 1.13/1.33 tff(3628,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3629,plain,
% 1.13/1.33 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3628, 3605, 106, 3188, 3587, 3591, 3595])).
% 1.13/1.33 tff(3630,plain,
% 1.13/1.33 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[496, 3629])).
% 1.13/1.33 tff(3631,plain,
% 1.13/1.33 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[959, 28, 3630, 3603])).
% 1.13/1.33 tff(3632,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[963, 60, 845, 3631])).
% 1.13/1.33 tff(3633,plain,
% 1.13/1.33 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[529, 28, 3630, 3603])).
% 1.13/1.33 tff(3634,plain,
% 1.13/1.33 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[517, 60, 12, 3633])).
% 1.13/1.33 tff(3635,plain,
% 1.13/1.33 (~r(s(s(s(s(z)))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[201, 3593, 3585])).
% 1.13/1.33 tff(3636,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[206, 3635])).
% 1.13/1.33 tff(3637,plain,
% 1.13/1.33 (~b(z, s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3277, 154, 3589, 2877, 3587, 3591])).
% 1.13/1.33 tff(3638,plain,
% 1.13/1.33 (r(z, s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[648, 3637])).
% 1.13/1.33 tff(3639,plain,
% 1.13/1.33 (~r(z, s(s(s(s(elem!1)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1872, 28, 3630, 3638])).
% 1.13/1.33 tff(3640,plain,
% 1.13/1.33 (b(z, s(s(s(s(elem!1)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[548, 3639])).
% 1.13/1.33 tff(3641,plain,
% 1.13/1.33 (~r(s(s(s(s(elem!1)))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3313, 3630, 3638])).
% 1.13/1.33 tff(3642,plain,
% 1.13/1.33 (b(s(s(s(s(elem!1)))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[418, 3641])).
% 1.13/1.33 tff(3643,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3644,plain,
% 1.13/1.33 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.33 inference(rewrite,[status(thm)],[])).
% 1.13/1.33 tff(3645,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.13/1.33 inference(monotonicity,[status(thm)],[3644])).
% 1.13/1.33 tff(3646,plain,
% 1.13/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.33 inference(transitivity,[status(thm)],[3645, 3643])).
% 1.13/1.33 tff(3647,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.13/1.33 inference(quant_inst,[status(thm)],[])).
% 1.13/1.33 tff(3648,plain,
% 1.13/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.33 inference(modus_ponens,[status(thm)],[3647, 3646])).
% 1.13/1.33 tff(3649,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3648, 154, 3642, 3640, 3636, 3634, 3632])).
% 1.13/1.33 tff(3650,plain,((~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3651,plain,
% 1.13/1.33 (~r(s(z), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3650, 106, 12, 17])).
% 1.13/1.33 tff(3652,plain,
% 1.13/1.33 (b(s(z), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1653, 3651])).
% 1.13/1.33 tff(3653,plain,
% 1.13/1.33 (~r(z, s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2080, 124, 106])).
% 1.13/1.33 tff(3654,plain,
% 1.13/1.33 (b(z, s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[648, 3653])).
% 1.13/1.33 tff(3655,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1094, 28, 124, 273, 17])).
% 1.13/1.33 tff(3656,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3657,plain,
% 1.13/1.33 (~r(s(z), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3656, 124, 17])).
% 1.13/1.33 tff(3658,plain,
% 1.13/1.33 (b(s(z), s(s(s(z))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[252, 3657])).
% 1.13/1.33 tff(3659,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3277, 154, 1726, 2604, 1, 232, 660])).
% 1.13/1.33 tff(3660,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3661,plain,
% 1.13/1.33 (~b(s(s(s(z))), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3660, 3658, 2604, 3174, 3654])).
% 1.13/1.33 tff(3662,plain,
% 1.13/1.33 (r(s(s(s(z))), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[818, 3661])).
% 1.13/1.33 tff(3663,plain,
% 1.13/1.33 (~r(s(s(z)), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1125, 3662, 124])).
% 1.13/1.33 tff(3664,plain,
% 1.13/1.33 (b(s(s(z)), s(z))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[296, 3663])).
% 1.13/1.33 tff(3665,plain,
% 1.13/1.33 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3199, 106, 2604, 17])).
% 1.13/1.33 tff(3666,plain,
% 1.13/1.33 (b(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1259, 3665])).
% 1.13/1.33 tff(3667,plain,
% 1.13/1.33 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2514, 154, 3174, 3666, 15])).
% 1.13/1.33 tff(3668,plain,
% 1.13/1.33 (~b(z, s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3667, 3664])).
% 1.13/1.33 tff(3669,plain,
% 1.13/1.33 (r(z, s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[64, 3668])).
% 1.13/1.33 tff(3670,plain,
% 1.13/1.33 (~r(s(s(s(z))), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3186, 106, 17, 2604])).
% 1.13/1.33 tff(3671,plain,
% 1.13/1.33 (b(s(s(s(z))), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[104, 3670])).
% 1.13/1.33 tff(3672,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[2905, 1298, 1296, 2604, 15, 855])).
% 1.13/1.33 tff(3673,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3674,plain,
% 1.13/1.33 (~r(s(s(s(z))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3673, 66, 15, 2604, 820])).
% 1.13/1.33 tff(3675,plain,
% 1.13/1.33 (b(s(s(s(z))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[169, 3674])).
% 1.13/1.33 tff(3676,plain,
% 1.13/1.33 (~b(s(s(s(s(z)))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3063, 855, 2604, 3666, 660, 820, 17, 231, 3675])).
% 1.13/1.33 tff(3677,plain,
% 1.13/1.33 (r(s(s(s(s(z)))), z)),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[206, 3676])).
% 1.13/1.33 tff(3678,plain,
% 1.13/1.33 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3067, 3677, 106])).
% 1.13/1.33 tff(3679,plain,
% 1.13/1.33 (b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[229, 3678])).
% 1.13/1.33 tff(3680,plain,
% 1.13/1.33 ($false),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[1546, 154, 3666, 15, 231, 855, 3679])).
% 1.13/1.33 tff(3681,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.33 tff(3682,plain,
% 1.13/1.33 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.33 inference(unit_resolution,[status(thm)],[3681, 3664, 15, 106, 2604, 3654, 3662, 17])).
% 1.13/1.34 tff(3683,plain,
% 1.13/1.34 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[564, 3682])).
% 1.13/1.34 tff(3684,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3685,plain,
% 1.13/1.34 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3686,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[3685])).
% 1.13/1.34 tff(3687,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[3686, 3684])).
% 1.13/1.34 tff(3688,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(3689,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[3688, 3687])).
% 1.13/1.34 tff(3690,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3689, 154, 232, 15, 141, 1603, 566])).
% 1.13/1.34 tff(3691,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3692,plain,
% 1.13/1.34 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3691, 3683, 15, 3671, 3658])).
% 1.13/1.34 tff(3693,plain,
% 1.13/1.34 (r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[229, 3692])).
% 1.13/1.34 tff(3694,plain,
% 1.13/1.34 (~r(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1251, 3693, 3669])).
% 1.13/1.34 tff(3695,plain,
% 1.13/1.34 (b(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[191, 3694])).
% 1.13/1.34 tff(3696,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3697,plain,
% 1.13/1.34 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3698,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[3697])).
% 1.13/1.34 tff(3699,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[3698, 3696])).
% 1.13/1.34 tff(3700,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(3701,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[3700, 3699])).
% 1.13/1.34 tff(3702,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3701, 154, 2604, 3658, 3654, 3683, 3695])).
% 1.13/1.34 tff(3703,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3704,plain,
% 1.13/1.34 (~r(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3703, 3652, 2877, 106, 17])).
% 1.13/1.34 tff(3705,plain,
% 1.13/1.34 (b(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[138, 3704])).
% 1.13/1.34 tff(3706,plain,
% 1.13/1.34 (~r(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[180, 171, 66])).
% 1.13/1.34 tff(3707,plain,
% 1.13/1.34 (b(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[191, 3706])).
% 1.13/1.34 tff(3708,plain,
% 1.13/1.34 (~r(s(s(s(s(z)))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[201, 171, 66])).
% 1.13/1.34 tff(3709,plain,
% 1.13/1.34 (b(s(s(s(s(z)))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[206, 3708])).
% 1.13/1.34 tff(3710,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3194, 154, 1726, 2604, 3709, 15, 3707])).
% 1.13/1.34 tff(3711,plain,((~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3712,plain,
% 1.13/1.34 (~r(s(s(s(z))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3711, 66, 2877, 3652, 3589])).
% 1.13/1.34 tff(3713,plain,
% 1.13/1.34 (b(s(s(s(z))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[169, 3712])).
% 1.13/1.34 tff(3714,plain,
% 1.13/1.34 (~b(z, s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3217, 1, 2604, 1726, 143])).
% 1.13/1.34 tff(3715,plain,
% 1.13/1.34 (r(z, s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[648, 3714])).
% 1.13/1.34 tff(3716,plain,
% 1.13/1.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3067, 193, 106])).
% 1.13/1.34 tff(3717,plain,
% 1.13/1.34 (b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[229, 3716])).
% 1.13/1.34 tff(3718,plain,
% 1.13/1.34 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3601, 154, 144, 1283, 141, 3717])).
% 1.13/1.34 tff(3719,plain,
% 1.13/1.34 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[343, 3718])).
% 1.13/1.34 tff(3720,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1459, 28, 628, 3719, 193])).
% 1.13/1.34 tff(3721,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3722,plain,
% 1.13/1.34 (~r(s(s(s(s(z)))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3721, 3715, 144, 1283, 141, 106])).
% 1.13/1.34 tff(3723,plain,
% 1.13/1.34 (b(s(s(s(s(z)))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[206, 3722])).
% 1.13/1.34 tff(3724,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3725,plain,
% 1.13/1.34 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3726,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[3725])).
% 1.13/1.34 tff(3727,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[3726, 3724])).
% 1.13/1.34 tff(3728,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(3729,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[3728, 3727])).
% 1.13/1.34 tff(3730,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3729, 154, 144, 143, 615, 1299, 1283])).
% 1.13/1.34 tff(3731,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3732,plain,
% 1.13/1.34 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3731, 3723, 144, 143, 1283])).
% 1.13/1.34 tff(3733,plain,
% 1.13/1.34 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[343, 3732])).
% 1.13/1.34 tff(3734,plain,
% 1.13/1.34 (~r(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1467, 28, 3715, 3733])).
% 1.13/1.34 tff(3735,plain,
% 1.13/1.34 (b(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[191, 3734])).
% 1.13/1.34 tff(3736,plain,
% 1.13/1.34 (~b(s(z), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3184, 1, 2604, 1726, 143])).
% 1.13/1.34 tff(3737,plain,
% 1.13/1.34 (r(s(z), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[252, 3736])).
% 1.13/1.34 tff(3738,plain,
% 1.13/1.34 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1586, 28, 3737, 3733])).
% 1.13/1.34 tff(3739,plain,
% 1.13/1.34 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[318, 3738])).
% 1.13/1.34 tff(3740,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2905, 3739, 3735, 2604, 15, 3723])).
% 1.13/1.34 tff(3741,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3742,plain,
% 1.13/1.34 (~b(s(s(s(z))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3741, 3713, 3652, 3705, 2877, 3201, 3188, 106, 3589])).
% 1.13/1.34 tff(3743,plain,
% 1.13/1.34 (r(s(s(s(z))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[818, 3742])).
% 1.13/1.34 tff(3744,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3745,plain,
% 1.13/1.34 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3746,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[3745])).
% 1.13/1.34 tff(3747,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[3746, 3744])).
% 1.13/1.34 tff(3748,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(3749,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.13/1.34 tff(3750,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3749, 28, 820, 628, 172, 66])).
% 1.13/1.34 tff(3751,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3752,plain,
% 1.13/1.34 (~r(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3751, 820, 628, 66])).
% 1.13/1.34 tff(3753,plain,
% 1.13/1.34 (b(z, s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[191, 3752])).
% 1.13/1.34 tff(3754,plain,
% 1.13/1.34 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[853, 820, 66])).
% 1.13/1.34 tff(3755,plain,
% 1.13/1.34 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[318, 3754])).
% 1.13/1.34 tff(3756,plain,
% 1.13/1.34 (~r(s(z), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1930, 820, 66])).
% 1.13/1.34 tff(3757,plain,
% 1.13/1.34 (b(s(z), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1653, 3756])).
% 1.13/1.34 tff(3758,plain,
% 1.13/1.34 (~r(z, s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[838, 820, 628])).
% 1.13/1.34 tff(3759,plain,
% 1.13/1.34 (b(z, s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1181, 3758])).
% 1.13/1.34 tff(3760,plain,
% 1.13/1.34 (~b(s(s(s(s(z)))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2189, 154, 3759, 3757, 3755, 3753])).
% 1.13/1.34 tff(3761,plain,
% 1.13/1.34 (r(s(s(s(s(z)))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[206, 3760])).
% 1.13/1.34 tff(3762,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3763,plain,
% 1.13/1.34 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3764,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[3763])).
% 1.13/1.34 tff(3765,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[3764, 3762])).
% 1.13/1.34 tff(3766,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(3767,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 1.13/1.34 tff(3768,plain,
% 1.13/1.34 ((~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3767, 154, 3759, 3757, 3755])).
% 1.13/1.34 tff(3769,plain,
% 1.13/1.34 (~b(s(z), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3768, 3753])).
% 1.13/1.34 tff(3770,plain,
% 1.13/1.34 (r(s(z), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[271, 3769])).
% 1.13/1.34 tff(3771,plain,
% 1.13/1.34 (~r(s(z), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1976, 3770, 628])).
% 1.13/1.34 tff(3772,plain,
% 1.13/1.34 (b(s(z), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[252, 3771])).
% 1.13/1.34 tff(3773,plain,
% 1.13/1.34 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[923, 106, 193])).
% 1.13/1.34 tff(3774,plain,
% 1.13/1.34 (b(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1259, 3773])).
% 1.13/1.34 tff(3775,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1389, 2268, 3774, 506, 15, 684])).
% 1.13/1.34 tff(3776,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3777,plain,
% 1.13/1.34 (~r(s(s(z)), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3776, 684, 3757, 3755, 13, 193])).
% 1.13/1.34 tff(3778,plain,
% 1.13/1.34 (b(s(s(z)), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[122, 3777])).
% 1.13/1.34 tff(3779,plain,
% 1.13/1.34 (~b(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1512, 3778, 232, 2468, 684])).
% 1.13/1.34 tff(3780,plain,
% 1.13/1.34 (r(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[138, 3779])).
% 1.13/1.34 tff(3781,plain,
% 1.13/1.34 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[132, 3780, 66])).
% 1.13/1.34 tff(3782,plain,
% 1.13/1.34 (b(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1259, 3781])).
% 1.13/1.34 tff(3783,plain,
% 1.13/1.34 (~r(s(s(z)), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1125, 3780, 820])).
% 1.13/1.34 tff(3784,plain,
% 1.13/1.34 (b(s(s(z)), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[296, 3783])).
% 1.13/1.34 tff(3785,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1389, 3784, 3782, 3755, 3757, 684])).
% 1.13/1.34 tff(3786,plain,((~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3787,plain,
% 1.13/1.34 (~b(s(z), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3786, 820, 66, 3772, 3770, 3761])).
% 1.13/1.34 tff(3788,plain,
% 1.13/1.34 (r(s(z), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[680, 3787])).
% 1.13/1.34 tff(3789,plain,
% 1.13/1.34 (~r(s(s(s(z))), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1556, 3788, 820])).
% 1.13/1.34 tff(3790,plain,
% 1.13/1.34 (b(s(s(s(z))), s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[104, 3789])).
% 1.13/1.34 tff(3791,plain,
% 1.13/1.34 (~r(s(s(s(z))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1268, 3770, 820])).
% 1.13/1.34 tff(3792,plain,
% 1.13/1.34 (b(s(s(s(z))), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[169, 3791])).
% 1.13/1.34 tff(3793,plain,
% 1.13/1.34 (~r(z, s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[36, 3788, 3770])).
% 1.13/1.34 tff(3794,plain,
% 1.13/1.34 (b(z, s(s(z)))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[64, 3793])).
% 1.13/1.34 tff(3795,plain,
% 1.13/1.34 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3027, 3792, 3790, 3794, 3753])).
% 1.13/1.34 tff(3796,plain,
% 1.13/1.34 (r(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1259, 3795])).
% 1.13/1.34 tff(3797,plain,
% 1.13/1.34 (~r(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[132, 3796, 66])).
% 1.13/1.34 tff(3798,plain,
% 1.13/1.34 (b(s(s(z)), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[138, 3797])).
% 1.13/1.34 tff(3799,plain,
% 1.13/1.34 (~r(s(s(z)), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[923, 3796, 3761])).
% 1.13/1.34 tff(3800,plain,
% 1.13/1.34 (b(s(s(z)), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[122, 3799])).
% 1.13/1.34 tff(3801,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[162, 3800, 3798, 3794, 3792, 3790])).
% 1.13/1.34 tff(3802,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3803,plain,
% 1.13/1.34 (~r(z, s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3802, 3743, 66])).
% 1.13/1.34 tff(3804,plain,
% 1.13/1.34 (b(z, s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[648, 3803])).
% 1.13/1.34 tff(3805,plain,
% 1.13/1.34 (~b(s(s(z)), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3681, 3804, 3652, 106, 2877, 66, 3743, 17])).
% 1.13/1.34 tff(3806,plain,
% 1.13/1.34 (r(s(s(z)), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[296, 3805])).
% 1.13/1.34 tff(3807,plain,
% 1.13/1.34 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[2354, 2340, 820, 144, 299])).
% 1.13/1.34 tff(3808,plain,
% 1.13/1.34 (b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[441, 3807])).
% 1.13/1.34 tff(3809,plain,
% 1.13/1.34 (~r(s(z), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[702, 299, 106])).
% 1.13/1.34 tff(3810,plain,
% 1.13/1.34 (b(s(z), z)),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[271, 3809])).
% 1.13/1.34 tff(3811,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.13/1.34 tff(3812,plain,
% 1.13/1.34 (~r(z, s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[881, 299, 820])).
% 1.13/1.34 tff(3813,plain,
% 1.13/1.34 (b(z, s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[1181, 3812])).
% 1.13/1.34 tff(3814,plain,
% 1.13/1.34 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3321, 154, 3813, 3811, 3810, 3808])).
% 1.13/1.34 tff(3815,plain,
% 1.13/1.34 (r(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[467, 3814])).
% 1.13/1.34 tff(3816,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3817,plain,
% 1.13/1.34 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.34 inference(rewrite,[status(thm)],[])).
% 1.13/1.34 tff(3818,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.13/1.34 inference(monotonicity,[status(thm)],[3817])).
% 1.13/1.34 tff(3819,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.34 inference(transitivity,[status(thm)],[3818, 3816])).
% 1.13/1.34 tff(3820,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.13/1.34 inference(quant_inst,[status(thm)],[])).
% 1.13/1.34 tff(3821,plain,
% 1.13/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.13/1.34 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 1.13/1.34 tff(3822,plain,
% 1.13/1.34 ($false),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3821, 28, 535, 299, 1476])).
% 1.13/1.34 tff(3823,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.34 tff(3824,plain,
% 1.13/1.34 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[3823, 3815, 299])).
% 1.13/1.34 tff(3825,plain,
% 1.13/1.34 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[373, 60, 370, 3824])).
% 1.13/1.34 tff(3826,plain,
% 1.13/1.34 (~r(s(z), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[788, 780, 3815])).
% 1.13/1.34 tff(3827,plain,
% 1.13/1.34 (b(s(z), s(s(s(z))))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[252, 3826])).
% 1.13/1.34 tff(3828,plain,
% 1.13/1.34 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.34 inference(unit_resolution,[status(thm)],[317, 854, 313])).
% 1.13/1.34 tff(3829,plain,
% 1.13/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3830,plain,
% 1.13/1.35 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3831,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3830])).
% 1.13/1.35 tff(3832,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[3831, 3829])).
% 1.13/1.35 tff(3833,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3834,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3833, 3832])).
% 1.13/1.35 tff(3835,plain,
% 1.13/1.35 ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3834, 154, 1726, 2604, 1299])).
% 1.13/1.35 tff(3836,plain,
% 1.13/1.35 (~b(z, s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3835, 3828])).
% 1.13/1.35 tff(3837,plain,
% 1.13/1.35 (r(z, s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[191, 3836])).
% 1.13/1.35 tff(3838,plain,
% 1.13/1.35 (~b(z, s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3057, 3828, 2604, 1299, 232])).
% 1.13/1.35 tff(3839,plain,
% 1.13/1.35 (r(z, s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[648, 3838])).
% 1.13/1.35 tff(3840,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3225, 28, 3839, 3837, 66])).
% 1.13/1.35 tff(3841,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3842,plain,
% 1.13/1.35 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3841, 1299, 3810, 3813, 3827, 820])).
% 1.13/1.35 tff(3843,plain,
% 1.13/1.35 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[564, 3842])).
% 1.13/1.35 tff(3844,plain,
% 1.13/1.35 (~b(s(z), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3194, 154, 1726, 3810, 1703, 1697])).
% 1.13/1.35 tff(3845,plain,
% 1.13/1.35 (r(s(z), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1372, 3844, 1361])).
% 1.13/1.35 tff(3846,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1824, 28, 16, 299, 3845])).
% 1.13/1.35 tff(3847,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3848,plain,
% 1.13/1.35 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3847, 299, 3813, 106])).
% 1.13/1.35 tff(3849,plain,
% 1.13/1.35 (b(s(s(z)), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[1259, 3848])).
% 1.13/1.35 tff(3850,plain,
% 1.13/1.35 (~b(s(s(s(z))), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[2553, 1299, 144, 3849, 3843])).
% 1.13/1.35 tff(3851,plain,
% 1.13/1.35 (r(s(s(s(z))), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[169, 3850])).
% 1.13/1.35 tff(3852,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.13/1.35 tff(3853,plain,
% 1.13/1.35 (~r(s(z), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[788, 780, 535])).
% 1.13/1.35 tff(3854,plain,
% 1.13/1.35 (b(s(z), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[252, 3853])).
% 1.13/1.35 tff(3855,plain,
% 1.13/1.35 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3841, 1299, 2604, 3813, 3854, 820])).
% 1.13/1.35 tff(3856,plain,
% 1.13/1.35 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[564, 3855])).
% 1.13/1.35 tff(3857,plain,
% 1.13/1.35 (~b(s(s(s(z))), z)),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[2553, 1299, 144, 1283, 3856])).
% 1.13/1.35 tff(3858,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.13/1.35 tff(3859,plain,
% 1.13/1.35 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3858])).
% 1.13/1.35 tff(3860,plain,
% 1.13/1.35 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.13/1.35 inference(symmetry,[status(thm)],[3859])).
% 1.13/1.35 tff(3861,plain,
% 1.13/1.35 ((~b(s(s(s(z))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3860])).
% 1.13/1.35 tff(3862,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.13/1.35 tff(3863,plain,
% 1.13/1.35 (~b(s(s(s(elem!1))), z)),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 1.13/1.35 tff(3864,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3852, 3863])).
% 1.13/1.35 tff(3865,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3866,plain,
% 1.13/1.35 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3865, 3852, 3857])).
% 1.13/1.35 tff(3867,plain,
% 1.13/1.35 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.13/1.35 inference(commutativity,[status(thm)],[])).
% 1.13/1.35 tff(3868,plain,
% 1.13/1.35 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(symmetry,[status(thm)],[3867])).
% 1.13/1.35 tff(3869,plain,
% 1.13/1.35 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3868])).
% 1.13/1.35 tff(3870,plain,
% 1.13/1.35 (~(z = s(s(s(s(elem!1)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[388, 3869])).
% 1.13/1.35 tff(3871,plain,
% 1.13/1.35 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[2354, 299, 141, 144, 820])).
% 1.13/1.35 tff(3872,plain,
% 1.13/1.35 (b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[441, 3871])).
% 1.13/1.35 tff(3873,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.35 tff(3874,plain,
% 1.13/1.35 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.13/1.35 inference(commutativity,[status(thm)],[])).
% 1.13/1.35 tff(3875,plain,
% 1.13/1.35 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.13/1.35 inference(symmetry,[status(thm)],[3874])).
% 1.13/1.35 tff(3876,plain,
% 1.13/1.35 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3875])).
% 1.13/1.35 tff(3877,plain,
% 1.13/1.35 (~(s(s(s(elem!1))) = s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[368, 3876])).
% 1.13/1.35 tff(3878,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.13/1.35 tff(3879,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.13/1.35 tff(3880,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.13/1.35 tff(3881,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3882,plain,
% 1.13/1.35 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3883,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3882])).
% 1.13/1.35 tff(3884,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[3883, 3881])).
% 1.13/1.35 tff(3885,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3886,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 1.13/1.35 tff(3887,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3886, 28, 299, 3879, 3880])).
% 1.13/1.35 tff(3888,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3889,plain,
% 1.13/1.35 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3888, 3879, 299])).
% 1.13/1.35 tff(3890,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 1.13/1.35 tff(3891,plain,
% 1.13/1.35 (s(s(z)) = s(s(s(elem!1)))),
% 1.13/1.35 inference(symmetry,[status(thm)],[3890])).
% 1.13/1.35 tff(3892,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.35 tff(3893,plain,
% 1.13/1.35 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3892])).
% 1.13/1.35 tff(3894,plain,
% 1.13/1.35 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.13/1.35 inference(symmetry,[status(thm)],[3893])).
% 1.13/1.35 tff(3895,plain,
% 1.13/1.35 (s(s(elem!1)) = s(z)),
% 1.13/1.35 inference(transitivity,[status(thm)],[363, 3894, 81])).
% 1.13/1.35 tff(3896,plain,
% 1.13/1.35 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.13/1.35 inference(commutativity,[status(thm)],[])).
% 1.13/1.35 tff(3897,plain,
% 1.13/1.35 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3896])).
% 1.13/1.35 tff(3898,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.35 tff(3899,plain,
% 1.13/1.35 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3898])).
% 1.13/1.35 tff(3900,plain,
% 1.13/1.35 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.13/1.35 inference(symmetry,[status(thm)],[3899])).
% 1.13/1.35 tff(3901,plain,
% 1.13/1.35 (s(elem!1) = z),
% 1.13/1.35 inference(transitivity,[status(thm)],[486, 3900, 91])).
% 1.13/1.35 tff(3902,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[489, 3901])).
% 1.13/1.35 tff(3903,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3904,plain,
% 1.13/1.35 (~(s(s(elem!1)) = s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3903, 3897])).
% 1.13/1.35 tff(3905,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3904, 3895])).
% 1.13/1.35 tff(3906,plain,(~(s(s(z)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3907,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3906, 3891])).
% 1.13/1.35 tff(3908,plain,(~(s(s(s(elem!1))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3909,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3910,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3911,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3910, 3909])).
% 1.13/1.35 tff(3912,plain,
% 1.13/1.35 (b(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3911, 60, 3908, 3889])).
% 1.13/1.35 tff(3913,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3914,plain,
% 1.13/1.35 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3915,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3914])).
% 1.13/1.35 tff(3916,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[3915, 3913])).
% 1.13/1.35 tff(3917,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3918,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 1.13/1.35 tff(3919,plain,
% 1.13/1.35 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3918, 28, 299, 3879])).
% 1.13/1.35 tff(3920,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3921,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3922,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3921, 3920])).
% 1.13/1.35 tff(3923,plain,
% 1.13/1.35 (b(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3922, 60, 3906, 3919])).
% 1.13/1.35 tff(3924,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3925,plain,
% 1.13/1.35 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3926,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3925])).
% 1.13/1.35 tff(3927,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[3926, 3924])).
% 1.13/1.35 tff(3928,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3929,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 1.13/1.35 tff(3930,plain,
% 1.13/1.35 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3929, 28, 820, 3879])).
% 1.13/1.35 tff(3931,assumption,(~r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.13/1.35 tff(3932,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.13/1.35 tff(3933,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3934,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3935,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3934, 3933])).
% 1.13/1.35 tff(3936,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3935, 60, 3878, 3932, 3931])).
% 1.13/1.35 tff(3937,plain,(b(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3938,plain,
% 1.13/1.35 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3937, 3930, 3878])).
% 1.13/1.35 tff(3939,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3940,plain,
% 1.13/1.35 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3941,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.13/1.35 inference(monotonicity,[status(thm)],[3940])).
% 1.13/1.35 tff(3942,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.35 inference(transitivity,[status(thm)],[3941, 3939])).
% 1.13/1.35 tff(3943,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3944,plain,
% 1.13/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3943, 3942])).
% 1.13/1.35 tff(3945,plain,
% 1.13/1.35 ($false),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3944, 154, 144, 3938, 141, 3923, 3912])).
% 1.13/1.35 tff(3946,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.35 tff(3947,plain,
% 1.13/1.35 (~r(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3946, 299, 141, 3878, 820, 144])).
% 1.13/1.35 tff(3948,plain,
% 1.13/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.35 tff(3949,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.13/1.35 inference(quant_inst,[status(thm)],[])).
% 1.13/1.35 tff(3950,plain,
% 1.13/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(modus_ponens,[status(thm)],[3949, 3948])).
% 1.13/1.35 tff(3951,plain,
% 1.13/1.35 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3950, 60, 3947])).
% 1.13/1.35 tff(3952,plain,
% 1.13/1.35 (b(s(s(s(elem!1))), s(z))),
% 1.13/1.35 inference(unit_resolution,[status(thm)],[3951, 3877])).
% 1.13/1.35 tff(3953,plain,
% 1.13/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.35 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3954,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(3955,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 1.13/1.36 tff(3956,plain,
% 1.13/1.36 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3955, 154, 3852, 2604, 3872, 3952])).
% 1.13/1.36 tff(3957,plain,
% 1.13/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3958,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(3959,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[3958, 3957])).
% 1.13/1.36 tff(3960,plain,
% 1.13/1.36 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3959, 60, 3956, 3873])).
% 1.13/1.36 tff(3961,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3962,plain,
% 1.13/1.36 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3963,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[3962])).
% 1.13/1.36 tff(3964,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[3963, 3961])).
% 1.13/1.36 tff(3965,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(3966,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[3965, 3964])).
% 1.13/1.36 tff(3967,plain,
% 1.13/1.36 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3966, 154, 3852, 3813, 2604])).
% 1.13/1.36 tff(3968,plain,
% 1.13/1.36 (~b(z, s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3967, 3952])).
% 1.13/1.36 tff(3969,plain,
% 1.13/1.36 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.13/1.36 inference(commutativity,[status(thm)],[])).
% 1.13/1.36 tff(3970,plain,
% 1.13/1.36 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[3969])).
% 1.13/1.36 tff(3971,plain,
% 1.13/1.36 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[3970])).
% 1.13/1.36 tff(3972,plain,
% 1.13/1.36 (~(z = s(s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[434, 3971])).
% 1.13/1.36 tff(3973,plain,
% 1.13/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3974,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(3975,plain,
% 1.13/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[3974, 3973])).
% 1.13/1.36 tff(3976,plain,
% 1.13/1.36 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3975, 60])).
% 1.13/1.36 tff(3977,plain,
% 1.13/1.36 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3976, 3972])).
% 1.13/1.36 tff(3978,plain,
% 1.13/1.36 (r(z, s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3977, 3968])).
% 1.13/1.36 tff(3979,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3980,plain,
% 1.13/1.36 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(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)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3981,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1)))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[3980])).
% 1.13/1.36 tff(3982,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[3981, 3979])).
% 1.13/1.36 tff(3983,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(3984,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(elem!1)))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[3983, 3982])).
% 1.13/1.36 tff(3985,plain,
% 1.13/1.36 (~r(s(s(s(s(elem!1)))), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3984, 28, 3978, 3960])).
% 1.13/1.36 tff(3986,plain,
% 1.13/1.36 (b(s(s(s(s(elem!1)))), z)),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[416, 60, 388, 3985])).
% 1.13/1.36 tff(3987,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3988,plain,
% 1.13/1.36 (((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3989,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[3988])).
% 1.13/1.36 tff(3990,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[3989, 3987])).
% 1.13/1.36 tff(3991,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(3992,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 1.13/1.36 tff(3993,plain,
% 1.13/1.36 (~b(z, s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3992, 154, 3813, 3986, 2604, 3872])).
% 1.13/1.36 tff(3994,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3995,plain,
% 1.13/1.36 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(3996,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[3995])).
% 1.13/1.36 tff(3997,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[3996, 3994])).
% 1.13/1.36 tff(3998,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(3999,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 1.13/1.36 tff(4000,plain,
% 1.13/1.36 (~r(z, s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3999, 28, 3978, 3960])).
% 1.13/1.36 tff(4001,plain,
% 1.13/1.36 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[400, 60, 4000])).
% 1.13/1.36 tff(4002,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4001, 3993, 3870])).
% 1.13/1.36 tff(4003,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4004,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4003, 3866, 299, 3852, 2340, 144, 820, 2604])).
% 1.13/1.36 tff(4005,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.36 tff(4006,plain,
% 1.13/1.36 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4005])).
% 1.13/1.36 tff(4007,plain,
% 1.13/1.36 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4006])).
% 1.13/1.36 tff(4008,plain,
% 1.13/1.36 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[363, 4007, 354])).
% 1.13/1.36 tff(4009,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.36 tff(4010,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4009, 4008])).
% 1.13/1.36 tff(4011,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4012,plain,
% 1.13/1.36 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4011, 4004])).
% 1.13/1.36 tff(4013,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.36 tff(4014,plain,
% 1.13/1.36 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4013])).
% 1.13/1.36 tff(4015,plain,
% 1.13/1.36 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[486, 4014, 362, 4013])).
% 1.13/1.36 tff(4016,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.36 tff(4017,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4016, 4015])).
% 1.13/1.36 tff(4018,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4019,plain,
% 1.13/1.36 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4018, 4012])).
% 1.13/1.36 tff(4020,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.36 tff(4021,plain,
% 1.13/1.36 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4020])).
% 1.13/1.36 tff(4022,plain,
% 1.13/1.36 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.13/1.36 inference(quant_inst,[status(thm)],[])).
% 1.13/1.36 tff(4023,plain,
% 1.13/1.36 (inj_0(s(elem!1)) = elem!1),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4022, 9])).
% 1.13/1.36 tff(4024,plain,
% 1.13/1.36 (elem!1 = inj_0(s(elem!1))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4023])).
% 1.13/1.36 tff(4025,plain,
% 1.13/1.36 (elem!1 = s(s(elem!1))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4024, 4021, 362])).
% 1.13/1.36 tff(4026,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.36 tff(4027,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4026, 4025])).
% 1.13/1.36 tff(4028,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4029,plain,
% 1.13/1.36 (elem!1 = s(s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4028, 4019])).
% 1.13/1.36 tff(4030,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(4031,plain,
% 1.13/1.36 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4030])).
% 1.13/1.36 tff(4032,plain,
% 1.13/1.36 (s(s(s(elem!1))) = s(elem!1)),
% 1.13/1.36 inference(symmetry,[status(thm)],[4031])).
% 1.13/1.36 tff(4033,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4032])).
% 1.13/1.36 tff(4034,plain,
% 1.13/1.36 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4033])).
% 1.13/1.36 tff(4035,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.36 tff(4036,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4035, 4034])).
% 1.13/1.36 tff(4037,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4038,plain,
% 1.13/1.36 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4037, 4029])).
% 1.13/1.36 tff(4039,plain,
% 1.13/1.36 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4012])).
% 1.13/1.36 tff(4040,plain,
% 1.13/1.36 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4039, 4038])).
% 1.13/1.36 tff(4041,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.36 tff(4042,plain,
% 1.13/1.36 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4041])).
% 1.13/1.36 tff(4043,plain,
% 1.13/1.36 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[363, 4042, 354, 4041])).
% 1.13/1.36 tff(4044,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4035, 4043])).
% 1.13/1.36 tff(4045,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4046,plain,
% 1.13/1.36 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4045, 4041])).
% 1.13/1.36 tff(4047,plain,
% 1.13/1.36 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(commutativity,[status(thm)],[])).
% 1.13/1.36 tff(4048,plain,
% 1.13/1.36 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4047])).
% 1.13/1.36 tff(4049,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.36 tff(4050,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 1.13/1.36 tff(4051,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.36 tff(4052,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4051, 4050])).
% 1.13/1.36 tff(4053,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4054,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4053, 4046])).
% 1.13/1.36 tff(4055,plain,
% 1.13/1.36 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.13/1.36 inference(commutativity,[status(thm)],[])).
% 1.13/1.36 tff(4056,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.36 tff(4057,plain,
% 1.13/1.36 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4056])).
% 1.13/1.36 tff(4058,plain,
% 1.13/1.36 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4057, 4055])).
% 1.13/1.36 tff(4059,plain,
% 1.13/1.36 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.13/1.36 inference(symmetry,[status(thm)],[4058])).
% 1.13/1.36 tff(4060,plain,
% 1.13/1.36 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4056])).
% 1.13/1.36 tff(4061,plain,
% 1.13/1.36 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4060])).
% 1.13/1.36 tff(4062,plain,
% 1.13/1.36 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[486, 4061, 354])).
% 1.13/1.36 tff(4063,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4016, 4062])).
% 1.13/1.36 tff(4064,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4065,plain,
% 1.13/1.36 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4064, 4056])).
% 1.13/1.36 tff(4066,plain,
% 1.13/1.36 (elem!1 = s(s(elem!1))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4028, 4065])).
% 1.13/1.36 tff(4067,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = elem!1),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4066, 4059])).
% 1.13/1.36 tff(4068,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.13/1.36 tff(4069,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4068, 4067])).
% 1.13/1.36 tff(4070,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4071,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = elem!1),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4070, 4054])).
% 1.13/1.36 tff(4072,plain,
% 1.13/1.36 (elem!1 = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4071])).
% 1.13/1.36 tff(4073,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.13/1.36 tff(4074,plain,
% 1.13/1.36 (s(s(s(s(z)))) = elem!1),
% 1.13/1.36 inference(symmetry,[status(thm)],[4073])).
% 1.13/1.36 tff(4075,plain,
% 1.13/1.36 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4074, 4072])).
% 1.13/1.36 tff(4076,plain,
% 1.13/1.36 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4075])).
% 1.13/1.36 tff(4077,plain,
% 1.13/1.36 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[220, 4076, 354, 4041])).
% 1.13/1.36 tff(4078,plain,
% 1.13/1.36 ($false),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[984, 4077])).
% 1.13/1.36 tff(4079,plain,((~(elem!1 = s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.36 tff(4080,plain,
% 1.13/1.36 (~(elem!1 = s(s(s(s(z)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[4079, 4040])).
% 1.13/1.36 tff(4081,plain,
% 1.13/1.36 (s(s(elem!1)) = elem!1),
% 1.13/1.36 inference(symmetry,[status(thm)],[4029])).
% 1.13/1.36 tff(4082,plain,
% 1.13/1.36 (s(s(s(elem!1))) = elem!1),
% 1.13/1.36 inference(transitivity,[status(thm)],[4039, 4081])).
% 1.13/1.36 tff(4083,plain,
% 1.13/1.36 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4082])).
% 1.13/1.36 tff(4084,plain,
% 1.13/1.36 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4083])).
% 1.13/1.36 tff(4085,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.13/1.36 inference(symmetry,[status(thm)],[4038])).
% 1.13/1.36 tff(4086,plain,
% 1.13/1.36 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4085, 4012])).
% 1.13/1.36 tff(4087,plain,
% 1.13/1.36 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4086])).
% 1.13/1.36 tff(4088,plain,
% 1.13/1.36 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[3823, 535, 299])).
% 1.13/1.36 tff(4089,plain,
% 1.13/1.36 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.36 inference(unit_resolution,[status(thm)],[373, 60, 370, 4088])).
% 1.13/1.36 tff(4090,plain,
% 1.13/1.36 (b(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.36 inference(modus_ponens,[status(thm)],[4089, 4087])).
% 1.13/1.36 tff(4091,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4092,plain,
% 1.13/1.36 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.36 inference(rewrite,[status(thm)],[])).
% 1.13/1.36 tff(4093,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.13/1.36 inference(monotonicity,[status(thm)],[4092])).
% 1.13/1.36 tff(4094,plain,
% 1.13/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.36 inference(transitivity,[status(thm)],[4093, 4091])).
% 1.13/1.36 tff(4095,plain,
% 1.13/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(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))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4096,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4095, 4094])).
% 1.13/1.37 tff(4097,plain,
% 1.13/1.37 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4096, 154, 3852, 1299, 1283, 4090])).
% 1.13/1.37 tff(4098,plain,
% 1.13/1.37 (~b(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4097, 4084])).
% 1.13/1.37 tff(4099,plain,
% 1.13/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4100,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4101,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4100, 4099])).
% 1.13/1.37 tff(4102,plain,
% 1.13/1.37 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4101, 60])).
% 1.13/1.37 tff(4103,plain,
% 1.13/1.37 (r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4102, 4098, 4080])).
% 1.13/1.37 tff(4104,plain,
% 1.13/1.37 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4018, 4013])).
% 1.13/1.37 tff(4105,plain,
% 1.13/1.37 (elem!1 = s(s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4028, 4104])).
% 1.13/1.37 tff(4106,plain,
% 1.13/1.37 (s(s(elem!1)) = elem!1),
% 1.13/1.37 inference(symmetry,[status(thm)],[4105])).
% 1.13/1.37 tff(4107,plain,
% 1.13/1.37 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4013])).
% 1.13/1.37 tff(4108,plain,
% 1.13/1.37 (s(s(s(elem!1))) = elem!1),
% 1.13/1.37 inference(transitivity,[status(thm)],[4107, 4106])).
% 1.13/1.37 tff(4109,plain,
% 1.13/1.37 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4108])).
% 1.13/1.37 tff(4110,plain,
% 1.13/1.37 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4109])).
% 1.13/1.37 tff(4111,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(4112,plain,
% 1.13/1.37 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4111, 4110])).
% 1.13/1.37 tff(4113,assumption,(~r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(4114,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4113, 4112])).
% 1.13/1.37 tff(4115,plain,(r(s(s(s(elem!1))), s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4116,plain,
% 1.13/1.37 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4115, 4103, 4012])).
% 1.13/1.37 tff(4117,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4012])).
% 1.13/1.37 tff(4118,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4034])).
% 1.13/1.37 tff(4119,plain,
% 1.13/1.37 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.37 inference(symmetry,[status(thm)],[4118])).
% 1.13/1.37 tff(4120,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[780, 4119])).
% 1.13/1.37 tff(4121,assumption,(~r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.13/1.37 tff(4122,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4121, 4120])).
% 1.13/1.37 tff(4123,plain,(r(s(s(elem!1)), s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4124,plain,
% 1.13/1.37 (r(s(s(elem!1)), s(s(s(z))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4123, 4029, 780])).
% 1.13/1.37 tff(4125,plain,
% 1.13/1.37 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4124, 4117])).
% 1.13/1.37 tff(4126,plain,
% 1.13/1.37 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4086])).
% 1.13/1.37 tff(4127,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), s(z))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[3808, 4126])).
% 1.13/1.37 tff(4128,plain,
% 1.13/1.37 (~b(z, s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[3966, 154, 3852, 3813, 2604, 4127])).
% 1.13/1.37 tff(4129,plain,
% 1.13/1.37 (r(z, s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[3977, 4128])).
% 1.13/1.37 tff(4130,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.37 tff(4131,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.13/1.37 tff(4132,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.37 tff(4133,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4134,plain,
% 1.13/1.37 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4135,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4134])).
% 1.13/1.37 tff(4136,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4135, 4133])).
% 1.13/1.37 tff(4137,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4138,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4137, 4136])).
% 1.13/1.37 tff(4139,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4138, 28, 4132, 172, 4131, 4130])).
% 1.13/1.37 tff(4140,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4141,plain,
% 1.13/1.37 (~r(z, s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4140, 4129, 4125, 4116])).
% 1.13/1.37 tff(4142,plain,
% 1.13/1.37 (b(z, s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[191, 4141])).
% 1.13/1.37 tff(4143,plain,
% 1.13/1.37 (~b(s(z), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[3194, 154, 3813, 2604, 1299, 4142])).
% 1.13/1.37 tff(4144,plain,
% 1.13/1.37 (r(s(z), s(s(s(s(z)))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[1372, 4143, 1361])).
% 1.13/1.37 tff(4145,plain,
% 1.13/1.37 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(elem!1))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4086])).
% 1.13/1.37 tff(4146,plain,
% 1.13/1.37 (r(s(z), s(s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[535, 4145])).
% 1.13/1.37 tff(4147,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4148,plain,
% 1.13/1.37 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4149,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4148])).
% 1.13/1.37 tff(4150,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4149, 4147])).
% 1.13/1.37 tff(4151,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4152,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 1.13/1.37 tff(4153,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4152, 28, 4146, 4125, 4144, 4116])).
% 1.13/1.37 tff(4154,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4155,plain,
% 1.13/1.37 (~b(s(s(s(elem!1))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4154, 1299, 3810, 3849, 3815, 780, 299, 144, 820])).
% 1.13/1.37 tff(4156,plain,
% 1.13/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4157,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4158,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4157, 4156])).
% 1.13/1.37 tff(4159,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4158, 60, 434])).
% 1.13/1.37 tff(4160,plain,
% 1.13/1.37 (r(s(s(s(elem!1))), z)),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4159, 4155])).
% 1.13/1.37 tff(4161,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.13/1.37 tff(4162,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4163,plain,
% 1.13/1.37 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4164,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4163])).
% 1.13/1.37 tff(4165,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4164, 4162])).
% 1.13/1.37 tff(4166,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4167,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4166, 4165])).
% 1.13/1.37 tff(4168,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4167, 28, 4161, 106, 3880])).
% 1.13/1.37 tff(4169,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4170,plain,
% 1.13/1.37 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4169, 4160, 106])).
% 1.13/1.37 tff(4171,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.13/1.37 tff(4172,assumption,(~b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.13/1.37 tff(4173,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[3911, 60, 3908, 4172, 4171])).
% 1.13/1.37 tff(4174,plain,(b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4175,plain,
% 1.13/1.37 (b(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4174, 4170])).
% 1.13/1.37 tff(4176,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.13/1.37 tff(4177,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4178,plain,
% 1.13/1.37 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4179,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4178])).
% 1.13/1.37 tff(4180,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4179, 4177])).
% 1.13/1.37 tff(4181,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4182,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4181, 4180])).
% 1.13/1.37 tff(4183,plain,
% 1.13/1.37 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4182, 28, 4161, 106])).
% 1.13/1.37 tff(4184,plain,
% 1.13/1.37 (b(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[3922, 60, 3906, 4183])).
% 1.13/1.37 tff(4185,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.37 tff(4186,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.37 tff(4187,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4188,plain,
% 1.13/1.37 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4189,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4188])).
% 1.13/1.37 tff(4190,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4189, 4187])).
% 1.13/1.37 tff(4191,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4192,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4191, 4190])).
% 1.13/1.37 tff(4193,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4192, 28, 4161, 4186, 171])).
% 1.13/1.37 tff(4194,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4195,plain,
% 1.13/1.37 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4194, 4161, 171])).
% 1.13/1.37 tff(4196,assumption,(~r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.37 tff(4197,assumption,(~b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.37 tff(4198,plain,
% 1.13/1.37 (((~![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)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4199,plain,
% 1.13/1.37 ((~![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)))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4200,plain,
% 1.13/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 1.13/1.37 tff(4201,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4200, 60, 4197, 4185, 4196])).
% 1.13/1.37 tff(4202,plain,(r(s(s(s(z))), s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | (s(s(s(z))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4203,plain,
% 1.13/1.37 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4202, 4195, 4185])).
% 1.13/1.37 tff(4204,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4205,plain,
% 1.13/1.37 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.37 inference(rewrite,[status(thm)],[])).
% 1.13/1.37 tff(4206,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4205])).
% 1.13/1.37 tff(4207,plain,
% 1.13/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.13/1.37 inference(transitivity,[status(thm)],[4206, 4204])).
% 1.13/1.37 tff(4208,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.13/1.37 inference(quant_inst,[status(thm)],[])).
% 1.13/1.37 tff(4209,plain,
% 1.13/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.13/1.37 inference(modus_ponens,[status(thm)],[4208, 4207])).
% 1.13/1.37 tff(4210,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4209, 154, 144, 4203, 141, 4184, 4176])).
% 1.13/1.37 tff(4211,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4212,plain,
% 1.13/1.37 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4211, 4175, 2340, 144, 106, 4160, 3851])).
% 1.13/1.37 tff(4213,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.37 tff(4214,plain,
% 1.13/1.37 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4213])).
% 1.13/1.37 tff(4215,plain,
% 1.13/1.37 (s(s(z)) = s(s(elem!1))),
% 1.13/1.37 inference(transitivity,[status(thm)],[87, 4214, 362])).
% 1.13/1.37 tff(4216,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 1.13/1.37 tff(4217,plain,
% 1.13/1.37 ($false),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4216, 4215])).
% 1.13/1.37 tff(4218,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.37 tff(4219,plain,
% 1.13/1.37 (s(s(z)) = s(s(elem!1))),
% 1.13/1.37 inference(unit_resolution,[status(thm)],[4218, 4212])).
% 1.13/1.37 tff(4220,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 1.13/1.37 tff(4221,plain,
% 1.13/1.37 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.13/1.37 inference(monotonicity,[status(thm)],[4220])).
% 1.13/1.37 tff(4222,plain,
% 1.13/1.37 (s(z) = s(elem!1)),
% 1.13/1.38 inference(transitivity,[status(thm)],[289, 4221, 485])).
% 1.13/1.38 tff(4223,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.13/1.38 tff(4224,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4223, 4222])).
% 1.13/1.38 tff(4225,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4226,plain,
% 1.13/1.38 (s(z) = s(elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4225, 4219])).
% 1.13/1.38 tff(4227,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.13/1.38 tff(4228,plain,
% 1.13/1.38 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4227])).
% 1.13/1.38 tff(4229,plain,
% 1.13/1.38 (z = inj_0(s(z))),
% 1.13/1.38 inference(symmetry,[status(thm)],[91])).
% 1.13/1.38 tff(4230,plain,
% 1.13/1.38 (z = elem!1),
% 1.13/1.38 inference(transitivity,[status(thm)],[4229, 4228, 4023])).
% 1.13/1.38 tff(4231,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.13/1.38 tff(4232,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4231, 4230])).
% 1.13/1.38 tff(4233,plain,((~(s(z) = s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4234,plain,
% 1.13/1.38 (z = elem!1),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4233, 4226])).
% 1.13/1.38 tff(4235,plain,
% 1.13/1.38 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4234])).
% 1.13/1.38 tff(4236,plain,
% 1.13/1.38 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4235])).
% 1.13/1.38 tff(4237,plain,
% 1.13/1.38 (s(z) = s(elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4234])).
% 1.13/1.38 tff(4238,plain,
% 1.13/1.38 (s(s(z)) = s(s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4237])).
% 1.13/1.38 tff(4239,plain,
% 1.13/1.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4238])).
% 1.13/1.38 tff(4240,plain,
% 1.13/1.38 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4239])).
% 1.13/1.38 tff(4241,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4240])).
% 1.13/1.38 tff(4242,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4241, 4236])).
% 1.13/1.38 tff(4243,plain,
% 1.13/1.38 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4244,plain,
% 1.13/1.38 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4243, 9])).
% 1.13/1.38 tff(4245,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.13/1.38 tff(4246,plain,
% 1.13/1.38 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4245])).
% 1.13/1.38 tff(4247,plain,
% 1.13/1.38 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4246])).
% 1.13/1.38 tff(4248,plain,
% 1.13/1.38 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[87, 4214, 362, 4247])).
% 1.13/1.38 tff(4249,plain,
% 1.13/1.38 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4248])).
% 1.13/1.38 tff(4250,plain,
% 1.13/1.38 (s(z) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[289, 4249, 4244])).
% 1.13/1.38 tff(4251,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[462, 4250])).
% 1.13/1.38 tff(4252,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4253,plain,
% 1.13/1.38 (~(elem!1 = s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4252, 4212])).
% 1.13/1.38 tff(4254,plain,
% 1.13/1.38 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.13/1.38 inference(commutativity,[status(thm)],[])).
% 1.13/1.38 tff(4255,plain,
% 1.13/1.38 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4254])).
% 1.13/1.38 tff(4256,plain,
% 1.13/1.38 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4234])).
% 1.13/1.38 tff(4257,plain,
% 1.13/1.38 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4256, 4255])).
% 1.13/1.38 tff(4258,plain,
% 1.13/1.38 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4257])).
% 1.13/1.38 tff(4259,plain,
% 1.13/1.38 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[388, 4258])).
% 1.13/1.38 tff(4260,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4237])).
% 1.13/1.38 tff(4261,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[3808, 4260])).
% 1.13/1.38 tff(4262,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4234])).
% 1.13/1.38 tff(4263,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[3811, 4262])).
% 1.13/1.38 tff(4264,plain,
% 1.13/1.38 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4237])).
% 1.13/1.38 tff(4265,plain,
% 1.13/1.38 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4234])).
% 1.13/1.38 tff(4266,plain,
% 1.13/1.38 (b(s(z), elem!1)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[3810, 4265])).
% 1.13/1.38 tff(4267,plain,
% 1.13/1.38 (b(s(elem!1), elem!1)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4266, 4264])).
% 1.13/1.38 tff(4268,plain,
% 1.13/1.38 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4237])).
% 1.13/1.38 tff(4269,plain,
% 1.13/1.38 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4234])).
% 1.13/1.38 tff(4270,plain,
% 1.13/1.38 (b(elem!1, s(z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[3813, 4269])).
% 1.13/1.38 tff(4271,plain,
% 1.13/1.38 (b(elem!1, s(elem!1))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4270, 4268])).
% 1.13/1.38 tff(4272,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4273,plain,
% 1.13/1.38 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4274,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4273])).
% 1.13/1.38 tff(4275,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4274, 4272])).
% 1.13/1.38 tff(4276,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4277,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4276, 4275])).
% 1.13/1.38 tff(4278,plain,
% 1.13/1.38 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4277, 154, 4271, 4267, 4263, 4261])).
% 1.13/1.38 tff(4279,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.38 tff(4280,assumption,(~r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.38 tff(4281,assumption,(~b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.38 tff(4282,plain,
% 1.13/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4283,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4284,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4283, 4282])).
% 1.13/1.38 tff(4285,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4284, 60, 4281, 4280, 4279])).
% 1.13/1.38 tff(4286,plain,(b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4287,plain,
% 1.13/1.38 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4286, 4278, 4259])).
% 1.13/1.38 tff(4288,assumption,(z = elem!1), introduced(assumption)).
% 1.13/1.38 tff(4289,plain,
% 1.13/1.38 (s(z) = s(elem!1)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4288])).
% 1.13/1.38 tff(4290,plain,
% 1.13/1.38 (s(s(z)) = s(s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4289])).
% 1.13/1.38 tff(4291,plain,
% 1.13/1.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4290])).
% 1.13/1.38 tff(4292,plain,
% 1.13/1.38 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4291])).
% 1.13/1.38 tff(4293,plain,
% 1.13/1.38 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4292])).
% 1.13/1.38 tff(4294,plain,
% 1.13/1.38 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4293])).
% 1.13/1.38 tff(4295,plain,
% 1.13/1.38 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[780, 4294])).
% 1.13/1.38 tff(4296,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.13/1.38 tff(4297,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.38 tff(4298,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4299,plain,
% 1.13/1.38 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4300,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4299])).
% 1.13/1.38 tff(4301,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4300, 4298])).
% 1.13/1.38 tff(4302,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4303,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4302, 4301])).
% 1.13/1.38 tff(4304,plain,
% 1.13/1.38 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4303, 28, 4297, 4296])).
% 1.13/1.38 tff(4305,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4304, 4295])).
% 1.13/1.38 tff(4306,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4307,plain,
% 1.13/1.38 (~r(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4306, 4287, 780, 4234])).
% 1.13/1.38 tff(4308,plain,
% 1.13/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4309,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4310,plain,
% 1.13/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4309, 4308])).
% 1.13/1.38 tff(4311,plain,
% 1.13/1.38 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4310, 60])).
% 1.13/1.38 tff(4312,plain,
% 1.13/1.38 (b(elem!1, s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4311, 4307, 4253])).
% 1.13/1.38 tff(4313,plain,
% 1.13/1.38 (b(z, s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4312, 4242])).
% 1.13/1.38 tff(4314,plain,
% 1.13/1.38 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4239])).
% 1.13/1.38 tff(4315,plain,
% 1.13/1.38 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4314, 4237])).
% 1.13/1.38 tff(4316,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4315])).
% 1.13/1.38 tff(4317,plain,
% 1.13/1.38 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4261, 4316])).
% 1.13/1.38 tff(4318,plain,
% 1.13/1.38 (~b(z, s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3057, 4317, 3810, 1299, 3827])).
% 1.13/1.38 tff(4319,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4318, 4313])).
% 1.13/1.38 tff(4320,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4321,plain,
% 1.13/1.38 (~b(s(s(s(s(z)))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4320, 780, 3811, 144, 106, 299, 820])).
% 1.13/1.38 tff(4322,plain,
% 1.13/1.38 (r(s(s(s(s(z)))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[206, 4321])).
% 1.13/1.38 tff(4323,plain,
% 1.13/1.38 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[2640, 28, 106, 4322])).
% 1.13/1.38 tff(4324,plain,
% 1.13/1.38 (b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[229, 4323])).
% 1.13/1.38 tff(4325,plain,
% 1.13/1.38 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3601, 154, 144, 3849, 2340, 4324])).
% 1.13/1.38 tff(4326,plain,
% 1.13/1.38 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[343, 4325])).
% 1.13/1.38 tff(4327,plain,
% 1.13/1.38 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[529, 28, 780, 4326])).
% 1.13/1.38 tff(4328,plain,
% 1.13/1.38 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3517, 154, 144, 3849, 2340, 4324])).
% 1.13/1.38 tff(4329,plain,
% 1.13/1.38 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[564, 4328])).
% 1.13/1.38 tff(4330,plain,
% 1.13/1.38 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[853, 4329, 820])).
% 1.13/1.38 tff(4331,plain,
% 1.13/1.38 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[317, 4330, 313])).
% 1.13/1.38 tff(4332,plain,
% 1.13/1.38 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1499, 154, 3808, 3849, 4331, 3825])).
% 1.13/1.38 tff(4333,plain,
% 1.13/1.38 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[517, 60, 4332, 4327])).
% 1.13/1.38 tff(4334,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4333])).
% 1.13/1.38 tff(4335,plain,
% 1.13/1.38 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.13/1.38 inference(symmetry,[status(thm)],[4334])).
% 1.13/1.38 tff(4336,plain,
% 1.13/1.38 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4335])).
% 1.13/1.38 tff(4337,plain,
% 1.13/1.38 (~b(s(s(s(s(elem!1)))), z)),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4321, 4336])).
% 1.13/1.38 tff(4338,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3811, 4337])).
% 1.13/1.38 tff(4339,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4340,plain,
% 1.13/1.38 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4339, 299, 820, 144, 106, 3811])).
% 1.13/1.38 tff(4341,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[496, 4340])).
% 1.13/1.38 tff(4342,plain,
% 1.13/1.38 (~b(s(s(s(z))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3462, 232, 3808, 443, 3810])).
% 1.13/1.38 tff(4343,plain,
% 1.13/1.38 (r(s(s(s(z))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[169, 4342])).
% 1.13/1.38 tff(4344,plain,
% 1.13/1.38 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4167, 28, 4161, 106])).
% 1.13/1.38 tff(4345,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3911, 60, 3908, 4344])).
% 1.13/1.38 tff(4346,plain,
% 1.13/1.38 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4209, 154, 144, 141, 4184, 4345])).
% 1.13/1.38 tff(4347,plain,
% 1.13/1.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4202, 4346, 4195])).
% 1.13/1.38 tff(4348,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4347])).
% 1.13/1.38 tff(4349,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[443, 4348])).
% 1.13/1.38 tff(4350,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4347])).
% 1.13/1.38 tff(4351,plain,
% 1.13/1.38 (s(s(z)) = s(s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4218, 4347])).
% 1.13/1.38 tff(4352,plain,
% 1.13/1.38 (s(z) = s(elem!1)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4225, 4351])).
% 1.13/1.38 tff(4353,plain,
% 1.13/1.38 (z = elem!1),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4233, 4352])).
% 1.13/1.38 tff(4354,plain,
% 1.13/1.38 ((elem!1 = z) <=> (z = elem!1)),
% 1.13/1.38 inference(commutativity,[status(thm)],[])).
% 1.13/1.38 tff(4355,plain,
% 1.13/1.38 ((z = elem!1) <=> (elem!1 = z)),
% 1.13/1.38 inference(symmetry,[status(thm)],[4354])).
% 1.13/1.38 tff(4356,plain,
% 1.13/1.38 (elem!1 = z),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4288, 4355])).
% 1.13/1.38 tff(4357,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.13/1.38 tff(4358,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4357, 4356])).
% 1.13/1.38 tff(4359,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4360,plain,
% 1.13/1.38 (elem!1 = z),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4359, 4353])).
% 1.13/1.38 tff(4361,assumption,(elem!1 = z), introduced(assumption)).
% 1.13/1.38 tff(4362,plain,
% 1.13/1.38 (s(elem!1) = s(z)),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4361])).
% 1.13/1.38 tff(4363,plain,
% 1.13/1.38 (s(s(elem!1)) = s(s(z))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4362])).
% 1.13/1.38 tff(4364,plain,
% 1.13/1.38 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4363])).
% 1.13/1.38 tff(4365,plain,
% 1.13/1.38 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4364])).
% 1.13/1.38 tff(4366,plain,
% 1.13/1.38 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4365])).
% 1.13/1.38 tff(4367,plain,
% 1.13/1.38 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4366])).
% 1.13/1.38 tff(4368,plain,
% 1.13/1.38 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4367])).
% 1.13/1.38 tff(4369,plain,
% 1.13/1.38 (r(s(z), s(s(s(s(z)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[535, 4368])).
% 1.13/1.38 tff(4370,plain,
% 1.13/1.38 (~r(s(z), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[1928, 28, 820, 66])).
% 1.13/1.38 tff(4371,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4370, 4369])).
% 1.13/1.38 tff(4372,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~(elem!1 = z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4373,plain,
% 1.13/1.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4372, 4360, 535, 820])).
% 1.13/1.38 tff(4374,plain,
% 1.13/1.38 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4366])).
% 1.13/1.38 tff(4375,plain,
% 1.13/1.38 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4374])).
% 1.13/1.38 tff(4376,plain,
% 1.13/1.38 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1019, 4375])).
% 1.13/1.38 tff(4377,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.13/1.38 tff(4378,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4377, 4376])).
% 1.13/1.38 tff(4379,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(z))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4380,plain,
% 1.13/1.38 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4379, 4373, 4360])).
% 1.13/1.38 tff(4381,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[989, 4380])).
% 1.13/1.38 tff(4382,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4381, 4350])).
% 1.13/1.38 tff(4383,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4347])).
% 1.13/1.38 tff(4384,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4213])).
% 1.13/1.38 tff(4385,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4384])).
% 1.13/1.38 tff(4386,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4213, 4215])).
% 1.13/1.38 tff(4387,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4386, 4385])).
% 1.13/1.38 tff(4388,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(elem!1)))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[141, 4387])).
% 1.13/1.38 tff(4389,assumption,(~b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.13/1.38 tff(4390,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4389, 4388])).
% 1.13/1.38 tff(4391,plain,((~b(s(s(s(z))), s(s(z)))) | b(s(s(s(z))), s(s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4392,plain,
% 1.13/1.38 (b(s(s(s(z))), s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4391, 4347, 141])).
% 1.13/1.38 tff(4393,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4392, 4383])).
% 1.13/1.38 tff(4394,plain,
% 1.13/1.38 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4347])).
% 1.13/1.38 tff(4395,plain,
% 1.13/1.38 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4347])).
% 1.13/1.38 tff(4396,plain,
% 1.13/1.38 (s(s(z)) = s(s(elem!1))),
% 1.13/1.38 inference(transitivity,[status(thm)],[87, 4395, 362])).
% 1.13/1.38 tff(4397,plain,
% 1.13/1.38 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4396, 4394])).
% 1.13/1.38 tff(4398,plain,
% 1.13/1.38 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[1283, 4397])).
% 1.13/1.38 tff(4399,plain,
% 1.13/1.38 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4396])).
% 1.13/1.38 tff(4400,plain,
% 1.13/1.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4184, 4399])).
% 1.13/1.38 tff(4401,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4402,plain,
% 1.13/1.38 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), 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(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4403,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4402])).
% 1.13/1.38 tff(4404,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4403, 4401])).
% 1.13/1.38 tff(4405,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.13/1.38 inference(quant_inst,[status(thm)],[])).
% 1.13/1.38 tff(4406,plain,
% 1.13/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[4405, 4404])).
% 1.13/1.38 tff(4407,plain,
% 1.13/1.38 ($false),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4406, 154, 4400, 4398, 4393, 4382, 4349])).
% 1.13/1.38 tff(4408,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.38 tff(4409,plain,
% 1.13/1.38 (~r(s(s(s(elem!1))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4408, 4343, 443, 535, 820, 2340, 144, 106, 1283])).
% 1.13/1.38 tff(4410,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), z)),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4159, 4409])).
% 1.13/1.38 tff(4411,plain,
% 1.13/1.38 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[3865, 4410, 4342])).
% 1.13/1.38 tff(4412,plain,
% 1.13/1.38 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4003, 4411, 299, 4410, 2340, 144, 820, 3810])).
% 1.13/1.38 tff(4413,plain,
% 1.13/1.38 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4011, 4412])).
% 1.13/1.38 tff(4414,plain,
% 1.13/1.38 (s(elem!1) = s(s(s(elem!1)))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4018, 4413])).
% 1.13/1.38 tff(4415,plain,
% 1.13/1.38 (elem!1 = s(s(elem!1))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4028, 4414])).
% 1.13/1.38 tff(4416,plain,
% 1.13/1.38 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.13/1.38 inference(unit_resolution,[status(thm)],[4037, 4415])).
% 1.13/1.38 tff(4417,plain,
% 1.13/1.38 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.13/1.38 inference(symmetry,[status(thm)],[4416])).
% 1.13/1.38 tff(4418,plain,
% 1.13/1.38 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.13/1.38 inference(transitivity,[status(thm)],[4417, 4413])).
% 1.13/1.38 tff(4419,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4418])).
% 1.13/1.38 tff(4420,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[443, 4419])).
% 1.13/1.38 tff(4421,plain,
% 1.13/1.38 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.13/1.38 inference(monotonicity,[status(thm)],[4418])).
% 1.13/1.38 tff(4422,plain,
% 1.13/1.38 (b(s(s(s(elem!1))), s(z))),
% 1.13/1.38 inference(modus_ponens,[status(thm)],[3808, 4421])).
% 1.13/1.38 tff(4423,plain,
% 1.13/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.38 inference(rewrite,[status(thm)],[])).
% 1.13/1.38 tff(4424,plain,
% 1.13/1.38 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4425,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4424])).
% 1.13/1.39 tff(4426,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4425, 4423])).
% 1.13/1.39 tff(4427,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4428,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4427, 4426])).
% 1.13/1.39 tff(4429,plain,
% 1.13/1.39 (~b(z, s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4428, 154, 3813, 232, 4422, 4420])).
% 1.13/1.39 tff(4430,plain,
% 1.13/1.39 (r(z, s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[3977, 4429])).
% 1.13/1.39 tff(4431,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.13/1.39 tff(4432,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4433,plain,
% 1.13/1.39 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4434,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4433])).
% 1.13/1.39 tff(4435,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4434, 4432])).
% 1.13/1.39 tff(4436,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4437,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4436, 4435])).
% 1.13/1.39 tff(4438,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4437, 28, 4132, 106, 4431])).
% 1.13/1.39 tff(4439,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4440,plain,
% 1.13/1.39 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4439, 4430, 106])).
% 1.13/1.39 tff(4441,plain,
% 1.13/1.39 (elem!1 = s(s(s(elem!1)))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4415, 4413])).
% 1.13/1.39 tff(4442,plain,
% 1.13/1.39 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4441])).
% 1.13/1.39 tff(4443,plain,
% 1.13/1.39 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.13/1.39 inference(symmetry,[status(thm)],[4442])).
% 1.13/1.39 tff(4444,plain,
% 1.13/1.39 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(elem!1))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4418])).
% 1.13/1.39 tff(4445,plain,
% 1.13/1.39 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), elem!1)),
% 1.13/1.39 inference(transitivity,[status(thm)],[4444, 4443])).
% 1.13/1.39 tff(4446,plain,
% 1.13/1.39 (r(s(z), elem!1)),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[535, 4445])).
% 1.13/1.39 tff(4447,plain,
% 1.13/1.39 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4441])).
% 1.13/1.39 tff(4448,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.13/1.39 inference(symmetry,[status(thm)],[4447])).
% 1.13/1.39 tff(4449,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4421, 4448])).
% 1.13/1.39 tff(4450,plain,
% 1.13/1.39 (b(elem!1, s(z))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[3808, 4449])).
% 1.13/1.39 tff(4451,plain,
% 1.13/1.39 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4441])).
% 1.13/1.39 tff(4452,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.39 inference(symmetry,[status(thm)],[4451])).
% 1.13/1.39 tff(4453,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4419, 4452])).
% 1.13/1.39 tff(4454,plain,
% 1.13/1.39 (b(elem!1, s(s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[443, 4453])).
% 1.13/1.39 tff(4455,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.13/1.39 tff(4456,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.13/1.39 tff(4457,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4458,plain,
% 1.13/1.39 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4459,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(s(z)))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4458])).
% 1.13/1.39 tff(4460,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4459, 4457])).
% 1.13/1.39 tff(4461,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4462,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(s(z)))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4461, 4460])).
% 1.13/1.39 tff(4463,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4462, 154, 4456, 232, 684, 141, 4455])).
% 1.13/1.39 tff(4464,plain,((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4465,plain,
% 1.13/1.39 (~b(s(z), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4464, 4454, 232, 4450, 2340])).
% 1.13/1.39 tff(4466,plain,
% 1.13/1.39 (r(s(z), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[680, 4465])).
% 1.13/1.39 tff(4467,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.13/1.39 tff(4468,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.13/1.39 tff(4469,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4470,plain,
% 1.13/1.39 (((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4471,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4470])).
% 1.13/1.39 tff(4472,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4471, 4469])).
% 1.13/1.39 tff(4473,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4474,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4473, 4472])).
% 1.13/1.39 tff(4475,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4474, 28, 4468, 17, 4467])).
% 1.13/1.39 tff(4476,plain,((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4477,plain,
% 1.13/1.39 (~r(elem!1, s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4476, 4466, 4446])).
% 1.13/1.39 tff(4478,plain,
% 1.13/1.39 (elem!1 = s(s(s(elem!1)))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4105, 4013])).
% 1.13/1.39 tff(4479,plain,
% 1.13/1.39 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4478])).
% 1.13/1.39 tff(4480,plain,
% 1.13/1.39 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.13/1.39 inference(symmetry,[status(thm)],[4479])).
% 1.13/1.39 tff(4481,plain,
% 1.13/1.39 (r(elem!1, s(s(z)))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[3880, 4480])).
% 1.13/1.39 tff(4482,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 1.13/1.39 tff(4483,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4482, 4481])).
% 1.13/1.39 tff(4484,plain,((~r(s(s(s(elem!1))), s(s(z)))) | r(elem!1, s(s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4485,plain,
% 1.13/1.39 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4484, 4477, 4413])).
% 1.13/1.39 tff(4486,plain,
% 1.13/1.39 (b(s(s(s(elem!1))), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4174, 4485])).
% 1.13/1.39 tff(4487,plain,
% 1.13/1.39 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[3944, 154, 144, 4420, 2340, 4486])).
% 1.13/1.39 tff(4488,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[3922, 60, 3906, 4487, 4440])).
% 1.13/1.39 tff(4489,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4490,plain,
% 1.13/1.39 (~b(s(z), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4489, 4341, 106, 3849, 3815, 299, 820, 144])).
% 1.13/1.39 tff(4491,plain,
% 1.13/1.39 (r(s(z), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[252, 4490])).
% 1.13/1.39 tff(4492,plain,
% 1.13/1.39 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1027, 4491, 3815])).
% 1.13/1.39 tff(4493,plain,
% 1.13/1.39 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[989, 4492])).
% 1.13/1.39 tff(4494,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[2352, 154, 144, 4493, 4341, 2340, 3825])).
% 1.13/1.39 tff(4495,plain,((~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4496,plain,
% 1.13/1.39 (~b(s(s(s(s(elem!1)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4495, 3806, 3743, 106, 3705])).
% 1.13/1.39 tff(4497,plain,
% 1.13/1.39 (r(s(s(s(s(elem!1)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[418, 4496])).
% 1.13/1.39 tff(4498,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4499,plain,
% 1.13/1.39 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4500,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4499])).
% 1.13/1.39 tff(4501,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4500, 4498])).
% 1.13/1.39 tff(4502,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4503,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 1.13/1.39 tff(4504,plain,
% 1.13/1.39 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4503, 28, 106, 4497])).
% 1.13/1.39 tff(4505,plain,
% 1.13/1.39 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[373, 60, 370, 4504])).
% 1.13/1.39 tff(4506,plain,
% 1.13/1.39 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[853, 3743, 66])).
% 1.13/1.39 tff(4507,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[318, 4506])).
% 1.13/1.39 tff(4508,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4509,plain,
% 1.13/1.39 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4510,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4509])).
% 1.13/1.39 tff(4511,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4510, 4508])).
% 1.13/1.39 tff(4512,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4513,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4512, 4511])).
% 1.13/1.39 tff(4514,plain,
% 1.13/1.39 (~b(s(s(s(s(z)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4513, 154, 3589, 2877, 3652, 4507])).
% 1.13/1.39 tff(4515,plain,
% 1.13/1.39 (r(s(s(s(s(z)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[206, 4514])).
% 1.13/1.39 tff(4516,plain,
% 1.13/1.39 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[2367, 28, 4497, 4515])).
% 1.13/1.39 tff(4517,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[517, 60, 12, 4516])).
% 1.13/1.39 tff(4518,plain,
% 1.13/1.39 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[2354, 3806, 3743, 3705, 3188])).
% 1.13/1.39 tff(4519,plain,
% 1.13/1.39 (b(s(s(s(s(elem!1)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[441, 4518])).
% 1.13/1.39 tff(4520,plain,
% 1.13/1.39 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1499, 154, 4519, 3201, 4507])).
% 1.13/1.39 tff(4521,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4520, 4517, 4505])).
% 1.13/1.39 tff(4522,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4523,plain,
% 1.13/1.39 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4522, 106, 12, 17])).
% 1.13/1.39 tff(4524,plain,
% 1.13/1.39 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[564, 4523])).
% 1.13/1.39 tff(4525,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[3517, 154, 144, 1283, 141, 1603, 566])).
% 1.13/1.39 tff(4526,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.39 tff(4527,plain,
% 1.13/1.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4526, 3705, 3201, 3188, 4524])).
% 1.13/1.39 tff(4528,plain,
% 1.13/1.39 (r(s(s(s(s(z)))), s(s(z)))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[229, 4527])).
% 1.13/1.39 tff(4529,plain,
% 1.13/1.39 (~r(s(s(s(s(z)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[3067, 4528, 106])).
% 1.13/1.39 tff(4530,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[206, 4529])).
% 1.13/1.39 tff(4531,plain,
% 1.13/1.39 (~b(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[2553, 4530, 3705, 3201, 4524])).
% 1.13/1.39 tff(4532,plain,
% 1.13/1.39 (r(s(s(s(z))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[169, 4531])).
% 1.13/1.39 tff(4533,plain,
% 1.13/1.39 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[3673, 820, 15, 2604, 171])).
% 1.13/1.39 tff(4534,plain,
% 1.13/1.39 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[564, 4533])).
% 1.13/1.39 tff(4535,plain,
% 1.13/1.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[2425, 4534, 144, 1283, 141])).
% 1.13/1.39 tff(4536,plain,
% 1.13/1.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[343, 4535])).
% 1.13/1.39 tff(4537,plain,
% 1.13/1.39 (~r(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[1411, 4536, 820])).
% 1.13/1.39 tff(4538,plain,
% 1.13/1.39 (b(s(s(s(s(z)))), s(z))),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[318, 4537])).
% 1.13/1.39 tff(4539,plain,
% 1.13/1.39 (~b(s(s(s(s(z)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4513, 154, 1726, 2604, 15, 4538])).
% 1.13/1.39 tff(4540,plain,
% 1.13/1.39 (r(s(s(s(s(z)))), z)),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[206, 4539])).
% 1.13/1.39 tff(4541,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4542,plain,
% 1.13/1.39 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.39 inference(rewrite,[status(thm)],[])).
% 1.13/1.39 tff(4543,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.13/1.39 inference(monotonicity,[status(thm)],[4542])).
% 1.13/1.39 tff(4544,plain,
% 1.13/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.13/1.39 inference(transitivity,[status(thm)],[4543, 4541])).
% 1.13/1.39 tff(4545,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.13/1.39 inference(quant_inst,[status(thm)],[])).
% 1.13/1.39 tff(4546,plain,
% 1.13/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.13/1.39 inference(modus_ponens,[status(thm)],[4545, 4544])).
% 1.13/1.39 tff(4547,plain,
% 1.13/1.39 ($false),
% 1.13/1.39 inference(unit_resolution,[status(thm)],[4546, 28, 820, 4536, 171, 4540])).
% 1.13/1.40 tff(4548,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.40 tff(4549,plain,
% 1.13/1.40 (~r(s(s(s(z))), s(z))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[4548, 4532, 3589, 2877, 3652, 3705, 3201, 3188])).
% 1.13/1.40 tff(4550,plain,
% 1.13/1.40 (b(s(s(s(z))), s(z))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[818, 4549])).
% 1.13/1.40 tff(4551,plain,
% 1.13/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.13/1.40 inference(rewrite,[status(thm)],[])).
% 1.13/1.40 tff(4552,plain,
% 1.13/1.40 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.13/1.40 inference(rewrite,[status(thm)],[])).
% 1.13/1.40 tff(4553,plain,
% 1.13/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.13/1.40 inference(monotonicity,[status(thm)],[4552])).
% 1.13/1.40 tff(4554,plain,
% 1.13/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.13/1.40 inference(transitivity,[status(thm)],[4553, 4551])).
% 1.13/1.40 tff(4555,plain,
% 1.13/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.13/1.40 inference(quant_inst,[status(thm)],[])).
% 1.13/1.40 tff(4556,plain,
% 1.13/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.13/1.40 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 1.13/1.40 tff(4557,plain,
% 1.13/1.40 ($false),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[4556, 154, 2877, 4550, 4530, 3652, 4524])).
% 1.13/1.40 tff(4558,plain,((~r(s(s(z)), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.40 tff(4559,plain,
% 1.13/1.40 (~r(s(s(z)), z)),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[4558, 17, 12])).
% 1.13/1.40 tff(4560,plain,
% 1.13/1.40 (b(s(s(z)), z)),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[122, 4559])).
% 1.13/1.40 tff(4561,plain,
% 1.13/1.40 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[132, 124, 16])).
% 1.13/1.40 tff(4562,plain,
% 1.13/1.40 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[564, 4561])).
% 1.13/1.40 tff(4563,plain,
% 1.13/1.40 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[75, 67, 16])).
% 1.13/1.40 tff(4564,plain,
% 1.13/1.40 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.13/1.40 inference(unit_resolution,[status(thm)],[564, 4563])).
% 1.13/1.40 tff(4565,plain,
% 1.23/1.40 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[585, 2881, 16, 2258, 4564, 3176])).
% 1.23/1.40 tff(4566,plain,
% 1.23/1.40 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[138, 4565])).
% 1.23/1.40 tff(4567,plain,
% 1.23/1.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[623, 4564, 2881, 2258, 3176])).
% 1.23/1.40 tff(4568,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[343, 4567])).
% 1.23/1.40 tff(4569,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[612, 4568, 4566, 16])).
% 1.23/1.40 tff(4570,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4571,plain,
% 1.23/1.40 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4570, 16, 17])).
% 1.23/1.40 tff(4572,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[104, 4571])).
% 1.23/1.40 tff(4573,plain,
% 1.23/1.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3691, 3658, 2258, 4572, 4562])).
% 1.23/1.40 tff(4574,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[229, 4573])).
% 1.23/1.40 tff(4575,plain,
% 1.23/1.40 (~b(s(s(s(z))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[623, 1076, 4562, 2258, 3658])).
% 1.23/1.40 tff(4576,plain,
% 1.23/1.40 (r(s(s(s(z))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[818, 4575])).
% 1.23/1.40 tff(4577,plain,
% 1.23/1.40 (~r(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1125, 4576, 124])).
% 1.23/1.40 tff(4578,plain,
% 1.23/1.40 (b(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[296, 4577])).
% 1.23/1.40 tff(4579,plain,
% 1.23/1.40 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3257, 154, 3174, 2604, 142])).
% 1.23/1.40 tff(4580,plain,
% 1.23/1.40 (~b(z, s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4579, 4578])).
% 1.23/1.40 tff(4581,plain,
% 1.23/1.40 (r(z, s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[64, 4580])).
% 1.23/1.40 tff(4582,plain,
% 1.23/1.40 (~r(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1251, 4581, 4574])).
% 1.23/1.40 tff(4583,plain,
% 1.23/1.40 (b(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[191, 4582])).
% 1.23/1.40 tff(4584,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4585,plain,
% 1.23/1.40 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4586,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4585])).
% 1.23/1.40 tff(4587,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4586, 4584])).
% 1.23/1.40 tff(4588,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4589,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4588, 4587])).
% 1.23/1.40 tff(4590,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4589, 154, 3174, 3658, 1076, 2258, 4583])).
% 1.23/1.40 tff(4591,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4592,plain,
% 1.23/1.40 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4591, 16, 4560, 2877, 17])).
% 1.23/1.40 tff(4593,plain,
% 1.23/1.40 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[138, 4592])).
% 1.23/1.40 tff(4594,plain,
% 1.23/1.40 (~r(s(s(s(z))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3711, 66, 2604, 15, 1726])).
% 1.23/1.40 tff(4595,plain,
% 1.23/1.40 (b(s(s(s(z))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[169, 4594])).
% 1.23/1.40 tff(4596,plain,
% 1.23/1.40 (~b(z, s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[162, 4595, 142, 141, 144])).
% 1.23/1.40 tff(4597,plain,
% 1.23/1.40 (r(z, s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[64, 4596])).
% 1.23/1.40 tff(4598,plain,
% 1.23/1.40 (~r(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2439, 4597, 16])).
% 1.23/1.40 tff(4599,plain,
% 1.23/1.40 (b(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[191, 4598])).
% 1.23/1.40 tff(4600,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3767, 154, 1726, 2604, 15, 855, 4599])).
% 1.23/1.40 tff(4601,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4602,plain,
% 1.23/1.40 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4601, 820, 2877, 2258, 16, 4560, 4572, 4593, 3589])).
% 1.23/1.40 tff(4603,plain,
% 1.23/1.40 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[564, 4602])).
% 1.23/1.40 tff(4604,plain,
% 1.23/1.40 (~b(s(s(s(s(z)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4513, 154, 1726, 2604, 15, 577])).
% 1.23/1.40 tff(4605,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[206, 4604])).
% 1.23/1.40 tff(4606,plain,
% 1.23/1.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4546, 28, 820, 171, 4605])).
% 1.23/1.40 tff(4607,plain,
% 1.23/1.40 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[343, 4606])).
% 1.23/1.40 tff(4608,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[1086, 154, 232, 4607, 15, 577, 566])).
% 1.23/1.40 tff(4609,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4610,plain,
% 1.23/1.40 (~b(s(z), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4609, 171, 4603, 820, 2258, 3589, 2877, 16, 4593])).
% 1.23/1.40 tff(4611,plain,
% 1.23/1.40 (r(s(z), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[252, 4610])).
% 1.23/1.40 tff(4612,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4613,plain,
% 1.23/1.40 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4614,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4613])).
% 1.23/1.40 tff(4615,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4614, 4612])).
% 1.23/1.40 tff(4616,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4617,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4616, 4615])).
% 1.23/1.40 tff(4618,plain,
% 1.23/1.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4617, 154, 1299, 142, 141, 566])).
% 1.23/1.40 tff(4619,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[229, 4618])).
% 1.23/1.40 tff(4620,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4621,plain,
% 1.23/1.40 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4622,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4621])).
% 1.23/1.40 tff(4623,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4622, 4620])).
% 1.23/1.40 tff(4624,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4625,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4624, 4623])).
% 1.23/1.40 tff(4626,plain,
% 1.23/1.40 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4625, 28, 273, 17, 4619])).
% 1.23/1.40 tff(4627,plain,
% 1.23/1.40 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[318, 4626])).
% 1.23/1.40 tff(4628,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4513, 154, 3174, 2604, 1299, 15, 4627])).
% 1.23/1.40 tff(4629,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4630,plain,
% 1.23/1.40 (~b(s(s(s(s(z)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4629, 4611, 2258, 2877, 17, 4560, 4572, 4603])).
% 1.23/1.40 tff(4631,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[206, 4630])).
% 1.23/1.40 tff(4632,plain,
% 1.23/1.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4546, 28, 820, 171, 4631])).
% 1.23/1.40 tff(4633,plain,
% 1.23/1.40 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[343, 4632])).
% 1.23/1.40 tff(4634,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4635,plain,
% 1.23/1.40 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4636,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.23/1.40 inference(monotonicity,[status(thm)],[4635])).
% 1.23/1.40 tff(4637,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.40 inference(transitivity,[status(thm)],[4636, 4634])).
% 1.23/1.40 tff(4638,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.23/1.40 inference(quant_inst,[status(thm)],[])).
% 1.23/1.40 tff(4639,plain,
% 1.23/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.40 inference(modus_ponens,[status(thm)],[4638, 4637])).
% 1.23/1.40 tff(4640,plain,
% 1.23/1.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4639, 154, 4593, 4633, 4572, 4603])).
% 1.23/1.40 tff(4641,plain,
% 1.23/1.40 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[229, 4640])).
% 1.23/1.40 tff(4642,plain,
% 1.23/1.40 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4625, 28, 4611, 17, 4641])).
% 1.23/1.40 tff(4643,plain,
% 1.23/1.40 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[318, 4642])).
% 1.23/1.40 tff(4644,plain,
% 1.23/1.40 (~b(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3767, 154, 3589, 2877, 2258, 4643])).
% 1.23/1.40 tff(4645,plain,
% 1.23/1.40 (r(z, s(s(s(s(z)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[191, 4644])).
% 1.23/1.40 tff(4646,plain,
% 1.23/1.40 (~r(z, s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2439, 4645, 16])).
% 1.23/1.40 tff(4647,plain,
% 1.23/1.40 (b(z, s(s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[64, 4646])).
% 1.23/1.40 tff(4648,plain,
% 1.23/1.40 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3257, 154, 3589, 2877, 4560])).
% 1.23/1.40 tff(4649,plain,
% 1.23/1.40 (~b(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4648, 4647])).
% 1.23/1.40 tff(4650,plain,
% 1.23/1.40 (r(s(s(z)), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[296, 4649])).
% 1.23/1.40 tff(4651,plain,
% 1.23/1.40 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[2354, 4650, 820, 4593, 4572])).
% 1.23/1.40 tff(4652,plain,
% 1.23/1.40 (b(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[441, 4651])).
% 1.23/1.40 tff(4653,plain,
% 1.23/1.40 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3322, 3811])).
% 1.23/1.40 tff(4654,plain,
% 1.23/1.40 (r(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[467, 4653])).
% 1.23/1.40 tff(4655,plain,
% 1.23/1.40 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3823, 4654, 299])).
% 1.23/1.40 tff(4656,plain,
% 1.23/1.40 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[3326, 3811])).
% 1.23/1.40 tff(4657,plain,
% 1.23/1.40 ($false),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[373, 60, 370, 4656, 4655])).
% 1.23/1.40 tff(4658,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.40 tff(4659,plain,
% 1.23/1.40 (~b(s(s(s(s(elem!1)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[4658, 4650, 3589, 4652, 4560, 2877])).
% 1.23/1.40 tff(4660,plain,
% 1.23/1.40 (r(s(s(s(s(elem!1)))), z)),
% 1.23/1.40 inference(unit_resolution,[status(thm)],[418, 4659])).
% 1.23/1.40 tff(4661,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4662,plain,
% 1.23/1.40 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.23/1.40 inference(rewrite,[status(thm)],[])).
% 1.23/1.40 tff(4663,plain,
% 1.23/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4662])).
% 1.23/1.41 tff(4664,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4663, 4661])).
% 1.23/1.41 tff(4665,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4666,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4665, 4664])).
% 1.23/1.41 tff(4667,plain,
% 1.23/1.41 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4666, 28, 4660, 4641, 4631])).
% 1.23/1.41 tff(4668,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4669,plain,
% 1.23/1.41 (((~r(s(s(s(s(elem!1)))), z)) | (~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))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4670,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4669])).
% 1.23/1.41 tff(4671,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4670, 4668])).
% 1.23/1.41 tff(4672,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~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)))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4673,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4672, 4671])).
% 1.23/1.41 tff(4674,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4673, 28, 4660, 171])).
% 1.23/1.41 tff(4675,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[989, 4674])).
% 1.23/1.41 tff(4676,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4677,plain,
% 1.23/1.41 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~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(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4678,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4677])).
% 1.23/1.41 tff(4679,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4678, 4676])).
% 1.23/1.41 tff(4680,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4681,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4680, 4679])).
% 1.23/1.41 tff(4682,plain,
% 1.23/1.41 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4681, 154, 4652, 4643, 4603])).
% 1.23/1.41 tff(4683,plain,
% 1.23/1.41 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4682, 4675])).
% 1.23/1.41 tff(4684,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[517, 60, 4683, 12, 4667])).
% 1.23/1.41 tff(4685,plain,((~r(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4686,plain,
% 1.23/1.41 (~r(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4685, 820, 12, 16, 17])).
% 1.23/1.41 tff(4687,plain,
% 1.23/1.41 (b(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[169, 4686])).
% 1.23/1.41 tff(4688,plain,
% 1.23/1.41 (~b(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[162, 4687, 4560, 4572, 4593])).
% 1.23/1.41 tff(4689,plain,
% 1.23/1.41 (r(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[64, 4688])).
% 1.23/1.41 tff(4690,plain,
% 1.23/1.41 (~r(z, s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2439, 4689, 16])).
% 1.23/1.41 tff(4691,plain,
% 1.23/1.41 (b(z, s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[191, 4690])).
% 1.23/1.41 tff(4692,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4693,plain,
% 1.23/1.41 (((~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(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4694,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4693])).
% 1.23/1.41 tff(4695,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4694, 4692])).
% 1.23/1.41 tff(4696,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4697,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4696, 4695])).
% 1.23/1.41 tff(4698,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4697, 154, 4593, 4687, 4560, 4603, 4691])).
% 1.23/1.41 tff(4699,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4700,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4699, 16, 12, 17])).
% 1.23/1.41 tff(4701,plain,
% 1.23/1.41 (b(s(s(s(z))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[818, 4700])).
% 1.23/1.41 tff(4702,plain,
% 1.23/1.41 (~b(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2712, 154, 4593, 3589, 4701, 4560])).
% 1.23/1.41 tff(4703,plain,
% 1.23/1.41 (r(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[169, 4702])).
% 1.23/1.41 tff(4704,plain,
% 1.23/1.41 (~b(s(s(z)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2957, 154, 2877, 4701, 4560, 4572])).
% 1.23/1.41 tff(4705,plain,
% 1.23/1.41 (r(s(s(z)), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[296, 4704])).
% 1.23/1.41 tff(4706,plain,
% 1.23/1.41 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[307, 4705, 16])).
% 1.23/1.41 tff(4707,plain,
% 1.23/1.41 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[318, 4706])).
% 1.23/1.41 tff(4708,plain,
% 1.23/1.41 (~b(s(s(s(s(z)))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2917, 4707, 2258, 2877, 4701, 4703])).
% 1.23/1.41 tff(4709,plain,
% 1.23/1.41 (r(s(s(s(s(z)))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[206, 4708])).
% 1.23/1.41 tff(4710,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3711, 4703, 2877, 2258, 3589])).
% 1.23/1.41 tff(4711,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[564, 4710])).
% 1.23/1.41 tff(4712,plain,
% 1.23/1.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[752, 4711, 4701, 2258, 4707])).
% 1.23/1.41 tff(4713,plain,
% 1.23/1.41 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[343, 4712])).
% 1.23/1.41 tff(4714,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2179, 28, 4713, 4703, 4709])).
% 1.23/1.41 tff(4715,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4716,plain,
% 1.23/1.41 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4715, 17, 12])).
% 1.23/1.41 tff(4717,plain,
% 1.23/1.41 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1259, 4716])).
% 1.23/1.41 tff(4718,plain,
% 1.23/1.41 (~r(z, s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3567, 1655, 4717, 12])).
% 1.23/1.41 tff(4719,plain,
% 1.23/1.41 (b(z, s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[191, 4718])).
% 1.23/1.41 tff(4720,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2010, 154, 1299, 1283, 142, 1603, 254])).
% 1.23/1.41 tff(4721,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4722,plain,
% 1.23/1.41 (~b(s(s(s(s(z)))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4721, 2879, 4560, 4717, 4719])).
% 1.23/1.41 tff(4723,plain,
% 1.23/1.41 (r(s(s(s(s(z)))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[206, 4722])).
% 1.23/1.41 tff(4724,plain,
% 1.23/1.41 (~r(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[201, 66, 193])).
% 1.23/1.41 tff(4725,plain,
% 1.23/1.41 (b(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[169, 4724])).
% 1.23/1.41 tff(4726,plain,
% 1.23/1.41 (~b(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3184, 4725, 2604, 1726, 3209])).
% 1.23/1.41 tff(4727,plain,
% 1.23/1.41 (r(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[252, 4726])).
% 1.23/1.41 tff(4728,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2064, 28, 4727, 66, 1655])).
% 1.23/1.41 tff(4729,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4730,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4729, 1655, 2877, 3589, 4723])).
% 1.23/1.41 tff(4731,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[564, 4730])).
% 1.23/1.41 tff(4732,plain,
% 1.23/1.41 (~b(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3184, 3176, 2877, 3589, 2881])).
% 1.23/1.41 tff(4733,plain,
% 1.23/1.41 (r(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[169, 4732])).
% 1.23/1.41 tff(4734,plain,
% 1.23/1.41 (~b(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3660, 3176, 2877, 3589, 2881])).
% 1.23/1.41 tff(4735,plain,
% 1.23/1.41 (r(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[648, 4734])).
% 1.23/1.41 tff(4736,plain,
% 1.23/1.41 (~r(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1346, 4733, 67])).
% 1.23/1.41 tff(4737,plain,
% 1.23/1.41 (b(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[64, 4736])).
% 1.23/1.41 tff(4738,plain,
% 1.23/1.41 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1471, 4737, 4560, 4717, 4735])).
% 1.23/1.41 tff(4739,plain,
% 1.23/1.41 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[343, 4738])).
% 1.23/1.41 tff(4740,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1309, 4737, 4560, 4717, 4733])).
% 1.23/1.41 tff(4741,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[564, 4740])).
% 1.23/1.41 tff(4742,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3359, 4741, 4739, 2877, 12, 3589, 4717, 1603, 4733])).
% 1.23/1.41 tff(4743,plain,((~r(s(s(s(z))), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4744,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4743, 2879, 12, 17])).
% 1.23/1.41 tff(4745,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[104, 4744])).
% 1.23/1.41 tff(4746,plain,
% 1.23/1.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3235, 154, 4717, 4745, 2879, 4731])).
% 1.23/1.41 tff(4747,plain,
% 1.23/1.41 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[343, 4746])).
% 1.23/1.41 tff(4748,plain,
% 1.23/1.41 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3578, 154, 4745, 2879, 4719])).
% 1.23/1.41 tff(4749,plain,
% 1.23/1.41 (~b(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4748, 4731])).
% 1.23/1.41 tff(4750,plain,
% 1.23/1.41 (r(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[648, 4749])).
% 1.23/1.41 tff(4751,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1459, 28, 4750, 4747, 4723])).
% 1.23/1.41 tff(4752,plain,((~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4753,plain,
% 1.23/1.41 (~r(s(z), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4752, 17, 12])).
% 1.23/1.41 tff(4754,plain,
% 1.23/1.41 (b(s(z), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1653, 4753])).
% 1.23/1.41 tff(4755,plain,
% 1.23/1.41 (~r(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3711, 66, 2604, 15, 3174])).
% 1.23/1.41 tff(4756,plain,
% 1.23/1.41 (b(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[169, 4755])).
% 1.23/1.41 tff(4757,plain,
% 1.23/1.41 (~b(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3184, 1, 2604, 3174, 143])).
% 1.23/1.41 tff(4758,plain,
% 1.23/1.41 (r(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[252, 4757])).
% 1.23/1.41 tff(4759,plain,
% 1.23/1.41 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3656, 4758, 17])).
% 1.23/1.41 tff(4760,plain,
% 1.23/1.41 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[138, 4759])).
% 1.23/1.41 tff(4761,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[2712, 154, 4760, 3174, 1, 143, 142])).
% 1.23/1.41 tff(4762,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4763,plain,
% 1.23/1.41 (~b(s(s(s(z))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4762, 4756, 142, 17, 2604])).
% 1.23/1.41 tff(4764,plain,
% 1.23/1.41 (r(s(s(s(z))), s(z))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[818, 4763])).
% 1.23/1.41 tff(4765,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1556, 4764, 17])).
% 1.23/1.41 tff(4766,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[104, 4765])).
% 1.23/1.41 tff(4767,plain,
% 1.23/1.41 (~r(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3802, 4764, 66])).
% 1.23/1.41 tff(4768,plain,
% 1.23/1.41 (b(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[648, 4767])).
% 1.23/1.41 tff(4769,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4770,plain,
% 1.23/1.41 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4771,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4770])).
% 1.23/1.41 tff(4772,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4771, 4769])).
% 1.23/1.41 tff(4773,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4774,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4773, 4772])).
% 1.23/1.41 tff(4775,plain,
% 1.23/1.41 (~b(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4774, 154, 3174, 2604, 4756, 4768])).
% 1.23/1.41 tff(4776,plain,
% 1.23/1.41 (r(s(z), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[252, 4775])).
% 1.23/1.41 tff(4777,plain,
% 1.23/1.41 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3656, 4776, 17])).
% 1.23/1.41 tff(4778,plain,
% 1.23/1.41 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[138, 4777])).
% 1.23/1.41 tff(4779,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[893, 154, 4778, 4756, 4768, 142, 4766])).
% 1.23/1.41 tff(4780,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4781,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4780, 142, 17, 2604, 15])).
% 1.23/1.41 tff(4782,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[564, 4781])).
% 1.23/1.41 tff(4783,plain,
% 1.23/1.41 (~b(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4762, 1, 142, 17, 2604])).
% 1.23/1.41 tff(4784,plain,
% 1.23/1.41 (r(s(s(s(z))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[169, 4783])).
% 1.23/1.41 tff(4785,plain,
% 1.23/1.41 ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1767, 154, 3174, 15, 4782])).
% 1.23/1.41 tff(4786,plain,
% 1.23/1.41 (~b(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4785, 1])).
% 1.23/1.41 tff(4787,plain,
% 1.23/1.41 (r(z, s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[648, 4786])).
% 1.23/1.41 tff(4788,plain,
% 1.23/1.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[623, 3176, 15, 1, 566])).
% 1.23/1.41 tff(4789,plain,
% 1.23/1.41 (~r(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1346, 67, 171])).
% 1.23/1.41 tff(4790,plain,
% 1.23/1.41 (b(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[64, 4789])).
% 1.23/1.41 tff(4791,plain,
% 1.23/1.41 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1471, 4790, 142, 1283, 628])).
% 1.23/1.41 tff(4792,plain,
% 1.23/1.41 ($false),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[343, 4791, 4788])).
% 1.23/1.41 tff(4793,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.41 tff(4794,plain,
% 1.23/1.41 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4793, 4787, 1283, 142, 15, 1, 4782, 4784, 17])).
% 1.23/1.41 tff(4795,plain,
% 1.23/1.41 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[104, 4794])).
% 1.23/1.41 tff(4796,plain,
% 1.23/1.41 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[3691, 232, 15, 4795, 4782])).
% 1.23/1.41 tff(4797,plain,
% 1.23/1.41 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[229, 4796])).
% 1.23/1.41 tff(4798,plain,
% 1.23/1.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[623, 232, 15, 1, 4782])).
% 1.23/1.41 tff(4799,plain,
% 1.23/1.41 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[343, 4798])).
% 1.23/1.41 tff(4800,plain,
% 1.23/1.41 (~b(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1471, 4799, 142, 1283, 4787])).
% 1.23/1.41 tff(4801,plain,
% 1.23/1.41 (r(z, s(s(z)))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[64, 4800])).
% 1.23/1.41 tff(4802,plain,
% 1.23/1.41 (~r(z, s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[1251, 4801, 4797])).
% 1.23/1.41 tff(4803,plain,
% 1.23/1.41 (b(z, s(s(s(s(z)))))),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[191, 4802])).
% 1.23/1.41 tff(4804,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4805,plain,
% 1.23/1.41 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4806,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.23/1.41 inference(monotonicity,[status(thm)],[4805])).
% 1.23/1.41 tff(4807,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.41 inference(transitivity,[status(thm)],[4806, 4804])).
% 1.23/1.41 tff(4808,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.23/1.41 inference(quant_inst,[status(thm)],[])).
% 1.23/1.41 tff(4809,plain,
% 1.23/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.41 inference(modus_ponens,[status(thm)],[4808, 4807])).
% 1.23/1.41 tff(4810,plain,
% 1.23/1.41 (~r(s(s(s(s(z)))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[4809, 28, 4787, 4801, 4797])).
% 1.23/1.41 tff(4811,plain,
% 1.23/1.41 (b(s(s(s(s(z)))), z)),
% 1.23/1.41 inference(unit_resolution,[status(thm)],[206, 4810])).
% 1.23/1.41 tff(4812,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4813,plain,
% 1.23/1.41 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.23/1.41 inference(rewrite,[status(thm)],[])).
% 1.23/1.41 tff(4814,plain,
% 1.23/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[4813])).
% 1.23/1.42 tff(4815,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[4814, 4812])).
% 1.23/1.42 tff(4816,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(4817,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 1.23/1.42 tff(4818,plain,
% 1.23/1.42 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4817, 28, 17, 4797])).
% 1.23/1.42 tff(4819,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[318, 4818])).
% 1.23/1.42 tff(4820,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2905, 4819, 4811, 2604, 15, 4803])).
% 1.23/1.42 tff(4821,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4822,plain,
% 1.23/1.42 (~b(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4821, 1, 15, 17, 142, 1283, 2604])).
% 1.23/1.42 tff(4823,plain,
% 1.23/1.42 (r(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[252, 4822])).
% 1.23/1.42 tff(4824,plain,
% 1.23/1.42 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3656, 4823, 17])).
% 1.23/1.42 tff(4825,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2425, 566, 144, 1283, 141])).
% 1.23/1.42 tff(4826,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[343, 4825])).
% 1.23/1.42 tff(4827,plain,
% 1.23/1.42 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1586, 28, 273, 4826])).
% 1.23/1.42 tff(4828,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[318, 4827])).
% 1.23/1.42 tff(4829,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1613, 154, 144, 1, 1283, 4828, 566])).
% 1.23/1.42 tff(4830,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4831,plain,
% 1.23/1.42 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4830, 4823, 1283, 4782, 1, 4795])).
% 1.23/1.42 tff(4832,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[138, 4831, 4824])).
% 1.23/1.42 tff(4833,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4834,plain,
% 1.23/1.42 (~b(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4833, 4717, 17, 4754, 4560, 2877])).
% 1.23/1.42 tff(4835,plain,
% 1.23/1.42 (r(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[818, 4834])).
% 1.23/1.42 tff(4836,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1556, 4835, 17])).
% 1.23/1.42 tff(4837,plain,
% 1.23/1.42 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[104, 4836])).
% 1.23/1.42 tff(4838,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4780, 4560, 17, 2877, 4754])).
% 1.23/1.42 tff(4839,plain,
% 1.23/1.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[564, 4838])).
% 1.23/1.42 tff(4840,plain,
% 1.23/1.42 (~b(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4833, 1283, 17, 15, 142, 2604])).
% 1.23/1.42 tff(4841,plain,
% 1.23/1.42 (r(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[818, 4840])).
% 1.23/1.42 tff(4842,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1556, 4841, 17])).
% 1.23/1.42 tff(4843,plain,
% 1.23/1.42 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[104, 4842])).
% 1.23/1.42 tff(4844,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4629, 273, 15, 2604, 17, 142, 4782, 4843])).
% 1.23/1.42 tff(4845,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[206, 4844])).
% 1.23/1.42 tff(4846,plain,
% 1.23/1.42 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3656, 273, 17])).
% 1.23/1.42 tff(4847,plain,
% 1.23/1.42 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[138, 4846])).
% 1.23/1.42 tff(4848,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4526, 4847, 1283, 4782, 4843])).
% 1.23/1.42 tff(4849,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[229, 4848])).
% 1.23/1.42 tff(4850,plain,
% 1.23/1.42 (~r(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4548, 4847, 3174, 2604, 1283, 15, 4841, 4843])).
% 1.23/1.42 tff(4851,plain,
% 1.23/1.42 (b(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[169, 4850])).
% 1.23/1.42 tff(4852,plain,
% 1.23/1.42 (~b(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[162, 4851, 142, 4843, 4847])).
% 1.23/1.42 tff(4853,plain,
% 1.23/1.42 (r(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[64, 4852])).
% 1.23/1.42 tff(4854,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2841, 28, 4853, 4849, 4845])).
% 1.23/1.42 tff(4855,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4856,plain,
% 1.23/1.42 (~r(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4855, 4560, 2877, 4717, 4754, 17])).
% 1.23/1.42 tff(4857,plain,
% 1.23/1.42 (b(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[252, 4856])).
% 1.23/1.42 tff(4858,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3691, 4857, 4754, 4837, 4839])).
% 1.23/1.42 tff(4859,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[229, 4858])).
% 1.23/1.42 tff(4860,plain,
% 1.23/1.42 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4817, 28, 17, 4859])).
% 1.23/1.42 tff(4861,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[318, 4860])).
% 1.23/1.42 tff(4862,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4863,plain,
% 1.23/1.42 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4864,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[4863])).
% 1.23/1.42 tff(4865,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[4864, 4862])).
% 1.23/1.42 tff(4866,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(4867,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[4866, 4865])).
% 1.23/1.42 tff(4868,plain,
% 1.23/1.42 (~b(z, s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4867, 154, 3589, 4717, 4861, 4560])).
% 1.23/1.42 tff(4869,plain,
% 1.23/1.42 (r(z, s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[191, 4868])).
% 1.23/1.42 tff(4870,plain,
% 1.23/1.42 (~r(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1251, 4869, 4859])).
% 1.23/1.42 tff(4871,plain,
% 1.23/1.42 (b(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[64, 4870])).
% 1.23/1.42 tff(4872,plain,
% 1.23/1.42 (~b(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4648, 4871])).
% 1.23/1.42 tff(4873,plain,
% 1.23/1.42 (r(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[296, 4872])).
% 1.23/1.42 tff(4874,plain,
% 1.23/1.42 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1125, 4873, 4835])).
% 1.23/1.42 tff(4875,plain,
% 1.23/1.42 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[138, 4874])).
% 1.23/1.42 tff(4876,plain,
% 1.23/1.42 (~r(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4548, 4875, 3589, 2877, 4717, 4754, 4835, 4837])).
% 1.23/1.42 tff(4877,plain,
% 1.23/1.42 (~b(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[162, 4875, 4560, 4837, 4871])).
% 1.23/1.42 tff(4878,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[169, 4877, 4876])).
% 1.23/1.42 tff(4879,plain,((~r(s(z), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4880,plain,
% 1.23/1.42 (~r(s(z), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4879, 12])).
% 1.23/1.42 tff(4881,plain,
% 1.23/1.42 (b(s(z), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[680, 4880])).
% 1.23/1.42 tff(4882,plain,
% 1.23/1.42 (~r(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2064, 28, 66, 1655])).
% 1.23/1.42 tff(4883,plain,
% 1.23/1.42 (b(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[252, 4882])).
% 1.23/1.42 tff(4884,plain,
% 1.23/1.42 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1691, 154, 3209, 684, 231])).
% 1.23/1.42 tff(4885,plain,
% 1.23/1.42 (~b(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4884, 4883])).
% 1.23/1.42 tff(4886,plain,
% 1.23/1.42 (r(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[104, 4885])).
% 1.23/1.42 tff(4887,plain,
% 1.23/1.42 (~r(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1280, 4886, 106])).
% 1.23/1.42 tff(4888,plain,
% 1.23/1.42 (b(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[169, 4887])).
% 1.23/1.42 tff(4889,plain,
% 1.23/1.42 (~b(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3091, 4888, 2604, 3209, 4883])).
% 1.23/1.42 tff(4890,plain,
% 1.23/1.42 (r(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[648, 4889])).
% 1.23/1.42 tff(4891,plain,
% 1.23/1.42 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2080, 4890, 106])).
% 1.23/1.42 tff(4892,plain,
% 1.23/1.42 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[138, 4891])).
% 1.23/1.42 tff(4893,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1419, 154, 4892, 3209, 4883, 684, 231])).
% 1.23/1.42 tff(4894,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4895,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4894, 1272, 684, 106, 2604, 1655])).
% 1.23/1.42 tff(4896,plain,
% 1.23/1.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[564, 4895])).
% 1.23/1.42 tff(4897,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4898,plain,
% 1.23/1.42 (((~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(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4899,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[4898])).
% 1.23/1.42 tff(4900,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[4899, 4897])).
% 1.23/1.42 tff(4901,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(4902,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[4901, 4900])).
% 1.23/1.42 tff(4903,plain,
% 1.23/1.42 ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4902, 154, 2604, 4896, 1934])).
% 1.23/1.42 tff(4904,plain,
% 1.23/1.42 (~b(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4903, 1701])).
% 1.23/1.42 tff(4905,plain,
% 1.23/1.42 (r(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[252, 4904])).
% 1.23/1.42 tff(4906,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2066, 4905, 14, 1701, 1655])).
% 1.23/1.42 tff(4907,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[206, 4906])).
% 1.23/1.42 tff(4908,plain,
% 1.23/1.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3067, 4907, 106])).
% 1.23/1.42 tff(4909,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[229, 4908])).
% 1.23/1.42 tff(4910,plain,
% 1.23/1.42 (~r(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[636, 4905, 14])).
% 1.23/1.42 tff(4911,plain,
% 1.23/1.42 (b(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[648, 4910])).
% 1.23/1.42 tff(4912,plain,
% 1.23/1.42 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[742, 4911, 14, 1701, 4896])).
% 1.23/1.42 tff(4913,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[318, 4912])).
% 1.23/1.42 tff(4914,plain,
% 1.23/1.42 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1705, 4911, 106, 67])).
% 1.23/1.42 tff(4915,plain,
% 1.23/1.42 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1259, 4914])).
% 1.23/1.42 tff(4916,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2103, 154, 4915, 684, 1272, 4913, 4909])).
% 1.23/1.42 tff(4917,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4918,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4917, 106, 684, 14, 1655, 2604])).
% 1.23/1.42 tff(4919,plain,
% 1.23/1.42 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[104, 4918])).
% 1.23/1.42 tff(4920,plain,
% 1.23/1.42 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1259, 2482])).
% 1.23/1.42 tff(4921,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3583, 3717, 4920, 106, 254, 566, 141])).
% 1.23/1.42 tff(4922,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4923,plain,
% 1.23/1.42 (~r(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4922, 106, 1934, 4896, 4919])).
% 1.23/1.42 tff(4924,plain,
% 1.23/1.42 (b(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[206, 4923])).
% 1.23/1.42 tff(4925,plain,
% 1.23/1.42 ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4902, 154, 2604, 566, 1934])).
% 1.23/1.42 tff(4926,plain,
% 1.23/1.42 (~b(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4925, 143])).
% 1.23/1.42 tff(4927,plain,
% 1.23/1.42 (~r(s(z), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2066, 143, 14, 1299, 1655])).
% 1.23/1.42 tff(4928,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[252, 4927, 4926])).
% 1.23/1.42 tff(4929,plain,((~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4930,plain,
% 1.23/1.42 (~b(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4929, 4924, 14, 1655, 2604, 4896])).
% 1.23/1.42 tff(4931,plain,
% 1.23/1.42 (r(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[169, 4930])).
% 1.23/1.42 tff(4932,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[828, 4931, 14])).
% 1.23/1.42 tff(4933,plain,
% 1.23/1.42 (b(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[818, 4932])).
% 1.23/1.42 tff(4934,plain,
% 1.23/1.42 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[692, 4933, 684, 4919, 1272])).
% 1.23/1.42 tff(4935,plain,
% 1.23/1.42 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[138, 4934])).
% 1.23/1.42 tff(4936,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[2276, 28, 4935, 106, 4931])).
% 1.23/1.42 tff(4937,plain,((~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4938,plain,
% 1.23/1.42 (~r(s(s(z)), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4937, 1655, 14, 684, 2604])).
% 1.23/1.42 tff(4939,plain,
% 1.23/1.42 (b(s(s(z)), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[122, 4938])).
% 1.23/1.42 tff(4940,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4941,plain,
% 1.23/1.42 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4942,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[4941])).
% 1.23/1.42 tff(4943,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[4942, 4940])).
% 1.23/1.42 tff(4944,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(4945,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 1.23/1.42 tff(4946,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4945, 154, 2604, 1283, 684, 142, 254])).
% 1.23/1.42 tff(4947,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4948,plain,
% 1.23/1.42 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4947, 4939, 684, 2604, 1934])).
% 1.23/1.42 tff(4949,plain,
% 1.23/1.42 (r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1259, 4948])).
% 1.23/1.42 tff(4950,plain,
% 1.23/1.42 (~r(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1824, 28, 16, 1655])).
% 1.23/1.42 tff(4951,plain,
% 1.23/1.42 (b(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[296, 4950])).
% 1.23/1.42 tff(4952,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[692, 139, 105, 684, 3209, 4951])).
% 1.23/1.42 tff(4953,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4954,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4953, 4949, 684, 1655])).
% 1.23/1.42 tff(4955,plain,
% 1.23/1.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[564, 4954])).
% 1.23/1.42 tff(4956,plain,
% 1.23/1.42 (~r(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1824, 28, 4949, 1655])).
% 1.23/1.42 tff(4957,plain,
% 1.23/1.42 (b(s(s(z)), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[296, 4956])).
% 1.23/1.42 tff(4958,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1783, 154, 2604, 684, 231, 142, 140])).
% 1.23/1.42 tff(4959,plain,((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4960,plain,
% 1.23/1.42 (~b(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4959, 4957, 684, 2604, 4939])).
% 1.23/1.42 tff(4961,plain,
% 1.23/1.42 (r(z, s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[64, 4960])).
% 1.23/1.42 tff(4962,plain,
% 1.23/1.42 (~r(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1346, 67, 18])).
% 1.23/1.42 tff(4963,plain,
% 1.23/1.42 (b(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[169, 4962])).
% 1.23/1.42 tff(4964,plain,
% 1.23/1.42 ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4697, 154, 142, 566, 254])).
% 1.23/1.42 tff(4965,plain,
% 1.23/1.42 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4964, 4963])).
% 1.23/1.42 tff(4966,plain,
% 1.23/1.42 (~r(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[3150, 67, 18])).
% 1.23/1.42 tff(4967,plain,
% 1.23/1.42 (b(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[648, 4966])).
% 1.23/1.42 tff(4968,plain,
% 1.23/1.42 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[1723, 4967, 16, 67, 18])).
% 1.23/1.42 tff(4969,plain,
% 1.23/1.42 ($false),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[138, 4968, 4965])).
% 1.23/1.42 tff(4970,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.42 tff(4971,plain,
% 1.23/1.42 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4970, 4949, 4961, 4939, 4955, 1934])).
% 1.23/1.42 tff(4972,plain,
% 1.23/1.42 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[104, 4971])).
% 1.23/1.42 tff(4973,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4974,plain,
% 1.23/1.42 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.23/1.42 inference(rewrite,[status(thm)],[])).
% 1.23/1.42 tff(4975,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 1.23/1.42 inference(monotonicity,[status(thm)],[4974])).
% 1.23/1.42 tff(4976,plain,
% 1.23/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.23/1.42 inference(transitivity,[status(thm)],[4975, 4973])).
% 1.23/1.42 tff(4977,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.42 inference(quant_inst,[status(thm)],[])).
% 1.23/1.42 tff(4978,plain,
% 1.23/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.23/1.42 inference(modus_ponens,[status(thm)],[4977, 4976])).
% 1.23/1.42 tff(4979,plain,
% 1.23/1.42 (~b(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4978, 154, 2604, 684, 4939, 4972])).
% 1.23/1.42 tff(4980,plain,
% 1.23/1.42 (r(s(s(s(z))), s(z))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[818, 4979])).
% 1.23/1.42 tff(4981,plain,
% 1.23/1.42 (~r(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[828, 4980, 14])).
% 1.23/1.42 tff(4982,plain,
% 1.23/1.42 (b(s(s(s(z))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[169, 4981])).
% 1.23/1.42 tff(4983,plain,
% 1.23/1.42 (~b(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[4929, 4982, 14, 1655, 2604, 4955])).
% 1.23/1.42 tff(4984,plain,
% 1.23/1.42 (r(s(s(s(s(z)))), z)),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[206, 4983])).
% 1.23/1.42 tff(4985,plain,
% 1.23/1.42 (~r(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[838, 4980, 14])).
% 1.23/1.42 tff(4986,plain,
% 1.23/1.42 (b(z, s(s(s(z))))),
% 1.23/1.42 inference(unit_resolution,[status(thm)],[648, 4985])).
% 1.23/1.43 tff(4987,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[742, 4982, 14, 4986, 4955])).
% 1.23/1.43 tff(4988,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[318, 4987])).
% 1.23/1.43 tff(4989,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(4990,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(4991,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[4990, 4989])).
% 1.23/1.43 tff(4992,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4991, 154, 2604, 4957, 4988, 4939])).
% 1.23/1.43 tff(4993,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[229, 4992])).
% 1.23/1.43 tff(4994,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(4995,plain,
% 1.23/1.43 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(4996,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[4995])).
% 1.23/1.43 tff(4997,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[4996, 4994])).
% 1.23/1.43 tff(4998,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(4999,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 1.23/1.43 tff(5000,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4999, 28, 14, 4961, 4993, 4984])).
% 1.23/1.43 tff(5001,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5002,plain,
% 1.23/1.43 (~r(s(z), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5001, 14, 2604, 684])).
% 1.23/1.43 tff(5003,plain,
% 1.23/1.43 (b(s(z), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1653, 5002])).
% 1.23/1.43 tff(5004,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[75, 67, 66])).
% 1.23/1.43 tff(5005,plain,
% 1.23/1.43 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5004])).
% 1.23/1.43 tff(5006,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1389, 5005, 684, 5003, 1272])).
% 1.23/1.43 tff(5007,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[318, 5006])).
% 1.23/1.43 tff(5008,plain,
% 1.23/1.43 (~r(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[724, 28, 14, 5007])).
% 1.23/1.43 tff(5009,plain,
% 1.23/1.43 (b(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[191, 5008])).
% 1.23/1.43 tff(5010,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[853, 5007, 66])).
% 1.23/1.43 tff(5011,plain,
% 1.23/1.43 (b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[818, 5010])).
% 1.23/1.43 tff(5012,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5013,plain,
% 1.23/1.43 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5014,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.23/1.43 inference(monotonicity,[status(thm)],[5013])).
% 1.23/1.43 tff(5015,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.43 inference(transitivity,[status(thm)],[5014, 5012])).
% 1.23/1.43 tff(5016,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.43 inference(quant_inst,[status(thm)],[])).
% 1.23/1.43 tff(5017,plain,
% 1.23/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.23/1.43 inference(modus_ponens,[status(thm)],[5016, 5015])).
% 1.23/1.43 tff(5018,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5017, 154, 2604, 5011, 1701, 5003, 5009])).
% 1.23/1.43 tff(5019,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5020,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5019, 106, 14, 66, 684, 2604])).
% 1.23/1.43 tff(5021,plain,
% 1.23/1.43 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[104, 5020])).
% 1.23/1.43 tff(5022,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3673, 171, 5003, 2604, 66])).
% 1.23/1.43 tff(5023,plain,
% 1.23/1.43 (b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[818, 5022])).
% 1.23/1.43 tff(5024,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[692, 5023, 684, 5021, 1272])).
% 1.23/1.43 tff(5025,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5024])).
% 1.23/1.43 tff(5026,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1292, 5023, 14, 5003, 171, 106])).
% 1.23/1.43 tff(5027,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5026])).
% 1.23/1.43 tff(5028,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[132, 5027, 5025, 66])).
% 1.23/1.43 tff(5029,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5030,plain,
% 1.23/1.43 (~r(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5029, 106, 14, 66, 684, 2604])).
% 1.23/1.43 tff(5031,plain,
% 1.23/1.43 (b(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[169, 5030])).
% 1.23/1.43 tff(5032,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3047, 820, 14, 5003, 106, 5031, 2604])).
% 1.23/1.43 tff(5033,plain,
% 1.23/1.43 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5032])).
% 1.23/1.43 tff(5034,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1389, 5033, 3755, 684, 5003, 1272])).
% 1.23/1.43 tff(5035,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5036,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5035, 106, 14, 684, 2604, 66])).
% 1.23/1.43 tff(5037,plain,
% 1.23/1.43 (b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[818, 5036])).
% 1.23/1.43 tff(5038,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[692, 5037, 684, 5021, 1272])).
% 1.23/1.43 tff(5039,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5038])).
% 1.23/1.43 tff(5040,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[132, 5039, 66])).
% 1.23/1.43 tff(5041,plain,
% 1.23/1.43 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5040])).
% 1.23/1.43 tff(5042,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1289, 154, 5037, 5041, 5003, 1272, 5021])).
% 1.23/1.43 tff(5043,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5044,plain,
% 1.23/1.43 (~r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5043, 66, 684, 14, 2604])).
% 1.23/1.43 tff(5045,plain,
% 1.23/1.43 (b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[122, 5044])).
% 1.23/1.43 tff(5046,plain,
% 1.23/1.43 (~b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4978, 154, 2604, 684, 5045, 2195])).
% 1.23/1.43 tff(5047,plain,
% 1.23/1.43 (r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[818, 5046])).
% 1.23/1.43 tff(5048,plain,
% 1.23/1.43 (~r(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[828, 5047, 14])).
% 1.23/1.43 tff(5049,plain,
% 1.23/1.43 (b(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[169, 5048])).
% 1.23/1.43 tff(5050,plain,
% 1.23/1.43 (~b(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[162, 5049, 5045, 2195, 2197])).
% 1.23/1.43 tff(5051,plain,
% 1.23/1.43 (r(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[64, 5050])).
% 1.23/1.43 tff(5052,plain,
% 1.23/1.43 (~r(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2439, 5051, 16])).
% 1.23/1.43 tff(5053,plain,
% 1.23/1.43 (b(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[191, 5052])).
% 1.23/1.43 tff(5054,plain,
% 1.23/1.43 (~r(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[881, 5047, 14])).
% 1.23/1.43 tff(5055,plain,
% 1.23/1.43 (b(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[296, 5054])).
% 1.23/1.43 tff(5056,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[260, 154, 2604, 5003, 5055, 5045, 5053])).
% 1.23/1.43 tff(5057,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5058,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5057, 66, 14, 684, 2604])).
% 1.23/1.43 tff(5059,plain,
% 1.23/1.43 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5058])).
% 1.23/1.43 tff(5060,plain,
% 1.23/1.43 (~b(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4947, 5059, 684, 2604, 5045])).
% 1.23/1.43 tff(5061,plain,
% 1.23/1.43 (r(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[191, 5060])).
% 1.23/1.43 tff(5062,plain,
% 1.23/1.43 (~r(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3225, 28, 5061, 66])).
% 1.23/1.43 tff(5063,plain,
% 1.23/1.43 (b(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[648, 5062])).
% 1.23/1.43 tff(5064,plain,
% 1.23/1.43 (~r(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[180, 5061, 66])).
% 1.23/1.43 tff(5065,plain,
% 1.23/1.43 (b(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[169, 5064])).
% 1.23/1.43 tff(5066,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[724, 28, 14, 172, 298])).
% 1.23/1.43 tff(5067,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5068,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5067, 5061, 14])).
% 1.23/1.43 tff(5069,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[318, 5068])).
% 1.23/1.43 tff(5070,plain,
% 1.23/1.43 (~b(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1389, 5069, 684, 5003, 5059])).
% 1.23/1.43 tff(5071,plain,
% 1.23/1.43 (r(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[296, 5070])).
% 1.23/1.43 tff(5072,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[881, 5071, 14])).
% 1.23/1.43 tff(5073,plain,
% 1.23/1.43 (b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[818, 5072])).
% 1.23/1.43 tff(5074,plain,
% 1.23/1.43 ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1240, 154, 143, 660, 142])).
% 1.23/1.43 tff(5075,plain,
% 1.23/1.43 (~b(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5074, 1598])).
% 1.23/1.43 tff(5076,plain,
% 1.23/1.43 (r(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[64, 5075])).
% 1.23/1.43 tff(5077,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[712, 28, 14, 5076, 299])).
% 1.23/1.43 tff(5078,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5079,plain,
% 1.23/1.43 (~r(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5078, 5071, 5065, 5063, 5045, 14])).
% 1.23/1.43 tff(5080,plain,
% 1.23/1.43 (b(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[252, 5079])).
% 1.23/1.43 tff(5081,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3091, 5080, 5073, 2604, 5065, 5063])).
% 1.23/1.43 tff(5082,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5083,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5082, 14, 2604, 684])).
% 1.23/1.43 tff(5084,plain,
% 1.23/1.43 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[564, 5083])).
% 1.23/1.43 tff(5085,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[764, 1272, 15, 566, 2895])).
% 1.23/1.43 tff(5086,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5085])).
% 1.23/1.43 tff(5087,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2276, 28, 5086, 106, 171])).
% 1.23/1.43 tff(5088,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5089,plain,
% 1.23/1.43 (~r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5088, 171, 5003, 5084, 14])).
% 1.23/1.43 tff(5090,plain,
% 1.23/1.43 (b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[122, 5089])).
% 1.23/1.43 tff(5091,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2917, 506, 15, 2604, 1, 171])).
% 1.23/1.43 tff(5092,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[206, 5091])).
% 1.23/1.43 tff(5093,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[752, 506, 15, 566, 1])).
% 1.23/1.43 tff(5094,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[343, 5093])).
% 1.23/1.43 tff(5095,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2179, 28, 5094, 171, 5092])).
% 1.23/1.43 tff(5096,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5097,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5096, 171, 5003, 5084, 2895, 2604])).
% 1.23/1.43 tff(5098,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[318, 5097])).
% 1.23/1.43 tff(5099,plain,
% 1.23/1.43 (~r(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5067, 5098, 14])).
% 1.23/1.43 tff(5100,plain,
% 1.23/1.43 (b(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[191, 5099])).
% 1.23/1.43 tff(5101,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4947, 5100, 684, 2604, 5090])).
% 1.23/1.43 tff(5102,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5101])).
% 1.23/1.43 tff(5103,plain,
% 1.23/1.43 (~r(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[307, 5102, 5098])).
% 1.23/1.43 tff(5104,plain,
% 1.23/1.43 (b(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[296, 5103])).
% 1.23/1.43 tff(5105,plain,
% 1.23/1.43 (~b(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4959, 5104, 684, 2604, 5090])).
% 1.23/1.43 tff(5106,plain,
% 1.23/1.43 (r(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[64, 5105])).
% 1.23/1.43 tff(5107,plain,
% 1.23/1.43 ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2957, 154, 2604, 2895, 5090])).
% 1.23/1.43 tff(5108,plain,
% 1.23/1.43 (~b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5107, 5104])).
% 1.23/1.43 tff(5109,plain,
% 1.23/1.43 (r(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[104, 5108])).
% 1.23/1.43 tff(5110,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1346, 5109, 5106, 171])).
% 1.23/1.43 tff(5111,plain,((~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5112,plain,
% 1.23/1.43 (~r(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5111, 14, 684, 2604])).
% 1.23/1.43 tff(5113,plain,
% 1.23/1.43 (b(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[169, 5112])).
% 1.23/1.43 tff(5114,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3016, 820, 14, 5113])).
% 1.23/1.43 tff(5115,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[318, 5114])).
% 1.23/1.43 tff(5116,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1389, 5115, 684, 5003, 883])).
% 1.23/1.43 tff(5117,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5116])).
% 1.23/1.43 tff(5118,plain,
% 1.23/1.43 (~r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3047, 5117, 14, 5003, 820, 5113, 2604])).
% 1.23/1.43 tff(5119,plain,
% 1.23/1.43 (b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[122, 5118])).
% 1.23/1.43 tff(5120,plain,
% 1.23/1.43 (~b(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4959, 5119, 684, 2604, 883])).
% 1.23/1.43 tff(5121,plain,
% 1.23/1.43 (r(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[64, 5120])).
% 1.23/1.43 tff(5122,plain,
% 1.23/1.43 (~r(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2439, 5121, 5117])).
% 1.23/1.43 tff(5123,plain,
% 1.23/1.43 (b(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[191, 5122])).
% 1.23/1.43 tff(5124,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[260, 154, 2604, 5003, 883, 5119, 5123])).
% 1.23/1.43 tff(5125,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5126,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5125, 14, 684, 2604])).
% 1.23/1.43 tff(5127,plain,
% 1.23/1.43 (b(s(s(s(z))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[818, 5126])).
% 1.23/1.43 tff(5128,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[752, 2282, 15, 566, 1])).
% 1.23/1.43 tff(5129,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[343, 5128])).
% 1.23/1.43 tff(5130,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[612, 5129, 16])).
% 1.23/1.43 tff(5131,plain,
% 1.23/1.43 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5130])).
% 1.23/1.43 tff(5132,plain,
% 1.23/1.43 (~b(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[585, 5131, 15, 566, 16, 1])).
% 1.23/1.43 tff(5133,plain,
% 1.23/1.43 (r(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[252, 5132])).
% 1.23/1.43 tff(5134,plain,
% 1.23/1.43 (~r(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[636, 5133, 14])).
% 1.23/1.43 tff(5135,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[764, 1272, 15, 566, 1])).
% 1.23/1.43 tff(5136,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1232, 106, 566, 143, 16])).
% 1.23/1.43 tff(5137,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[343, 5136])).
% 1.23/1.43 tff(5138,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[612, 5137, 16])).
% 1.23/1.43 tff(5139,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5138, 5135])).
% 1.23/1.43 tff(5140,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5141,plain,
% 1.23/1.43 (~r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5140, 16, 15, 566, 1, 143, 14])).
% 1.23/1.43 tff(5142,plain,
% 1.23/1.43 (b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[122, 5141])).
% 1.23/1.43 tff(5143,plain,
% 1.23/1.43 (~b(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5078, 5133, 143, 299, 5142, 14])).
% 1.23/1.43 tff(5144,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[648, 5143, 5134])).
% 1.23/1.43 tff(5145,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5146,plain,
% 1.23/1.43 (~r(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5145, 16, 14, 5003, 5084, 5113, 5127])).
% 1.23/1.43 tff(5147,plain,
% 1.23/1.43 (b(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[296, 5146])).
% 1.23/1.43 tff(5148,plain,
% 1.23/1.43 (~r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5140, 16, 5003, 5084, 5127, 5113, 14])).
% 1.23/1.43 tff(5149,plain,
% 1.23/1.43 (b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[122, 5148])).
% 1.23/1.43 tff(5150,plain,
% 1.23/1.43 ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2957, 154, 2604, 5127, 5149])).
% 1.23/1.43 tff(5151,plain,
% 1.23/1.43 (~b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5150, 5147])).
% 1.23/1.43 tff(5152,plain,
% 1.23/1.43 (r(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[104, 5151])).
% 1.23/1.43 tff(5153,plain,
% 1.23/1.43 (~b(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4959, 5147, 684, 2604, 5149])).
% 1.23/1.43 tff(5154,plain,
% 1.23/1.43 (r(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[64, 5153])).
% 1.23/1.43 tff(5155,plain,
% 1.23/1.43 (~r(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3150, 5154, 5152])).
% 1.23/1.43 tff(5156,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[764, 5147, 5003, 5084, 5127])).
% 1.23/1.43 tff(5157,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5156])).
% 1.23/1.43 tff(5158,plain,
% 1.23/1.43 (~b(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1723, 5152, 5157, 16, 5154])).
% 1.23/1.43 tff(5159,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[648, 5158, 5155])).
% 1.23/1.43 tff(5160,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5161,plain,
% 1.23/1.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5160, 14, 684, 2604])).
% 1.23/1.43 tff(5162,plain,
% 1.23/1.43 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5161])).
% 1.23/1.43 tff(5163,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5135])).
% 1.23/1.43 tff(5164,plain,
% 1.23/1.43 (~r(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2080, 5163, 106])).
% 1.23/1.43 tff(5165,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1389, 1272, 684, 15, 1283])).
% 1.23/1.43 tff(5166,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[318, 5165])).
% 1.23/1.43 tff(5167,plain,
% 1.23/1.43 (~b(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[742, 5166, 14, 566, 143])).
% 1.23/1.43 tff(5168,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[648, 5167, 5164])).
% 1.23/1.43 tff(5169,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5170,plain,
% 1.23/1.43 (~r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5169, 14, 5084, 5113, 684, 5003, 5162, 5127])).
% 1.23/1.43 tff(5171,plain,
% 1.23/1.43 (b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[122, 5170])).
% 1.23/1.43 tff(5172,plain,
% 1.23/1.43 (~b(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4947, 5171, 684, 2604, 5162])).
% 1.23/1.43 tff(5173,plain,
% 1.23/1.43 (r(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[191, 5172])).
% 1.23/1.43 tff(5174,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5067, 5173, 14])).
% 1.23/1.43 tff(5175,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[318, 5174])).
% 1.23/1.43 tff(5176,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[752, 5175, 5003, 5084, 5127])).
% 1.23/1.43 tff(5177,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[343, 5176])).
% 1.23/1.43 tff(5178,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1605, 5175, 684, 5003, 5162])).
% 1.23/1.43 tff(5179,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[229, 5178])).
% 1.23/1.43 tff(5180,plain,
% 1.23/1.43 (~r(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1251, 5179, 5173])).
% 1.23/1.43 tff(5181,plain,
% 1.23/1.43 (b(z, s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[64, 5180])).
% 1.23/1.43 tff(5182,plain,
% 1.23/1.43 (~r(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1471, 5181, 5162, 5171, 5177])).
% 1.23/1.43 tff(5183,plain,
% 1.23/1.43 (b(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[648, 5182])).
% 1.23/1.43 tff(5184,plain,
% 1.23/1.43 (~b(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3091, 5183, 2604, 5113, 5127])).
% 1.23/1.43 tff(5185,plain,
% 1.23/1.43 (~b(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1389, 5175, 684, 5003, 5162])).
% 1.23/1.43 tff(5186,plain,
% 1.23/1.43 (r(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[296, 5185])).
% 1.23/1.43 tff(5187,plain,
% 1.23/1.43 (~r(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5078, 5183, 5113, 5186, 5171, 14])).
% 1.23/1.43 tff(5188,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[252, 5187, 5184])).
% 1.23/1.43 tff(5189,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5190,plain,
% 1.23/1.43 (~r(z, s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5189, 2877, 4881])).
% 1.23/1.43 tff(5191,plain,
% 1.23/1.43 (b(z, s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1181, 5190])).
% 1.23/1.43 tff(5192,plain,
% 1.23/1.43 (~b(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2306, 1283, 684, 566, 141])).
% 1.23/1.43 tff(5193,plain,
% 1.23/1.43 (r(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[252, 5192])).
% 1.23/1.43 tff(5194,plain,
% 1.23/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2425, 1283, 566, 141, 144])).
% 1.23/1.43 tff(5195,plain,
% 1.23/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[343, 5194])).
% 1.23/1.43 tff(5196,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1957, 5195, 5193, 1655])).
% 1.23/1.43 tff(5197,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5198,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5197, 2340, 1932, 1655, 2344, 684])).
% 1.23/1.43 tff(5199,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1259, 5198])).
% 1.23/1.43 tff(5200,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1824, 28, 5199, 299, 1655])).
% 1.23/1.43 tff(5201,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5202,plain,
% 1.23/1.43 (~r(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5201, 820, 4881, 1655])).
% 1.23/1.43 tff(5203,plain,
% 1.23/1.43 (b(s(s(z)), s(z))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[296, 5202])).
% 1.23/1.43 tff(5204,plain,
% 1.23/1.43 (~b(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3436, 5203, 2877, 4881, 5191])).
% 1.23/1.43 tff(5205,plain,
% 1.23/1.43 (r(s(s(z)), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[122, 5204])).
% 1.23/1.43 tff(5206,plain,
% 1.23/1.43 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1280, 171, 106])).
% 1.23/1.43 tff(5207,plain,
% 1.23/1.43 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[104, 5206])).
% 1.23/1.43 tff(5208,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5197, 5207, 566, 1655, 1283, 684])).
% 1.23/1.43 tff(5209,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5208])).
% 1.23/1.43 tff(5210,plain,
% 1.23/1.43 ($false),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2276, 28, 5209, 106, 171])).
% 1.23/1.43 tff(5211,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.43 tff(5212,plain,
% 1.23/1.43 (~r(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5211, 1283, 1932, 1655, 5205, 4881])).
% 1.23/1.43 tff(5213,plain,
% 1.23/1.43 (b(s(s(s(z))), z)),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[169, 5212])).
% 1.23/1.43 tff(5214,plain,
% 1.23/1.43 (~r(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3567, 1283, 1655, 12])).
% 1.23/1.43 tff(5215,plain,
% 1.23/1.43 (b(z, s(s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[191, 5214])).
% 1.23/1.43 tff(5216,plain,
% 1.23/1.43 ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[4902, 154, 2877, 1932, 5215])).
% 1.23/1.43 tff(5217,plain,
% 1.23/1.43 (~b(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[5216, 5213])).
% 1.23/1.43 tff(5218,plain,
% 1.23/1.43 (r(s(z), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[252, 5217])).
% 1.23/1.43 tff(5219,plain,
% 1.23/1.43 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1957, 5218, 1655])).
% 1.23/1.43 tff(5220,plain,
% 1.23/1.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[343, 5219])).
% 1.23/1.43 tff(5221,plain,
% 1.23/1.43 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[3481, 5220, 2877, 4881, 5191, 820, 1283, 1932])).
% 1.23/1.43 tff(5222,plain,
% 1.23/1.43 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[138, 5221])).
% 1.23/1.43 tff(5223,plain,
% 1.23/1.43 (~r(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[2080, 5222, 5205])).
% 1.23/1.43 tff(5224,plain,
% 1.23/1.43 (b(z, s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[648, 5223])).
% 1.23/1.43 tff(5225,plain,
% 1.23/1.43 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[1135, 5222, 4881, 820])).
% 1.23/1.43 tff(5226,plain,
% 1.23/1.43 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.43 inference(unit_resolution,[status(thm)],[496, 5225])).
% 1.23/1.43 tff(5227,plain,
% 1.23/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.43 inference(rewrite,[status(thm)],[])).
% 1.23/1.43 tff(5228,plain,
% 1.23/1.44 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5229,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5228])).
% 1.23/1.44 tff(5230,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5229, 5227])).
% 1.23/1.44 tff(5231,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5232,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5231, 5230])).
% 1.23/1.44 tff(5233,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5232, 154, 3811, 443, 660, 566, 254])).
% 1.23/1.44 tff(5234,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5235,plain,
% 1.23/1.44 (~b(s(s(s(s(elem!1)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5234, 5226, 5215, 1932, 5224])).
% 1.23/1.44 tff(5236,plain,
% 1.23/1.44 (r(s(s(s(s(elem!1)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[418, 5235])).
% 1.23/1.44 tff(5237,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[4503, 28, 5205, 5236])).
% 1.23/1.44 tff(5238,plain,
% 1.23/1.44 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[373, 60, 370, 5237])).
% 1.23/1.44 tff(5239,plain,
% 1.23/1.44 (~b(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1816, 154, 5220, 5224, 1932, 5215])).
% 1.23/1.44 tff(5240,plain,
% 1.23/1.44 (r(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[206, 5239])).
% 1.23/1.44 tff(5241,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2367, 28, 5236, 5240])).
% 1.23/1.44 tff(5242,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[517, 60, 12, 5241])).
% 1.23/1.44 tff(5243,plain,
% 1.23/1.44 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3399, 154, 5226, 5220, 1283])).
% 1.23/1.44 tff(5244,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5243, 5242, 5238])).
% 1.23/1.44 tff(5245,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5246,plain,
% 1.23/1.44 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5245, 820, 12, 1655])).
% 1.23/1.44 tff(5247,plain,
% 1.23/1.44 (r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1259, 5246])).
% 1.23/1.44 tff(5248,plain,
% 1.23/1.44 (~r(z, s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[913, 5247, 5205])).
% 1.23/1.44 tff(5249,plain,
% 1.23/1.44 (b(z, s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[191, 5248])).
% 1.23/1.44 tff(5250,plain,
% 1.23/1.44 (~r(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[923, 5247, 5205])).
% 1.23/1.44 tff(5251,plain,
% 1.23/1.44 (b(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[206, 5250])).
% 1.23/1.44 tff(5252,plain,
% 1.23/1.44 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3834, 154, 5191, 2877, 5251, 5249])).
% 1.23/1.44 tff(5253,plain,
% 1.23/1.44 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[318, 5252])).
% 1.23/1.44 tff(5254,plain,
% 1.23/1.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1411, 5253, 820])).
% 1.23/1.44 tff(5255,plain,
% 1.23/1.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[343, 5254])).
% 1.23/1.44 tff(5256,plain,
% 1.23/1.44 (~b(s(s(s(z))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1232, 5255, 1932, 5247, 5205])).
% 1.23/1.44 tff(5257,plain,
% 1.23/1.44 (r(s(s(s(z))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[169, 5256])).
% 1.23/1.44 tff(5258,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2276, 28, 5205, 5257])).
% 1.23/1.44 tff(5259,plain,
% 1.23/1.44 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[138, 5258])).
% 1.23/1.44 tff(5260,plain,
% 1.23/1.44 (~b(s(z), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2660, 5259, 4881, 5203, 820, 5205])).
% 1.23/1.44 tff(5261,plain,
% 1.23/1.44 (r(s(z), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[252, 5260])).
% 1.23/1.44 tff(5262,plain,
% 1.23/1.44 (~b(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1816, 154, 5251, 5255, 1932, 5249])).
% 1.23/1.44 tff(5263,plain,
% 1.23/1.44 (r(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[648, 5262])).
% 1.23/1.44 tff(5264,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3311, 28, 780, 628])).
% 1.23/1.44 tff(5265,plain,
% 1.23/1.44 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[786, 28, 780, 273])).
% 1.23/1.44 tff(5266,plain,
% 1.23/1.44 (b(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[467, 5265])).
% 1.23/1.44 tff(5267,plain,
% 1.23/1.44 (~b(s(s(s(s(elem!1)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3322, 5266])).
% 1.23/1.44 tff(5268,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[416, 60, 388, 5267, 5264])).
% 1.23/1.44 tff(5269,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5270,plain,
% 1.23/1.44 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5269, 780, 2604, 628, 1726, 273])).
% 1.23/1.44 tff(5271,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[441, 943, 5270])).
% 1.23/1.44 tff(5272,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5273,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5272, 820, 2877, 5263, 5191, 5261])).
% 1.23/1.44 tff(5274,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[496, 5273])).
% 1.23/1.44 tff(5275,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3420, 5274, 12, 820, 5253, 1932, 5255])).
% 1.23/1.44 tff(5276,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[441, 5275])).
% 1.23/1.44 tff(5277,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[4673, 28, 402, 171])).
% 1.23/1.44 tff(5278,plain,
% 1.23/1.44 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[989, 5277])).
% 1.23/1.44 tff(5279,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3313, 402, 628])).
% 1.23/1.44 tff(5280,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[496, 5279])).
% 1.23/1.44 tff(5281,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2276, 28, 106, 171])).
% 1.23/1.44 tff(5282,plain,
% 1.23/1.44 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[138, 5281])).
% 1.23/1.44 tff(5283,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5284,plain,
% 1.23/1.44 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5285,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5284])).
% 1.23/1.44 tff(5286,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5285, 5283])).
% 1.23/1.44 tff(5287,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5288,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5287, 5286])).
% 1.23/1.44 tff(5289,plain,
% 1.23/1.44 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5288, 154, 5282, 5280, 5207])).
% 1.23/1.44 tff(5290,plain,
% 1.23/1.44 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5289, 5278])).
% 1.23/1.44 tff(5291,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5292,plain,
% 1.23/1.44 (((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5293,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5292])).
% 1.23/1.44 tff(5294,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5293, 5291])).
% 1.23/1.44 tff(5295,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5296,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.23/1.44 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 1.23/1.44 tff(5297,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5296, 28, 16, 106, 402])).
% 1.23/1.44 tff(5298,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1051, 60, 5297, 1048, 5290])).
% 1.23/1.44 tff(5299,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5300,plain,
% 1.23/1.44 (~r(s(s(s(s(elem!1)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5299, 5247, 5205, 5257, 5263])).
% 1.23/1.44 tff(5301,plain,
% 1.23/1.44 (b(s(s(s(s(elem!1)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[418, 5300])).
% 1.23/1.44 tff(5302,plain,
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% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5303,plain,
% 1.23/1.44 (((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5304,plain,
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% 1.23/1.44 inference(monotonicity,[status(thm)],[5303])).
% 1.23/1.44 tff(5305,plain,
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% 1.23/1.44 inference(transitivity,[status(thm)],[5304, 5302])).
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% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
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% 1.23/1.44 inference(modus_ponens,[status(thm)],[5306, 5305])).
% 1.23/1.44 tff(5308,plain,
% 1.23/1.44 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5307, 154, 5301, 2877, 5203])).
% 1.23/1.44 tff(5309,plain,
% 1.23/1.44 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5308, 5276])).
% 1.23/1.44 tff(5310,plain,
% 1.23/1.44 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[373, 60, 370, 5309])).
% 1.23/1.44 tff(5311,plain,
% 1.23/1.44 ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3992, 154, 5191, 5301, 2877])).
% 1.23/1.44 tff(5312,plain,
% 1.23/1.44 (~b(z, s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5311, 5276])).
% 1.23/1.44 tff(5313,plain,
% 1.23/1.44 (r(z, s(s(s(s(elem!1)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[548, 5312])).
% 1.23/1.44 tff(5314,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5315,plain,
% 1.23/1.44 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5316,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.23/1.44 inference(monotonicity,[status(thm)],[5315])).
% 1.23/1.44 tff(5317,plain,
% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.23/1.44 inference(transitivity,[status(thm)],[5316, 5314])).
% 1.23/1.44 tff(5318,plain,
% 1.23/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)))),
% 1.23/1.44 inference(quant_inst,[status(thm)],[])).
% 1.23/1.44 tff(5319,plain,
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% 1.23/1.44 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 1.23/1.44 tff(5320,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5319, 28, 5205, 5313, 5310])).
% 1.23/1.44 tff(5321,plain,((~r(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5322,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5321, 1655, 12])).
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% 1.23/1.44 (b(s(s(s(z))), s(z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[818, 5322])).
% 1.23/1.44 tff(5324,plain,
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% 1.23/1.44 inference(unit_resolution,[status(thm)],[5189, 2604, 684])).
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% 1.23/1.44 inference(unit_resolution,[status(thm)],[1181, 5324])).
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% 1.23/1.44 (~b(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3436, 4951, 2604, 684, 5325])).
% 1.23/1.44 tff(5327,plain,
% 1.23/1.44 (r(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[122, 5326])).
% 1.23/1.44 tff(5328,plain,
% 1.23/1.44 (~r(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2080, 5327, 124])).
% 1.23/1.44 tff(5329,plain,
% 1.23/1.44 (b(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[648, 5328])).
% 1.23/1.44 tff(5330,plain,
% 1.23/1.44 (~r(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[923, 5327, 16])).
% 1.23/1.44 tff(5331,plain,
% 1.23/1.44 (b(s(s(s(s(z)))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[206, 5330])).
% 1.23/1.44 tff(5332,plain,
% 1.23/1.44 ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2811, 154, 5325, 1, 1711])).
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% 1.23/1.44 inference(unit_resolution,[status(thm)],[5332, 5331, 5329])).
% 1.23/1.44 tff(5334,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5335,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(s(z)))))),
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% 1.23/1.44 tff(5336,plain,
% 1.23/1.44 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[1259, 5335])).
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% 1.23/1.44 (~r(z, s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3567, 5336, 1655, 12])).
% 1.23/1.44 tff(5338,plain,
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% 1.23/1.44 tff(5339,plain,
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% 1.23/1.44 inference(unit_resolution,[status(thm)],[4947, 5338, 4881, 2877, 5336])).
% 1.23/1.44 tff(5340,plain,
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% 1.23/1.44 inference(unit_resolution,[status(thm)],[122, 5339])).
% 1.23/1.44 tff(5341,plain,
% 1.23/1.44 (~r(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2080, 5340, 124])).
% 1.23/1.44 tff(5342,plain,
% 1.23/1.44 (b(z, s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[648, 5341])).
% 1.23/1.44 tff(5343,plain,
% 1.23/1.44 (~r(z, s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3227, 66, 1655])).
% 1.23/1.44 tff(5344,plain,
% 1.23/1.44 (b(z, s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[191, 5343])).
% 1.23/1.44 tff(5345,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[4953, 66, 684, 1655])).
% 1.23/1.44 tff(5346,plain,
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% 1.23/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.44 inference(rewrite,[status(thm)],[])).
% 1.23/1.44 tff(5348,plain,
% 1.23/1.44 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
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% 1.23/1.44 inference(unit_resolution,[status(thm)],[64, 5353])).
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% 1.23/1.44 inference(unit_resolution,[status(thm)],[648, 5355])).
% 1.23/1.44 tff(5357,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3150, 5356, 5354])).
% 1.23/1.44 tff(5358,plain,
% 1.23/1.44 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[104, 5357])).
% 1.23/1.44 tff(5359,plain,
% 1.23/1.44 (~b(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[4947, 5344, 684, 2604, 5346])).
% 1.23/1.44 tff(5360,plain,
% 1.23/1.44 (r(s(s(z)), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[122, 5359])).
% 1.23/1.44 tff(5361,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[2080, 5356, 5360])).
% 1.23/1.44 tff(5362,plain,
% 1.23/1.44 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[138, 5361])).
% 1.23/1.44 tff(5363,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[802, 154, 5362, 1, 4883, 684, 5358])).
% 1.23/1.44 tff(5364,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5365,plain,
% 1.23/1.44 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5364, 5323, 4881, 2877, 1655])).
% 1.23/1.44 tff(5366,plain,
% 1.23/1.44 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[564, 5365])).
% 1.23/1.44 tff(5367,plain,
% 1.23/1.44 (~r(s(s(s(z))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5211, 5340, 5366, 1655, 5336, 4881])).
% 1.23/1.44 tff(5368,plain,
% 1.23/1.44 (b(s(s(s(z))), z)),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[169, 5367])).
% 1.23/1.44 tff(5369,plain,
% 1.23/1.44 ($false),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3217, 5368, 5342, 2877, 5191, 5323])).
% 1.23/1.44 tff(5370,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.44 tff(5371,plain,
% 1.23/1.44 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[5370, 1655, 12])).
% 1.23/1.44 tff(5372,plain,
% 1.23/1.44 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[138, 5371])).
% 1.23/1.44 tff(5373,plain,
% 1.23/1.44 (~b(z, s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[3557, 142, 2604, 684, 5325])).
% 1.23/1.44 tff(5374,plain,
% 1.23/1.44 (r(z, s(s(z)))),
% 1.23/1.44 inference(unit_resolution,[status(thm)],[64, 5373])).
% 1.23/1.45 tff(5375,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5376,plain,
% 1.23/1.45 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5377,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5376])).
% 1.23/1.45 tff(5378,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5377, 5375])).
% 1.23/1.45 tff(5379,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5380,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5379, 5378])).
% 1.23/1.45 tff(5381,plain,
% 1.23/1.45 ((~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5380, 154, 144, 5325, 1])).
% 1.23/1.45 tff(5382,plain,
% 1.23/1.45 (~b(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5381, 142])).
% 1.23/1.45 tff(5383,plain,
% 1.23/1.45 (r(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[648, 5382])).
% 1.23/1.45 tff(5384,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3150, 5383, 5374])).
% 1.23/1.45 tff(5385,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[104, 5384])).
% 1.23/1.45 tff(5386,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[4978, 154, 2604, 1, 684, 142, 5385])).
% 1.23/1.45 tff(5387,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5388,plain,
% 1.23/1.45 (~b(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5387, 5323, 2877, 4881, 5372])).
% 1.23/1.45 tff(5389,plain,
% 1.23/1.45 (r(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[122, 5388])).
% 1.23/1.45 tff(5390,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5364, 1, 684, 2604, 1655])).
% 1.23/1.45 tff(5391,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[564, 5390])).
% 1.23/1.45 tff(5392,plain,
% 1.23/1.45 (~b(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5387, 1, 2604, 684, 144])).
% 1.23/1.45 tff(5393,plain,
% 1.23/1.45 (r(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[122, 5392])).
% 1.23/1.45 tff(5394,plain,
% 1.23/1.45 (~r(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5211, 1283, 5391, 1655, 5393, 684])).
% 1.23/1.45 tff(5395,plain,
% 1.23/1.45 (b(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[169, 5394])).
% 1.23/1.45 tff(5396,plain,
% 1.23/1.45 (~b(s(s(s(s(z)))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2553, 5395, 5391, 144, 1283])).
% 1.23/1.45 tff(5397,plain,
% 1.23/1.45 (r(s(s(s(s(z)))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[206, 5396])).
% 1.23/1.45 tff(5398,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3067, 5397, 5393])).
% 1.23/1.45 tff(5399,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[229, 5398])).
% 1.23/1.45 tff(5400,plain,
% 1.23/1.45 (~b(s(z), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3184, 5395, 2604, 5325, 1])).
% 1.23/1.45 tff(5401,plain,
% 1.23/1.45 (r(s(z), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[252, 5400])).
% 1.23/1.45 tff(5402,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1957, 5401, 1655])).
% 1.23/1.45 tff(5403,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[343, 5402])).
% 1.23/1.45 tff(5404,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2654, 154, 144, 5403, 1283, 5399, 5391])).
% 1.23/1.45 tff(5405,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5406,plain,
% 1.23/1.45 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5405, 5372, 1655, 2877, 5323, 4881])).
% 1.23/1.45 tff(5407,plain,
% 1.23/1.45 (r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1259, 5406])).
% 1.23/1.45 tff(5408,plain,
% 1.23/1.45 (~r(s(s(z)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3847, 5407, 5191, 5389])).
% 1.23/1.45 tff(5409,plain,
% 1.23/1.45 (b(s(s(z)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[296, 5408])).
% 1.23/1.45 tff(5410,plain,
% 1.23/1.45 (~b(s(s(s(z))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[692, 5409, 4881, 5323, 5372])).
% 1.23/1.45 tff(5411,plain,
% 1.23/1.45 (r(s(s(s(z))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[104, 5410])).
% 1.23/1.45 tff(5412,plain,
% 1.23/1.45 (~b(z, s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2612, 5409, 2877, 4881, 5191])).
% 1.23/1.45 tff(5413,plain,
% 1.23/1.45 (r(z, s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[64, 5412])).
% 1.23/1.45 tff(5414,plain,
% 1.23/1.45 (~r(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3150, 5413, 5411])).
% 1.23/1.45 tff(5415,plain,
% 1.23/1.45 (~b(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1705, 5411, 5407, 5389])).
% 1.23/1.45 tff(5416,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[648, 5415, 5414])).
% 1.23/1.45 tff(5417,plain,((~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5418,plain,
% 1.23/1.45 (~r(s(z), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5417, 12])).
% 1.23/1.45 tff(5419,plain,
% 1.23/1.45 (b(s(z), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1653, 5418])).
% 1.23/1.45 tff(5420,plain,
% 1.23/1.45 (~b(s(s(z)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3436, 142, 2604, 684, 5325])).
% 1.23/1.45 tff(5421,plain,
% 1.23/1.45 (r(s(s(z)), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[296, 5420])).
% 1.23/1.45 tff(5422,plain,
% 1.23/1.45 (~r(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2439, 16, 18])).
% 1.23/1.45 tff(5423,plain,
% 1.23/1.45 (b(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[191, 5422])).
% 1.23/1.45 tff(5424,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3767, 154, 1726, 2604, 15, 2897, 5423])).
% 1.23/1.45 tff(5425,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5426,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5425, 5421, 2604, 15, 5325, 5374])).
% 1.23/1.45 tff(5427,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1259, 5426])).
% 1.23/1.45 tff(5428,plain,
% 1.23/1.45 (~b(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[4947, 5427, 684, 2604, 142])).
% 1.23/1.45 tff(5429,plain,
% 1.23/1.45 (r(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[191, 5428])).
% 1.23/1.45 tff(5430,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1251, 5429, 5374])).
% 1.23/1.45 tff(5431,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[229, 5430])).
% 1.23/1.45 tff(5432,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1125, 124, 299])).
% 1.23/1.45 tff(5433,plain,
% 1.23/1.45 (b(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[818, 5432])).
% 1.23/1.45 tff(5434,plain,
% 1.23/1.45 (~r(s(z), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[657, 124, 299])).
% 1.23/1.45 tff(5435,plain,
% 1.23/1.45 (b(s(z), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[252, 5434])).
% 1.23/1.45 tff(5436,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1749, 5435, 299, 124, 5433])).
% 1.23/1.45 tff(5437,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1259, 5436])).
% 1.23/1.45 tff(5438,plain,
% 1.23/1.45 (~b(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3660, 5435, 2604, 5325, 5433])).
% 1.23/1.45 tff(5439,plain,
% 1.23/1.45 (r(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[648, 5438])).
% 1.23/1.45 tff(5440,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3150, 5439, 18])).
% 1.23/1.45 tff(5441,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[104, 5440])).
% 1.23/1.45 tff(5442,plain,
% 1.23/1.45 (~b(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3184, 5435, 2604, 5325, 5433])).
% 1.23/1.45 tff(5443,plain,
% 1.23/1.45 (r(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[169, 5442])).
% 1.23/1.45 tff(5444,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3711, 5443, 2604, 5325, 15])).
% 1.23/1.45 tff(5445,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[564, 5444])).
% 1.23/1.45 tff(5446,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2306, 5445, 5441, 684, 5435, 5437])).
% 1.23/1.45 tff(5447,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5448,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5447, 5374, 2604, 15, 684, 5421])).
% 1.23/1.45 tff(5449,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[138, 5448])).
% 1.23/1.45 tff(5450,plain,
% 1.23/1.45 (~b(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5387, 5449, 2604, 684, 142])).
% 1.23/1.45 tff(5451,plain,
% 1.23/1.45 (r(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[818, 5450])).
% 1.23/1.45 tff(5452,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5453,plain,
% 1.23/1.45 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5454,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5453])).
% 1.23/1.45 tff(5455,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5454, 5452])).
% 1.23/1.45 tff(5456,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5457,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5456, 5455])).
% 1.23/1.45 tff(5458,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5457, 154, 144, 615, 1283, 684, 15])).
% 1.23/1.45 tff(5459,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5460,plain,
% 1.23/1.45 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5459, 5427, 684, 15, 5449])).
% 1.23/1.45 tff(5461,plain,
% 1.23/1.45 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[343, 5460])).
% 1.23/1.45 tff(5462,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1411, 5461, 5451])).
% 1.23/1.45 tff(5463,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[318, 5462])).
% 1.23/1.45 tff(5464,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1605, 5463, 5431, 684, 15, 5427])).
% 1.23/1.45 tff(5465,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5466,plain,
% 1.23/1.45 (~b(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5465, 4881, 5419, 2877])).
% 1.23/1.45 tff(5467,plain,
% 1.23/1.45 (r(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[122, 5466])).
% 1.23/1.45 tff(5468,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3196, 5467, 2877, 5191, 5419])).
% 1.23/1.45 tff(5469,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1259, 5468])).
% 1.23/1.45 tff(5470,plain,
% 1.23/1.45 (~b(z, s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2612, 1127, 2877, 4881, 5191])).
% 1.23/1.45 tff(5471,plain,
% 1.23/1.45 (r(z, s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[64, 5470])).
% 1.23/1.45 tff(5472,plain,
% 1.23/1.45 (~r(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2080, 124, 5467])).
% 1.23/1.45 tff(5473,plain,
% 1.23/1.45 (b(z, s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[648, 5472])).
% 1.23/1.45 tff(5474,plain,
% 1.23/1.45 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1389, 1127, 4881, 5419, 5469])).
% 1.23/1.45 tff(5475,plain,
% 1.23/1.45 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[318, 5474])).
% 1.23/1.45 tff(5476,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[853, 5475, 820])).
% 1.23/1.45 tff(5477,plain,
% 1.23/1.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[564, 5476])).
% 1.23/1.45 tff(5478,plain,
% 1.23/1.45 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1135, 124, 4881, 820])).
% 1.23/1.45 tff(5479,plain,
% 1.23/1.45 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[496, 5478])).
% 1.23/1.45 tff(5480,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1411, 5475, 820])).
% 1.23/1.45 tff(5481,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[343, 5480])).
% 1.23/1.45 tff(5482,plain,
% 1.23/1.45 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3420, 5477, 12, 820, 5479, 5475, 5481])).
% 1.23/1.45 tff(5483,plain,
% 1.23/1.45 (b(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[441, 5482])).
% 1.23/1.45 tff(5484,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5485,plain,
% 1.23/1.45 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5486,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5485])).
% 1.23/1.45 tff(5487,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5486, 5484])).
% 1.23/1.45 tff(5488,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5489,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5488, 5487])).
% 1.23/1.45 tff(5490,plain,
% 1.23/1.45 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5489, 154, 5483, 5469, 5419, 1127])).
% 1.23/1.45 tff(5491,plain,
% 1.23/1.45 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1051, 60, 1048, 5490])).
% 1.23/1.45 tff(5492,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5493,plain,
% 1.23/1.45 (((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5494,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5493])).
% 1.23/1.45 tff(5495,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5494, 5492])).
% 1.23/1.45 tff(5496,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5497,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5496, 5495])).
% 1.23/1.45 tff(5498,plain,
% 1.23/1.45 (~r(s(s(s(s(elem!1)))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5497, 28, 5471, 5491])).
% 1.23/1.45 tff(5499,plain,
% 1.23/1.45 (b(s(s(s(s(elem!1)))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[418, 5498])).
% 1.23/1.45 tff(5500,plain,
% 1.23/1.45 (~b(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5234, 5499, 5479, 5477, 5473])).
% 1.23/1.45 tff(5501,plain,
% 1.23/1.45 (r(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[191, 5500])).
% 1.23/1.45 tff(5502,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1251, 5501, 5471])).
% 1.23/1.45 tff(5503,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[229, 5502])).
% 1.23/1.45 tff(5504,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1435, 154, 5469, 5419, 4881, 1127, 5503])).
% 1.23/1.45 tff(5505,plain,((~r(s(s(z)), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5506,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5505, 820, 12])).
% 1.23/1.45 tff(5507,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[138, 5506])).
% 1.23/1.45 tff(5508,plain,
% 1.23/1.45 (~b(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5465, 684, 15, 2604])).
% 1.23/1.45 tff(5509,plain,
% 1.23/1.45 (r(s(s(z)), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[122, 5508])).
% 1.23/1.45 tff(5510,plain,
% 1.23/1.45 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3196, 5509, 2604, 5325, 15])).
% 1.23/1.45 tff(5511,plain,
% 1.23/1.45 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1259, 5510])).
% 1.23/1.45 tff(5512,plain,
% 1.23/1.45 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1605, 506, 684, 15, 5511])).
% 1.23/1.45 tff(5513,plain,
% 1.23/1.45 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[229, 5512])).
% 1.23/1.45 tff(5514,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3067, 5513, 5509])).
% 1.23/1.45 tff(5515,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[206, 5514])).
% 1.23/1.45 tff(5516,plain,
% 1.23/1.45 (~b(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[2905, 5515, 2604, 15, 506])).
% 1.23/1.45 tff(5517,plain,
% 1.23/1.45 (r(z, s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[191, 5516])).
% 1.23/1.45 tff(5518,plain,
% 1.23/1.45 (~r(z, s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1251, 5517, 5513])).
% 1.23/1.45 tff(5519,plain,
% 1.23/1.45 (b(z, s(s(z)))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[64, 5518])).
% 1.23/1.45 tff(5520,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5521,plain,
% 1.23/1.45 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.23/1.45 inference(rewrite,[status(thm)],[])).
% 1.23/1.45 tff(5522,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.23/1.45 inference(monotonicity,[status(thm)],[5521])).
% 1.23/1.45 tff(5523,plain,
% 1.23/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.23/1.45 inference(transitivity,[status(thm)],[5522, 5520])).
% 1.23/1.45 tff(5524,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.23/1.45 inference(quant_inst,[status(thm)],[])).
% 1.23/1.45 tff(5525,plain,
% 1.23/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.23/1.45 inference(modus_ponens,[status(thm)],[5524, 5523])).
% 1.23/1.45 tff(5526,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5525, 154, 5325, 5515, 684, 506, 5519])).
% 1.23/1.45 tff(5527,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5528,plain,
% 1.23/1.45 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5527, 4881, 2877, 5419])).
% 1.23/1.45 tff(5529,plain,
% 1.23/1.45 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[318, 5528])).
% 1.23/1.45 tff(5530,plain,
% 1.23/1.45 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[1411, 820, 5529])).
% 1.23/1.45 tff(5531,plain,
% 1.23/1.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[343, 5530])).
% 1.23/1.45 tff(5532,plain,
% 1.23/1.45 ($false),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5459, 5531, 5507, 4881, 5419, 5469])).
% 1.23/1.45 tff(5533,plain,((~r(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.45 tff(5534,plain,
% 1.23/1.45 (~r(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5533, 12])).
% 1.23/1.45 tff(5535,plain,
% 1.23/1.45 (b(s(s(s(z))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[818, 5534])).
% 1.23/1.45 tff(5536,plain,
% 1.23/1.45 (~b(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[5527, 684, 2604, 15])).
% 1.23/1.45 tff(5537,plain,
% 1.23/1.45 (r(s(s(s(s(z)))), s(z))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[318, 5536])).
% 1.23/1.45 tff(5538,plain,
% 1.23/1.45 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[764, 231, 15, 144, 1])).
% 1.23/1.45 tff(5539,plain,
% 1.23/1.45 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[564, 5538])).
% 1.23/1.45 tff(5540,plain,
% 1.23/1.45 (~r(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[3711, 5539, 2604, 5325, 15])).
% 1.23/1.45 tff(5541,plain,
% 1.23/1.45 (b(s(s(s(z))), z)),
% 1.23/1.45 inference(unit_resolution,[status(thm)],[169, 5540])).
% 1.23/1.45 tff(5542,plain,
% 1.23/1.46 (~b(z, s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2612, 231, 2604, 684, 5325])).
% 1.23/1.46 tff(5543,plain,
% 1.23/1.46 (r(z, s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[64, 5542])).
% 1.23/1.46 tff(5544,plain,
% 1.23/1.46 (~b(s(s(s(z))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[692, 231, 684, 1, 144])).
% 1.23/1.46 tff(5545,plain,
% 1.23/1.46 (r(s(s(s(z))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[104, 5544])).
% 1.23/1.46 tff(5546,plain,
% 1.23/1.46 (~r(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3150, 5545, 5543])).
% 1.23/1.46 tff(5547,plain,
% 1.23/1.46 (b(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[648, 5546])).
% 1.23/1.46 tff(5548,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3217, 5547, 5541, 2604, 5325, 1])).
% 1.23/1.46 tff(5549,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5550,plain,
% 1.23/1.46 (~b(s(s(z)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5549, 144, 1, 15, 684, 2604])).
% 1.23/1.46 tff(5551,plain,
% 1.23/1.46 (r(s(s(z)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[296, 5550])).
% 1.23/1.46 tff(5552,plain,
% 1.23/1.46 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2252, 28, 5551, 5537])).
% 1.23/1.46 tff(5553,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[229, 5552])).
% 1.23/1.46 tff(5554,plain,
% 1.23/1.46 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3196, 106, 2604, 1726, 15])).
% 1.23/1.46 tff(5555,plain,
% 1.23/1.46 (b(s(s(z)), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1259, 5554])).
% 1.23/1.46 tff(5556,plain,
% 1.23/1.46 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3711, 171, 2604, 1726, 15])).
% 1.23/1.46 tff(5557,plain,
% 1.23/1.46 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[564, 5556])).
% 1.23/1.46 tff(5558,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[4526, 5207, 5557, 144, 1603, 5555])).
% 1.23/1.46 tff(5559,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5560,plain,
% 1.23/1.46 (~r(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5559, 144, 5553, 5509, 2604, 5325, 15])).
% 1.23/1.46 tff(5561,plain,
% 1.23/1.46 (b(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[169, 5560])).
% 1.23/1.46 tff(5562,plain,
% 1.23/1.46 (~b(s(s(s(z))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3741, 5561, 15, 5509, 2604, 5511, 1, 144, 5325])).
% 1.23/1.46 tff(5563,plain,
% 1.23/1.46 (r(s(s(s(z))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[104, 5562])).
% 1.23/1.46 tff(5564,plain,
% 1.23/1.46 (~b(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3217, 5561, 2604, 5325, 1])).
% 1.23/1.46 tff(5565,plain,
% 1.23/1.46 (r(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[648, 5564])).
% 1.23/1.46 tff(5566,plain,
% 1.23/1.46 (~r(z, s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3150, 5565, 5563])).
% 1.23/1.46 tff(5567,plain,
% 1.23/1.46 (b(z, s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[64, 5566])).
% 1.23/1.46 tff(5568,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5569,plain,
% 1.23/1.46 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5570,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5569])).
% 1.23/1.46 tff(5571,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5570, 5568])).
% 1.23/1.46 tff(5572,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5573,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5572, 5571])).
% 1.23/1.46 tff(5574,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5573, 154, 2604, 1, 5561, 684, 5567])).
% 1.23/1.46 tff(5575,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5576,plain,
% 1.23/1.46 (~b(s(s(z)), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5575, 2877, 5535, 4881, 5419])).
% 1.23/1.46 tff(5577,plain,
% 1.23/1.46 (r(s(s(z)), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[138, 5576])).
% 1.23/1.46 tff(5578,plain,
% 1.23/1.46 (~r(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2080, 5577, 5467])).
% 1.23/1.46 tff(5579,plain,
% 1.23/1.46 (b(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[648, 5578])).
% 1.23/1.46 tff(5580,plain,
% 1.23/1.46 (~b(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3217, 5579, 2877, 5191, 5535])).
% 1.23/1.46 tff(5581,plain,
% 1.23/1.46 (r(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[169, 5580])).
% 1.23/1.46 tff(5582,plain,
% 1.23/1.46 (~r(s(s(s(z))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1280, 5581, 5467])).
% 1.23/1.46 tff(5583,plain,
% 1.23/1.46 (b(s(s(s(z))), s(s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[104, 5582])).
% 1.23/1.46 tff(5584,plain,
% 1.23/1.46 (~b(s(z), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3660, 5579, 2877, 5191, 5535])).
% 1.23/1.46 tff(5585,plain,
% 1.23/1.46 (r(s(z), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[252, 5584])).
% 1.23/1.46 tff(5586,plain,
% 1.23/1.46 (~r(s(s(z)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[657, 5585, 5577])).
% 1.23/1.46 tff(5587,plain,
% 1.23/1.46 (b(s(s(z)), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[296, 5586])).
% 1.23/1.46 tff(5588,plain,
% 1.23/1.46 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1289, 154, 5535, 5469, 5419])).
% 1.23/1.46 tff(5589,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5588, 5587, 5583])).
% 1.23/1.46 tff(5590,plain,(s(s(s(s(elem!1)))) = s(s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5591,plain,
% 1.23/1.46 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5590])).
% 1.23/1.46 tff(5592,plain,
% 1.23/1.46 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[431, 5591, 11])).
% 1.23/1.46 tff(5593,plain,
% 1.23/1.46 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5592])).
% 1.23/1.46 tff(5594,plain,
% 1.23/1.46 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5593])).
% 1.23/1.46 tff(5595,plain,
% 1.23/1.46 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5592])).
% 1.23/1.46 tff(5596,plain,
% 1.23/1.46 (s(s(elem!1)) = s(s(z))),
% 1.23/1.46 inference(transitivity,[status(thm)],[363, 5595, 86])).
% 1.23/1.46 tff(5597,plain,
% 1.23/1.46 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5596])).
% 1.23/1.46 tff(5598,plain,
% 1.23/1.46 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5597])).
% 1.23/1.46 tff(5599,plain,
% 1.23/1.46 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5598, 5594])).
% 1.23/1.46 tff(5600,plain,
% 1.23/1.46 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[124, 5599])).
% 1.23/1.46 tff(5601,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(z))))), introduced(assumption)).
% 1.23/1.46 tff(5602,plain,
% 1.23/1.46 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5601])).
% 1.23/1.46 tff(5603,plain,
% 1.23/1.46 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[431, 5602, 11])).
% 1.23/1.46 tff(5604,plain,
% 1.23/1.46 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5603])).
% 1.23/1.46 tff(5605,plain,
% 1.23/1.46 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5604])).
% 1.23/1.46 tff(5606,plain,
% 1.23/1.46 (s(s(z)) = s(s(elem!1))),
% 1.23/1.46 inference(transitivity,[status(thm)],[87, 5605, 362])).
% 1.23/1.46 tff(5607,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[4216, 5606])).
% 1.23/1.46 tff(5608,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5609,plain,
% 1.23/1.46 (s(s(z)) = s(s(elem!1))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5608, 5590])).
% 1.23/1.46 tff(5610,plain,
% 1.23/1.46 (s(z) = s(elem!1)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[4225, 5609])).
% 1.23/1.46 tff(5611,plain,
% 1.23/1.46 (z = elem!1),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[4233, 5610])).
% 1.23/1.46 tff(5612,plain,
% 1.23/1.46 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5613,plain,
% 1.23/1.46 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.23/1.46 inference(symmetry,[status(thm)],[5612])).
% 1.23/1.46 tff(5614,plain,
% 1.23/1.46 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5596])).
% 1.23/1.46 tff(5615,plain,
% 1.23/1.46 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.23/1.46 inference(symmetry,[status(thm)],[5614])).
% 1.23/1.46 tff(5616,plain,
% 1.23/1.46 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5617,plain,
% 1.23/1.46 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.23/1.46 inference(transitivity,[status(thm)],[5616, 5615, 5613])).
% 1.23/1.46 tff(5618,plain,
% 1.23/1.46 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5590])).
% 1.23/1.46 tff(5619,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5618])).
% 1.23/1.46 tff(5620,plain,
% 1.23/1.46 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5619])).
% 1.23/1.46 tff(5621,plain,
% 1.23/1.46 (s(z) = s(elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5622,plain,
% 1.23/1.46 (s(elem!1) = s(z)),
% 1.23/1.46 inference(symmetry,[status(thm)],[5621])).
% 1.23/1.46 tff(5623,plain,
% 1.23/1.46 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5590, 5622])).
% 1.23/1.46 tff(5624,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5623])).
% 1.23/1.46 tff(5625,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5624, 5620])).
% 1.23/1.46 tff(5626,plain,
% 1.23/1.46 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5621])).
% 1.23/1.46 tff(5627,plain,
% 1.23/1.46 (b(s(elem!1), s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5626])).
% 1.23/1.46 tff(5628,plain,
% 1.23/1.46 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(z), s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5627])).
% 1.23/1.46 tff(5629,plain,
% 1.23/1.46 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5618])).
% 1.23/1.46 tff(5630,plain,
% 1.23/1.46 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5629])).
% 1.23/1.46 tff(5631,plain,
% 1.23/1.46 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5622, 5590])).
% 1.23/1.46 tff(5632,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5631])).
% 1.23/1.46 tff(5633,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.46 tff(5634,plain,
% 1.23/1.46 (r(s(z), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1653, 5633])).
% 1.23/1.46 tff(5635,plain,
% 1.23/1.46 (~r(s(s(s(s(z)))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1839, 5634, 13])).
% 1.23/1.46 tff(5636,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[206, 5635])).
% 1.23/1.46 tff(5637,plain,
% 1.23/1.46 (elem!1 = z),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[4359, 5611])).
% 1.23/1.46 tff(5638,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[4366])).
% 1.23/1.46 tff(5639,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5638])).
% 1.23/1.46 tff(5640,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(z)))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[505, 5639])).
% 1.23/1.46 tff(5641,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5633, 5640])).
% 1.23/1.46 tff(5642,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5643,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5642, 5637])).
% 1.23/1.46 tff(5644,plain,
% 1.23/1.46 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5643, 5633])).
% 1.23/1.46 tff(5645,plain,
% 1.23/1.46 (r(s(z), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[467, 5644])).
% 1.23/1.46 tff(5646,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5592])).
% 1.23/1.46 tff(5647,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5646])).
% 1.23/1.46 tff(5648,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5596])).
% 1.23/1.46 tff(5649,plain,
% 1.23/1.46 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5648])).
% 1.23/1.46 tff(5650,plain,
% 1.23/1.46 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5649, 5647])).
% 1.23/1.46 tff(5651,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[144, 5650])).
% 1.23/1.46 tff(5652,plain,
% 1.23/1.46 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5621])).
% 1.23/1.46 tff(5653,plain,
% 1.23/1.46 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5654,plain,
% 1.23/1.46 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.23/1.46 inference(transitivity,[status(thm)],[5653, 5652])).
% 1.23/1.46 tff(5655,plain,
% 1.23/1.46 (r(s(elem!1), elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[13, 5654])).
% 1.23/1.46 tff(5656,plain,
% 1.23/1.46 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5595])).
% 1.23/1.46 tff(5657,plain,
% 1.23/1.46 (s(s(z)) = s(s(elem!1))),
% 1.23/1.46 inference(transitivity,[status(thm)],[87, 5656, 362])).
% 1.23/1.46 tff(5658,plain,
% 1.23/1.46 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5621, 5657])).
% 1.23/1.46 tff(5659,plain,
% 1.23/1.46 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5660,plain,
% 1.23/1.46 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5659])).
% 1.23/1.46 tff(5661,plain,
% 1.23/1.46 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5592])).
% 1.23/1.46 tff(5662,plain,
% 1.23/1.46 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5661, 5660])).
% 1.23/1.46 tff(5663,plain,
% 1.23/1.46 (~r(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1268, 820, 13])).
% 1.23/1.46 tff(5664,plain,
% 1.23/1.46 (~b(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2326, 820, 13, 17])).
% 1.23/1.46 tff(5665,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[169, 5664, 5663])).
% 1.23/1.46 tff(5666,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5667,plain,
% 1.23/1.46 (~r(s(s(s(z))), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5666, 17, 13])).
% 1.23/1.46 tff(5668,plain,
% 1.23/1.46 (b(s(s(s(z))), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[818, 5667])).
% 1.23/1.46 tff(5669,plain,
% 1.23/1.46 (~b(z, s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2773, 5668, 13, 17])).
% 1.23/1.46 tff(5670,plain,
% 1.23/1.46 (r(z, s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1181, 5669])).
% 1.23/1.46 tff(5671,plain,
% 1.23/1.46 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5590])).
% 1.23/1.46 tff(5672,plain,
% 1.23/1.46 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5671])).
% 1.23/1.46 tff(5673,plain,
% 1.23/1.46 (b(elem!1, s(s(s(s(s(s(elem!1))))))) <=> b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5672])).
% 1.23/1.46 tff(5674,plain,
% 1.23/1.46 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5596])).
% 1.23/1.46 tff(5675,plain,
% 1.23/1.46 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5674])).
% 1.23/1.46 tff(5676,plain,
% 1.23/1.46 (b(s(s(s(z))), s(s(elem!1)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[4572, 5675])).
% 1.23/1.46 tff(5677,plain,
% 1.23/1.46 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[4363])).
% 1.23/1.46 tff(5678,plain,
% 1.23/1.46 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.23/1.46 inference(symmetry,[status(thm)],[5677])).
% 1.23/1.46 tff(5679,plain,
% 1.23/1.46 (b(s(s(elem!1)), z)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[142, 5678])).
% 1.23/1.46 tff(5680,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.23/1.46 tff(5681,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5680, 5679])).
% 1.23/1.46 tff(5682,plain,((~(elem!1 = z)) | b(s(s(elem!1)), z) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5683,plain,
% 1.23/1.46 (b(s(s(elem!1)), z) | (~b(s(s(z)), z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5682, 5637])).
% 1.23/1.46 tff(5684,plain,
% 1.23/1.46 (b(s(s(elem!1)), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5683, 2205])).
% 1.23/1.46 tff(5685,plain,
% 1.23/1.46 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5686,plain,
% 1.23/1.46 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5685])).
% 1.23/1.46 tff(5687,plain,
% 1.23/1.46 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5596])).
% 1.23/1.46 tff(5688,plain,
% 1.23/1.46 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5687])).
% 1.23/1.46 tff(5689,plain,
% 1.23/1.46 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5690,plain,
% 1.23/1.46 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5689, 5688, 5686])).
% 1.23/1.46 tff(5691,plain,
% 1.23/1.46 (b(z, s(s(elem!1)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[65, 5690])).
% 1.23/1.46 tff(5692,plain,
% 1.23/1.46 (~r(s(z), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[3144, 5670, 17, 2205])).
% 1.23/1.46 tff(5693,plain,
% 1.23/1.46 (b(s(z), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[1653, 5692])).
% 1.23/1.46 tff(5694,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[623, 1076, 3658, 1, 15, 4562])).
% 1.23/1.46 tff(5695,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5696,plain,
% 1.23/1.46 (~r(s(s(z)), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5695, 16, 5693, 5668, 17])).
% 1.23/1.46 tff(5697,plain,
% 1.23/1.46 (b(s(s(z)), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[138, 5696])).
% 1.23/1.46 tff(5698,plain,
% 1.23/1.46 (b(s(s(elem!1)), s(s(s(z))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5697, 5649])).
% 1.23/1.46 tff(5699,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.23/1.46 tff(5700,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.23/1.46 tff(5701,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.23/1.46 tff(5702,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.23/1.46 tff(5703,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5704,plain,
% 1.23/1.46 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5705,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5704])).
% 1.23/1.46 tff(5706,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5705, 5703])).
% 1.23/1.46 tff(5707,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5708,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5707, 5706])).
% 1.23/1.46 tff(5709,plain,
% 1.23/1.46 ($false),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5708, 154, 5702, 5701, 5700, 5699, 660])).
% 1.23/1.46 tff(5710,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.46 tff(5711,plain,
% 1.23/1.46 (~b(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5710, 5698, 5691, 5684, 5676])).
% 1.23/1.46 tff(5712,plain,
% 1.23/1.46 (r(z, s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[648, 5711])).
% 1.23/1.46 tff(5713,plain,
% 1.23/1.46 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5693, 5632])).
% 1.23/1.46 tff(5714,plain,
% 1.23/1.46 (b(s(elem!1), s(s(s(s(z)))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5713, 5630])).
% 1.23/1.46 tff(5715,plain,
% 1.23/1.46 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[601, 5697, 13, 17, 5668, 16, 5693])).
% 1.23/1.46 tff(5716,plain,
% 1.23/1.46 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[564, 5715])).
% 1.23/1.46 tff(5717,plain,
% 1.23/1.46 (~b(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[162, 5697, 65, 2205, 4572])).
% 1.23/1.46 tff(5718,plain,
% 1.23/1.46 (r(s(s(s(z))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[169, 5717])).
% 1.23/1.46 tff(5719,plain,
% 1.23/1.46 (~r(s(z), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[281, 5718, 13])).
% 1.23/1.46 tff(5720,plain,
% 1.23/1.46 (b(s(z), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[252, 5719])).
% 1.23/1.46 tff(5721,plain,
% 1.23/1.46 (~r(s(s(s(s(z)))), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[2201, 5720, 16, 5716, 5668])).
% 1.23/1.46 tff(5722,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), s(z))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[318, 5721])).
% 1.23/1.46 tff(5723,plain,
% 1.23/1.46 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5722, 5624])).
% 1.23/1.46 tff(5724,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5723, 5620])).
% 1.23/1.46 tff(5725,plain,
% 1.23/1.46 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5591])).
% 1.23/1.46 tff(5726,plain,
% 1.23/1.46 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.23/1.46 inference(transitivity,[status(thm)],[220, 5725, 354])).
% 1.23/1.46 tff(5727,plain,
% 1.23/1.46 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5726])).
% 1.23/1.46 tff(5728,plain,
% 1.23/1.46 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(elem!1))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5727])).
% 1.23/1.46 tff(5729,plain,
% 1.23/1.46 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5592, 5622])).
% 1.23/1.46 tff(5730,plain,
% 1.23/1.46 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.46 inference(symmetry,[status(thm)],[5729])).
% 1.23/1.46 tff(5731,plain,
% 1.23/1.46 (b(s(s(s(elem!1))), s(elem!1))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5668, 5730])).
% 1.23/1.46 tff(5732,plain,
% 1.23/1.46 (b(s(s(s(z))), s(elem!1))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5731, 5728])).
% 1.23/1.46 tff(5733,plain,
% 1.23/1.46 (b(s(elem!1), s(s(s(z))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5720, 5626])).
% 1.23/1.46 tff(5734,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5735,plain,
% 1.23/1.46 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.46 inference(rewrite,[status(thm)],[])).
% 1.23/1.46 tff(5736,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5735])).
% 1.23/1.46 tff(5737,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.46 inference(transitivity,[status(thm)],[5736, 5734])).
% 1.23/1.46 tff(5738,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.46 inference(quant_inst,[status(thm)],[])).
% 1.23/1.46 tff(5739,plain,
% 1.23/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5738, 5737])).
% 1.23/1.46 tff(5740,plain,
% 1.23/1.46 ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5739, 154, 5733])).
% 1.23/1.46 tff(5741,plain,
% 1.23/1.46 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[5740, 5732, 5724, 5714])).
% 1.23/1.46 tff(5742,plain,
% 1.23/1.46 (b(elem!1, s(s(z)))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[65, 5689])).
% 1.23/1.46 tff(5743,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5744,plain,
% 1.23/1.46 (~r(s(s(s(s(z)))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[201, 5716, 5718])).
% 1.23/1.46 tff(5745,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), z)),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[206, 5744])).
% 1.23/1.46 tff(5746,plain,
% 1.23/1.46 (b(s(s(s(s(z)))), elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5745, 5743])).
% 1.23/1.46 tff(5747,plain,
% 1.23/1.46 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5748,plain,
% 1.23/1.46 (~r(z, s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[180, 5718, 5716])).
% 1.23/1.46 tff(5749,plain,
% 1.23/1.46 (b(z, s(s(s(s(z)))))),
% 1.23/1.46 inference(unit_resolution,[status(thm)],[191, 5748])).
% 1.23/1.46 tff(5750,plain,
% 1.23/1.46 (b(elem!1, s(s(s(s(z)))))),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[5749, 5747])).
% 1.23/1.46 tff(5751,plain,
% 1.23/1.46 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.23/1.46 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.46 tff(5752,plain,
% 1.23/1.46 (b(s(s(z)), elem!1)),
% 1.23/1.46 inference(modus_ponens,[status(thm)],[2205, 5751])).
% 1.23/1.46 tff(5753,plain,
% 1.23/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5754,plain,
% 1.23/1.47 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5755,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5754])).
% 1.23/1.47 tff(5756,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5755, 5753])).
% 1.23/1.47 tff(5757,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5758,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5757, 5756])).
% 1.23/1.47 tff(5759,plain,
% 1.23/1.47 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5758, 154, 5742, 5752, 5750, 5746])).
% 1.23/1.47 tff(5760,plain,
% 1.23/1.47 (r(s(s(s(s(z)))), s(s(z)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[229, 5759])).
% 1.23/1.47 tff(5761,plain,
% 1.23/1.47 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5601])).
% 1.23/1.47 tff(5762,plain,
% 1.23/1.47 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5761])).
% 1.23/1.47 tff(5763,plain,
% 1.23/1.47 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5762])).
% 1.23/1.47 tff(5764,plain,
% 1.23/1.47 (s(s(z)) = s(s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5608, 5601])).
% 1.23/1.47 tff(5765,plain,
% 1.23/1.47 (s(z) = s(elem!1)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4225, 5764])).
% 1.23/1.47 tff(5766,plain,
% 1.23/1.47 (z = elem!1),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[4233, 5765])).
% 1.23/1.47 tff(5767,plain,
% 1.23/1.47 (s(z) = s(elem!1)),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5766])).
% 1.23/1.47 tff(5768,plain,
% 1.23/1.47 (s(elem!1) = s(z)),
% 1.23/1.47 inference(symmetry,[status(thm)],[5767])).
% 1.23/1.47 tff(5769,plain,
% 1.23/1.47 (b(s(elem!1), s(s(s(s(s(s(z))))))) <=> b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5768, 5763])).
% 1.23/1.47 tff(5770,plain,
% 1.23/1.47 (b(s(z), s(s(s(s(s(s(elem!1))))))) <=> b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5769])).
% 1.23/1.47 tff(5771,plain,
% 1.23/1.47 (r(s(elem!1), s(s(s(s(s(s(z))))))) <=> r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5768, 5763])).
% 1.23/1.47 tff(5772,plain,
% 1.23/1.47 ((~r(s(elem!1), s(s(s(s(s(s(z)))))))) <=> (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5771])).
% 1.23/1.47 tff(5773,plain,
% 1.23/1.47 (r(s(elem!1), s(s(z))) <=> r(s(z), s(s(z)))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5768])).
% 1.23/1.47 tff(5774,plain,
% 1.23/1.47 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5773])).
% 1.23/1.47 tff(5775,plain,
% 1.23/1.47 (r(s(elem!1), s(s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[17, 5774])).
% 1.23/1.47 tff(5776,plain,
% 1.23/1.47 (s(s(elem!1)) = s(s(z))),
% 1.23/1.47 inference(transitivity,[status(thm)],[363, 5604, 86])).
% 1.23/1.47 tff(5777,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5762, 5776])).
% 1.23/1.47 tff(5778,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))), introduced(assumption)).
% 1.23/1.47 tff(5779,plain,
% 1.23/1.47 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5761])).
% 1.23/1.47 tff(5780,plain,
% 1.23/1.47 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5779])).
% 1.23/1.47 tff(5781,plain,
% 1.23/1.47 (s(s(s(s(s(s(z)))))) = s(s(z))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5780, 5778, 363, 5604, 86])).
% 1.23/1.47 tff(5782,plain,
% 1.23/1.47 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5781])).
% 1.23/1.47 tff(5783,plain,
% 1.23/1.47 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5784,plain,
% 1.23/1.47 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5783, 9])).
% 1.23/1.47 tff(5785,plain,
% 1.23/1.47 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5784])).
% 1.23/1.47 tff(5786,plain,
% 1.23/1.47 (s(s(s(s(s(z))))) = s(z)),
% 1.23/1.47 inference(transitivity,[status(thm)],[5785, 5782, 81])).
% 1.23/1.47 tff(5787,plain,
% 1.23/1.47 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5786])).
% 1.23/1.47 tff(5788,plain,
% 1.23/1.47 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5789,plain,
% 1.23/1.47 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5788, 9])).
% 1.23/1.47 tff(5790,plain,
% 1.23/1.47 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5789])).
% 1.23/1.47 tff(5791,plain,
% 1.23/1.47 (s(s(s(s(z)))) = z),
% 1.23/1.47 inference(transitivity,[status(thm)],[5790, 5787, 91])).
% 1.23/1.47 tff(5792,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[185, 5791])).
% 1.23/1.47 tff(5793,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5794,plain,
% 1.23/1.47 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5793, 5601])).
% 1.23/1.47 tff(5795,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 1.23/1.47 tff(5796,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5762, 5776])).
% 1.23/1.47 tff(5797,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), introduced(assumption)).
% 1.23/1.47 tff(5798,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5797, 5796])).
% 1.23/1.47 tff(5799,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5795, 5798])).
% 1.23/1.47 tff(5800,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5801,plain,
% 1.23/1.47 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5800, 5795, 5601])).
% 1.23/1.47 tff(5802,plain,
% 1.23/1.47 (((~![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))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5803,plain,
% 1.23/1.47 ((~![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))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5804,plain,
% 1.23/1.47 ((~![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)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 1.23/1.47 tff(5805,plain,
% 1.23/1.47 ((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)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5804, 60])).
% 1.23/1.47 tff(5806,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5805, 5801, 5794])).
% 1.23/1.47 tff(5807,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5806, 5777])).
% 1.23/1.47 tff(5808,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5809,plain,
% 1.23/1.47 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5810,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5809])).
% 1.23/1.47 tff(5811,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5810, 5808])).
% 1.23/1.47 tff(5812,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5813,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5812, 5811])).
% 1.23/1.47 tff(5814,plain,
% 1.23/1.47 ((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5813, 28, 5807])).
% 1.23/1.47 tff(5815,plain,
% 1.23/1.47 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5814, 5775])).
% 1.23/1.47 tff(5816,plain,
% 1.23/1.47 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5815, 5772])).
% 1.23/1.47 tff(5817,assumption,(s(z) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.23/1.47 tff(5818,plain,
% 1.23/1.47 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5817])).
% 1.23/1.47 tff(5819,plain,
% 1.23/1.47 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5818])).
% 1.23/1.47 tff(5820,plain,
% 1.23/1.47 ((~![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))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5821,plain,
% 1.23/1.47 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5820, 9])).
% 1.23/1.47 tff(5822,plain,
% 1.23/1.47 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5821])).
% 1.23/1.47 tff(5823,plain,
% 1.23/1.47 (s(s(s(s(s(elem!1))))) = z),
% 1.23/1.47 inference(transitivity,[status(thm)],[5822, 5819, 91])).
% 1.23/1.47 tff(5824,plain,
% 1.23/1.47 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5825,plain,
% 1.23/1.47 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5824, 46])).
% 1.23/1.47 tff(5826,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5825, 5823])).
% 1.23/1.47 tff(5827,plain,(~(s(z) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5828,plain,
% 1.23/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5829,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5830,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5829, 5828])).
% 1.23/1.47 tff(5831,plain,
% 1.23/1.47 ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5830, 60])).
% 1.23/1.47 tff(5832,plain,
% 1.23/1.47 (b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5831, 5827])).
% 1.23/1.47 tff(5833,plain,
% 1.23/1.47 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5832, 5816])).
% 1.23/1.47 tff(5834,plain,
% 1.23/1.47 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5833, 5770])).
% 1.23/1.47 tff(5835,plain,
% 1.23/1.47 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5601])).
% 1.23/1.47 tff(5836,plain,
% 1.23/1.47 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5835])).
% 1.23/1.47 tff(5837,plain,
% 1.23/1.47 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5836])).
% 1.23/1.47 tff(5838,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.23/1.47 tff(5839,plain,
% 1.23/1.47 (b(s(s(s(s(z)))), s(elem!1))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5838, 5837])).
% 1.23/1.47 tff(5840,plain,
% 1.23/1.47 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5835])).
% 1.23/1.47 tff(5841,plain,
% 1.23/1.47 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5840])).
% 1.23/1.47 tff(5842,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.47 tff(5843,plain,
% 1.23/1.47 (b(s(elem!1), s(s(s(s(z)))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5842, 5841])).
% 1.23/1.47 tff(5844,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(z)))))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5763, 5768])).
% 1.23/1.47 tff(5845,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5844])).
% 1.23/1.47 tff(5846,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(z)))))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5763, 5768])).
% 1.23/1.47 tff(5847,plain,
% 1.23/1.47 ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5846])).
% 1.23/1.47 tff(5848,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.23/1.47 tff(5849,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5850,plain,
% 1.23/1.47 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5851,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5850])).
% 1.23/1.47 tff(5852,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5851, 5849])).
% 1.23/1.47 tff(5853,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5854,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5853, 5852])).
% 1.23/1.47 tff(5855,plain,
% 1.23/1.47 ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5854, 28, 5848, 5807])).
% 1.23/1.47 tff(5856,plain,
% 1.23/1.47 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5855, 5775])).
% 1.23/1.47 tff(5857,plain,
% 1.23/1.47 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5856, 5847])).
% 1.23/1.47 tff(5858,plain,
% 1.23/1.47 ((s(s(s(s(s(s(elem!1)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(commutativity,[status(thm)],[])).
% 1.23/1.47 tff(5859,plain,
% 1.23/1.47 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5858])).
% 1.23/1.47 tff(5860,plain,
% 1.23/1.47 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(z)))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5859])).
% 1.23/1.47 tff(5861,plain,
% 1.23/1.47 (~(s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5827, 5860])).
% 1.23/1.47 tff(5862,plain,
% 1.23/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5863,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5864,plain,
% 1.23/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5863, 5862])).
% 1.23/1.47 tff(5865,plain,
% 1.23/1.47 ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5864, 60])).
% 1.23/1.47 tff(5866,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5865, 5861])).
% 1.23/1.47 tff(5867,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5866, 5857])).
% 1.23/1.47 tff(5868,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5867, 5845])).
% 1.23/1.47 tff(5869,plain,
% 1.23/1.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5763])).
% 1.23/1.47 tff(5870,plain,
% 1.23/1.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5869])).
% 1.23/1.47 tff(5871,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.23/1.47 tff(5872,plain,
% 1.23/1.47 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5871])).
% 1.23/1.47 tff(5873,plain,
% 1.23/1.47 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(z)))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5872])).
% 1.23/1.47 tff(5874,plain,
% 1.23/1.47 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5822, 5873, 11])).
% 1.23/1.47 tff(5875,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(z)))), introduced(assumption)).
% 1.23/1.47 tff(5876,plain,
% 1.23/1.47 (s(s(s(z))) = s(s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5875])).
% 1.23/1.47 tff(5877,plain,
% 1.23/1.47 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5876])).
% 1.23/1.47 tff(5878,plain,
% 1.23/1.47 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[87, 5877, 4244])).
% 1.23/1.47 tff(5879,plain,
% 1.23/1.47 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5878])).
% 1.23/1.47 tff(5880,plain,
% 1.23/1.47 (s(z) = s(s(s(elem!1)))),
% 1.23/1.47 inference(transitivity,[status(thm)],[289, 5879, 354])).
% 1.23/1.47 tff(5881,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[368, 5880])).
% 1.23/1.47 tff(5882,plain,(~(s(s(s(s(s(elem!1))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5883,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5882, 5874])).
% 1.23/1.47 tff(5884,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5885,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.23/1.47 tff(5886,plain,
% 1.23/1.47 (b(s(s(s(s(s(s(z)))))), s(s(z))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.23/1.47 inference(symmetry,[status(thm)],[5796])).
% 1.23/1.47 tff(5887,plain,
% 1.23/1.47 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5886])).
% 1.23/1.47 tff(5888,plain,
% 1.23/1.47 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5795, 5887])).
% 1.23/1.47 tff(5889,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5805, 5888, 5794])).
% 1.23/1.47 tff(5890,plain,
% 1.23/1.47 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5889, 5777])).
% 1.23/1.47 tff(5891,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5892,plain,
% 1.23/1.47 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~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(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.23/1.47 inference(rewrite,[status(thm)],[])).
% 1.23/1.47 tff(5893,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~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(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 1.23/1.47 inference(monotonicity,[status(thm)],[5892])).
% 1.23/1.47 tff(5894,plain,
% 1.23/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~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(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.23/1.47 inference(transitivity,[status(thm)],[5893, 5891])).
% 1.23/1.47 tff(5895,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~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(z)))), s(s(s(s(s(s(z)))))))))),
% 1.23/1.47 inference(quant_inst,[status(thm)],[])).
% 1.23/1.47 tff(5896,plain,
% 1.23/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.23/1.47 inference(modus_ponens,[status(thm)],[5895, 5894])).
% 1.23/1.47 tff(5897,plain,
% 1.23/1.47 ($false),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5896, 28, 1243, 5890, 5885])).
% 1.23/1.47 tff(5898,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.47 tff(5899,plain,
% 1.23/1.47 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.47 inference(unit_resolution,[status(thm)],[5898, 5795, 5601, 1243])).
% 1.23/1.48 tff(5900,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5763])).
% 1.23/1.48 tff(5901,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[5900])).
% 1.23/1.48 tff(5902,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.23/1.48 tff(5903,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5902, 5901])).
% 1.23/1.48 tff(5904,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.23/1.48 tff(5905,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5904, 5903])).
% 1.23/1.48 tff(5906,plain,(r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5907,plain,
% 1.23/1.48 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5906, 5899, 5601])).
% 1.23/1.48 tff(5908,plain,
% 1.23/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5909,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5910,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5909, 5908])).
% 1.23/1.48 tff(5911,plain,
% 1.23/1.48 ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5910, 60])).
% 1.23/1.48 tff(5912,plain,
% 1.23/1.48 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5911, 5907, 5884])).
% 1.23/1.48 tff(5913,plain,
% 1.23/1.48 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5912, 5870])).
% 1.23/1.48 tff(5914,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5915,plain,
% 1.23/1.48 (((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5916,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5915])).
% 1.23/1.48 tff(5917,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5916, 5914])).
% 1.23/1.48 tff(5918,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5919,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5918, 5917])).
% 1.23/1.48 tff(5920,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5919, 154, 5913, 5868, 5843, 5839, 5834])).
% 1.23/1.48 tff(5921,plain,(b(s(s(s(s(s(s(z)))))), s(s(z))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5922,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(z)))))), s(s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5921, 5590])).
% 1.23/1.48 tff(5923,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5922, 5760, 5713, 5655, 17, 5723])).
% 1.23/1.48 tff(5924,plain,
% 1.23/1.48 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5590])).
% 1.23/1.48 tff(5925,plain,
% 1.23/1.48 (~b(s(s(z)), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[283, 5749, 2205, 5668, 5693, 4572, 5697, 5718])).
% 1.23/1.48 tff(5926,plain,
% 1.23/1.48 (r(s(s(z)), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[296, 5925])).
% 1.23/1.48 tff(5927,plain,
% 1.23/1.48 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[427, 5926, 13, 5670, 65])).
% 1.23/1.48 tff(5928,plain,
% 1.23/1.48 (b(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[441, 5927])).
% 1.23/1.48 tff(5929,plain,
% 1.23/1.48 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[476, 5928, 5668, 17, 5697, 5720])).
% 1.23/1.48 tff(5930,plain,
% 1.23/1.48 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[496, 5929])).
% 1.23/1.48 tff(5931,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5930, 5924])).
% 1.23/1.48 tff(5932,plain,
% 1.23/1.48 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[5672])).
% 1.23/1.48 tff(5933,plain,
% 1.23/1.48 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5657, 5932])).
% 1.23/1.48 tff(5934,plain,
% 1.23/1.48 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[5933])).
% 1.23/1.48 tff(5935,plain,
% 1.23/1.48 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5596, 5672])).
% 1.23/1.48 tff(5936,plain,
% 1.23/1.48 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[5935])).
% 1.23/1.48 tff(5937,plain,
% 1.23/1.48 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5936])).
% 1.23/1.48 tff(5938,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.48 tff(5939,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5940,plain,
% 1.23/1.48 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5941,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5940])).
% 1.23/1.48 tff(5942,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5941, 5939])).
% 1.23/1.48 tff(5943,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5944,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5943, 5942])).
% 1.23/1.48 tff(5945,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5944, 28, 604, 5938, 5885])).
% 1.23/1.48 tff(5946,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5947,plain,
% 1.23/1.48 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5946, 5885, 604])).
% 1.23/1.48 tff(5948,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(z)))), introduced(assumption)).
% 1.23/1.48 tff(5949,plain,
% 1.23/1.48 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5948])).
% 1.23/1.48 tff(5950,plain,
% 1.23/1.48 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(symmetry,[status(thm)],[5949])).
% 1.23/1.48 tff(5951,plain,
% 1.23/1.48 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[87, 5950, 5784])).
% 1.23/1.48 tff(5952,plain,
% 1.23/1.48 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5951])).
% 1.23/1.48 tff(5953,plain,
% 1.23/1.48 (s(z) = s(s(s(s(z))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[289, 5952, 5789])).
% 1.23/1.48 tff(5954,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[1361, 5953])).
% 1.23/1.48 tff(5955,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5956,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.48 tff(5957,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.48 tff(5958,plain,
% 1.23/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5959,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5960,plain,
% 1.23/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5959, 5958])).
% 1.23/1.48 tff(5961,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5960, 60, 5957, 5956, 5955])).
% 1.23/1.48 tff(5962,plain,(b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5963,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5962, 5947])).
% 1.23/1.48 tff(5964,assumption,(b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 1.23/1.48 tff(5965,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5966,plain,
% 1.23/1.48 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5967,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5966])).
% 1.23/1.48 tff(5968,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5967, 5965])).
% 1.23/1.48 tff(5969,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5970,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5969, 5968])).
% 1.23/1.48 tff(5971,plain,
% 1.23/1.48 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5970, 154, 144, 141, 5964])).
% 1.23/1.48 tff(5972,plain,
% 1.23/1.48 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5971, 5963])).
% 1.23/1.48 tff(5973,plain,
% 1.23/1.48 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5972, 5937])).
% 1.23/1.48 tff(5974,plain,
% 1.23/1.48 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5793, 5590])).
% 1.23/1.48 tff(5975,plain,
% 1.23/1.48 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.23/1.48 inference(commutativity,[status(thm)],[])).
% 1.23/1.48 tff(5976,assumption,(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.23/1.48 tff(5977,plain,
% 1.23/1.48 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5976, 5975])).
% 1.23/1.48 tff(5978,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))), introduced(assumption)).
% 1.23/1.48 tff(5979,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5978, 5977])).
% 1.23/1.48 tff(5980,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5981,plain,
% 1.23/1.48 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5980, 5974])).
% 1.23/1.48 tff(5982,plain,
% 1.23/1.48 (((~![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))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5983,plain,
% 1.23/1.48 ((~![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))))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5984,plain,
% 1.23/1.48 ((~![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)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5983, 5982])).
% 1.23/1.48 tff(5985,plain,
% 1.23/1.48 ((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)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5984, 60])).
% 1.23/1.48 tff(5986,plain,
% 1.23/1.48 (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)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5985, 5981])).
% 1.23/1.48 tff(5987,plain,
% 1.23/1.48 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5986, 5973])).
% 1.23/1.48 tff(5988,plain,
% 1.23/1.48 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5987, 5934])).
% 1.23/1.48 tff(5989,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5990,plain,
% 1.23/1.48 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(5991,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5990])).
% 1.23/1.48 tff(5992,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[5991, 5989])).
% 1.23/1.48 tff(5993,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(5994,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[5993, 5992])).
% 1.23/1.48 tff(5995,plain,
% 1.23/1.48 ($false),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5994, 28, 1243, 5885, 5988])).
% 1.23/1.48 tff(5996,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.48 tff(5997,plain,
% 1.23/1.48 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5996, 5760, 5697, 4572, 5923, 5931])).
% 1.23/1.48 tff(5998,plain,
% 1.23/1.48 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5906, 5590])).
% 1.23/1.48 tff(5999,plain,
% 1.23/1.48 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5998, 5997])).
% 1.23/1.48 tff(6000,plain,
% 1.23/1.48 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[5911, 5884])).
% 1.23/1.48 tff(6001,plain,
% 1.23/1.48 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[6000, 5999])).
% 1.23/1.48 tff(6002,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.23/1.48 tff(6003,plain,
% 1.23/1.48 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5763])).
% 1.23/1.48 tff(6004,plain,
% 1.23/1.48 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.23/1.48 inference(symmetry,[status(thm)],[6003])).
% 1.23/1.48 tff(6005,plain,
% 1.23/1.48 ((s(s(s(s(s(s(elem!1)))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(commutativity,[status(thm)],[])).
% 1.23/1.48 tff(6006,plain,
% 1.23/1.48 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.48 inference(symmetry,[status(thm)],[6005])).
% 1.23/1.48 tff(6007,plain,
% 1.23/1.48 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5766])).
% 1.23/1.48 tff(6008,plain,
% 1.23/1.48 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.48 inference(transitivity,[status(thm)],[6007, 6005])).
% 1.23/1.48 tff(6009,plain,
% 1.23/1.48 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.48 inference(transitivity,[status(thm)],[6008, 6006])).
% 1.23/1.48 tff(6010,plain,
% 1.23/1.48 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[6009])).
% 1.23/1.48 tff(6011,plain,
% 1.23/1.48 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(6012,plain,
% 1.23/1.48 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 1.23/1.48 inference(unit_resolution,[status(thm)],[6011, 46])).
% 1.23/1.48 tff(6013,plain,
% 1.23/1.48 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[6012, 6010])).
% 1.23/1.48 tff(6014,plain,
% 1.23/1.48 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.48 inference(monotonicity,[status(thm)],[5763])).
% 1.23/1.48 tff(6015,plain,
% 1.23/1.48 ((~b(s(s(s(s(s(s(z)))))), elem!1)) <=> (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[6014])).
% 1.23/1.48 tff(6016,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.23/1.48 tff(6017,plain,
% 1.23/1.48 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.48 inference(modus_ponens,[status(thm)],[6016, 5870])).
% 1.23/1.48 tff(6018,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.23/1.48 tff(6019,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.23/1.48 tff(6020,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(6021,plain,
% 1.23/1.48 (((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.48 inference(rewrite,[status(thm)],[])).
% 1.23/1.48 tff(6022,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.23/1.48 inference(monotonicity,[status(thm)],[6021])).
% 1.23/1.48 tff(6023,plain,
% 1.23/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.48 inference(transitivity,[status(thm)],[6022, 6020])).
% 1.23/1.48 tff(6024,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.23/1.48 inference(quant_inst,[status(thm)],[])).
% 1.23/1.48 tff(6025,plain,
% 1.23/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6024, 6023])).
% 1.23/1.49 tff(6026,plain,
% 1.23/1.49 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6025, 154, 6019, 6018, 5964])).
% 1.23/1.49 tff(6027,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6026, 6017])).
% 1.23/1.49 tff(6028,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6027, 6015])).
% 1.23/1.49 tff(6029,plain,
% 1.23/1.49 (((~![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))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6030,plain,
% 1.23/1.49 ((~![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))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(6031,plain,
% 1.23/1.49 ((~![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)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6030, 6029])).
% 1.23/1.49 tff(6032,plain,
% 1.23/1.49 ((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)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6031, 60])).
% 1.23/1.49 tff(6033,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6032, 6028, 6013])).
% 1.23/1.49 tff(6034,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6033, 6004])).
% 1.23/1.49 tff(6035,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6036,plain,
% 1.23/1.49 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6037,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6036])).
% 1.23/1.49 tff(6038,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[6037, 6035])).
% 1.23/1.49 tff(6039,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(6040,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6039, 6038])).
% 1.23/1.49 tff(6041,plain,
% 1.23/1.49 ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6040, 28, 5848])).
% 1.23/1.49 tff(6042,plain,
% 1.23/1.49 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6041, 6034])).
% 1.23/1.49 tff(6043,plain,
% 1.23/1.49 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6042, 5772])).
% 1.23/1.49 tff(6044,plain,
% 1.23/1.49 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5832, 6043])).
% 1.23/1.49 tff(6045,plain,
% 1.23/1.49 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6044, 5770])).
% 1.23/1.49 tff(6046,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6047,plain,
% 1.23/1.49 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6048,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6047])).
% 1.23/1.49 tff(6049,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[6048, 6046])).
% 1.23/1.49 tff(6050,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(6051,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6050, 6049])).
% 1.23/1.49 tff(6052,plain,
% 1.23/1.49 ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6051, 154, 141, 5964])).
% 1.23/1.49 tff(6053,plain,
% 1.23/1.49 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6052, 6045, 6002])).
% 1.23/1.49 tff(6054,plain,
% 1.23/1.49 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5960, 60, 5957])).
% 1.23/1.49 tff(6055,plain,
% 1.23/1.49 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6054, 6053])).
% 1.23/1.49 tff(6056,plain,
% 1.23/1.49 (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))),
% 1.23/1.49 inference(transitivity,[status(thm)],[5762, 6055])).
% 1.23/1.49 tff(6057,plain,
% 1.23/1.49 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6056])).
% 1.23/1.49 tff(6058,plain,
% 1.23/1.49 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[6057])).
% 1.23/1.49 tff(6059,plain,
% 1.23/1.49 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6058])).
% 1.23/1.49 tff(6060,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.23/1.49 tff(6061,plain,
% 1.23/1.49 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6060, 6059])).
% 1.23/1.49 tff(6062,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6016, 6061])).
% 1.23/1.49 tff(6063,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(6064,plain,
% 1.23/1.49 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6063, 5590])).
% 1.23/1.49 tff(6065,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6064, 6001, 5746, 5733, 4572, 5923, 5655, 5742, 5741])).
% 1.23/1.49 tff(6066,plain,
% 1.23/1.49 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5776])).
% 1.23/1.49 tff(6067,plain,
% 1.23/1.49 (s(elem!1) = s(z)),
% 1.23/1.49 inference(transitivity,[status(thm)],[486, 6066, 81])).
% 1.23/1.49 tff(6068,plain,
% 1.23/1.49 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6067])).
% 1.23/1.49 tff(6069,plain,
% 1.23/1.49 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.23/1.49 inference(symmetry,[status(thm)],[6068])).
% 1.23/1.49 tff(6070,plain,
% 1.23/1.49 (z = elem!1),
% 1.23/1.49 inference(transitivity,[status(thm)],[4229, 6069, 4023])).
% 1.23/1.49 tff(6071,plain,
% 1.23/1.49 (r(z, s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6070, 5763])).
% 1.23/1.49 tff(6072,plain,
% 1.23/1.49 (r(elem!1, s(s(s(s(s(s(elem!1))))))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[6071])).
% 1.23/1.49 tff(6073,assumption,(r(elem!1, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.23/1.49 tff(6074,plain,
% 1.23/1.49 (r(z, s(s(s(s(s(s(z)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6073, 6072])).
% 1.23/1.49 tff(6075,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6076,plain,
% 1.23/1.49 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6077,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6076])).
% 1.23/1.49 tff(6078,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[6077, 6075])).
% 1.23/1.49 tff(6079,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(6080,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6079, 6078])).
% 1.23/1.49 tff(6081,plain,
% 1.23/1.49 ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6080, 28, 628])).
% 1.23/1.49 tff(6082,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6081, 6074, 5938])).
% 1.23/1.49 tff(6083,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(6084,plain,
% 1.23/1.49 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6083, 5590])).
% 1.23/1.49 tff(6085,plain,
% 1.23/1.49 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6084, 6065, 5712])).
% 1.23/1.49 tff(6086,plain,
% 1.23/1.49 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5611])).
% 1.23/1.49 tff(6087,plain,
% 1.23/1.49 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[6086, 6005])).
% 1.23/1.49 tff(6088,plain,
% 1.23/1.49 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6087])).
% 1.23/1.49 tff(6089,plain,
% 1.23/1.49 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6012, 6088])).
% 1.23/1.49 tff(6090,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6091,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(6092,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6091, 6090])).
% 1.23/1.49 tff(6093,plain,
% 1.23/1.49 ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6092, 60])).
% 1.23/1.49 tff(6094,plain,
% 1.23/1.49 (b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6093, 6089])).
% 1.23/1.49 tff(6095,plain,
% 1.23/1.49 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6094, 6085])).
% 1.23/1.49 tff(6096,plain,
% 1.23/1.49 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6095, 5673])).
% 1.23/1.49 tff(6097,plain,
% 1.23/1.49 (r(s(s(z)), s(s(s(s(s(s(z))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5606, 5763])).
% 1.23/1.49 tff(6098,plain,
% 1.23/1.49 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[6097])).
% 1.23/1.49 tff(6099,plain,
% 1.23/1.49 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[5980, 5794])).
% 1.23/1.49 tff(6100,plain,
% 1.23/1.49 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5776, 5762])).
% 1.23/1.49 tff(6101,plain,
% 1.23/1.49 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[6100])).
% 1.23/1.49 tff(6102,plain,
% 1.23/1.49 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6101])).
% 1.23/1.49 tff(6103,assumption,(b(elem!1, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.23/1.49 tff(6104,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.23/1.49 tff(6105,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.23/1.49 tff(6106,plain,
% 1.23/1.49 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5762])).
% 1.23/1.49 tff(6107,plain,
% 1.23/1.49 ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.23/1.49 inference(commutativity,[status(thm)],[])).
% 1.23/1.49 tff(6108,plain,
% 1.23/1.49 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6107])).
% 1.23/1.49 tff(6109,plain,
% 1.23/1.49 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[5884, 6108])).
% 1.23/1.49 tff(6110,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[5762])).
% 1.23/1.49 tff(6111,plain,
% 1.23/1.49 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[6110])).
% 1.23/1.49 tff(6112,plain,
% 1.23/1.49 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6111])).
% 1.23/1.49 tff(6113,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~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)))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6114,plain,
% 1.23/1.49 (((~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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(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)))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6115,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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))))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[6114])).
% 1.23/1.49 tff(6116,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~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)))))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[6115, 6113])).
% 1.23/1.49 tff(6117,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(6118,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~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))))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6117, 6116])).
% 1.23/1.49 tff(6119,plain,
% 1.23/1.49 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6118, 28, 604, 1243, 5890])).
% 1.23/1.49 tff(6120,plain,
% 1.23/1.49 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6119, 6112])).
% 1.23/1.49 tff(6121,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6122,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(6123,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6122, 6121])).
% 1.23/1.49 tff(6124,plain,
% 1.23/1.49 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6123, 60])).
% 1.23/1.49 tff(6125,plain,
% 1.23/1.49 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[6124, 6120, 6109])).
% 1.23/1.49 tff(6126,plain,
% 1.23/1.49 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[6125, 6106])).
% 1.23/1.49 tff(6127,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6128,plain,
% 1.23/1.49 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6129,plain,
% 1.23/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[6128])).
% 1.23/1.50 tff(6130,plain,
% 1.23/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.50 inference(transitivity,[status(thm)],[6129, 6127])).
% 1.23/1.50 tff(6131,plain,
% 1.23/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.23/1.50 inference(quant_inst,[status(thm)],[])).
% 1.23/1.50 tff(6132,plain,
% 1.23/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[6131, 6130])).
% 1.23/1.50 tff(6133,plain,
% 1.23/1.50 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[6132, 154, 6105, 6018, 6103, 6126])).
% 1.23/1.50 tff(6134,plain,
% 1.23/1.50 ($false),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[6133, 5913])).
% 1.23/1.50 tff(6135,plain,(b(s(s(s(s(s(s(z)))))), s(s(z))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.50 tff(6136,plain,
% 1.23/1.50 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.23/1.50 inference(unit_resolution,[status(thm)],[6135, 6103, 6105, 6018, 5601, 604, 1243])).
% 1.23/1.50 tff(6137,assumption,(b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.23/1.50 tff(6138,plain,
% 1.23/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(6139,plain,
% 1.23/1.50 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(6140,plain,
% 1.23/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[6139])).
% 1.33/1.50 tff(6141,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6140, 6138])).
% 1.33/1.50 tff(6142,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(6143,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6142, 6141])).
% 1.33/1.50 tff(6144,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6143, 154, 6019, 6104, 5964, 6137, 6103])).
% 1.33/1.50 tff(6145,plain,((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(6146,plain,
% 1.33/1.50 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6145, 6136, 6104, 6103, 6019])).
% 1.33/1.50 tff(6147,plain,
% 1.33/1.50 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6146, 6102])).
% 1.33/1.50 tff(6148,plain,
% 1.33/1.50 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5985, 6147, 6099])).
% 1.33/1.50 tff(6149,plain,
% 1.33/1.50 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6148, 6098])).
% 1.33/1.50 tff(6150,plain,
% 1.33/1.50 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5869])).
% 1.33/1.50 tff(6151,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.33/1.50 tff(6152,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6153,plain,
% 1.33/1.50 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6154,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6153])).
% 1.33/1.50 tff(6155,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6154, 6152])).
% 1.33/1.50 tff(6156,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(6157,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6156, 6155])).
% 1.33/1.50 tff(6158,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6157, 154, 6019, 6018, 5964, 6103, 6151])).
% 1.33/1.50 tff(6159,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(6160,plain,
% 1.33/1.50 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6159, 6136, 6018, 6019, 6103])).
% 1.33/1.50 tff(6161,plain,
% 1.33/1.50 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6160, 6150])).
% 1.33/1.50 tff(6162,plain,
% 1.33/1.50 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5911, 6161, 5884])).
% 1.33/1.50 tff(6163,plain,
% 1.33/1.50 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[5906, 6162, 5601])).
% 1.33/1.50 tff(6164,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6165,plain,
% 1.33/1.50 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6166,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6165])).
% 1.33/1.50 tff(6167,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6166, 6164])).
% 1.33/1.50 tff(6168,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(6169,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6168, 6167])).
% 1.33/1.50 tff(6170,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6169, 28, 16, 6163, 6149])).
% 1.33/1.50 tff(6171,plain,((~b(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(6172,plain,
% 1.33/1.50 ((~b(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6171, 5590])).
% 1.33/1.50 tff(6173,plain,
% 1.33/1.50 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6172, 5760, 16, 5742, 5752, 5750, 5931, 5746])).
% 1.33/1.50 tff(6174,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6173, 6096])).
% 1.33/1.50 tff(6175,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(6176,plain,
% 1.33/1.50 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6175, 17, 13])).
% 1.33/1.50 tff(6177,plain,
% 1.33/1.50 (b(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1259, 6176])).
% 1.33/1.50 tff(6178,plain,
% 1.33/1.50 (b(s(s(s(s(s(s(z)))))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5932, 5622])).
% 1.33/1.50 tff(6179,plain,
% 1.33/1.50 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.33/1.50 inference(symmetry,[status(thm)],[6178])).
% 1.33/1.50 tff(6180,plain,
% 1.33/1.50 (r(s(s(s(s(s(s(z)))))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5932, 5622])).
% 1.33/1.50 tff(6181,plain,
% 1.33/1.50 ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6180])).
% 1.33/1.50 tff(6182,plain,
% 1.33/1.50 (r(s(elem!1), s(s(z))) <=> r(s(z), s(s(z)))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5622])).
% 1.33/1.50 tff(6183,plain,
% 1.33/1.50 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.33/1.50 inference(symmetry,[status(thm)],[6182])).
% 1.33/1.50 tff(6184,plain,
% 1.33/1.50 (r(s(elem!1), s(s(z)))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[17, 6183])).
% 1.33/1.50 tff(6185,plain,
% 1.33/1.50 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5672, 5596])).
% 1.33/1.50 tff(6186,plain,
% 1.33/1.50 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5592])).
% 1.33/1.50 tff(6187,plain,
% 1.33/1.50 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5611])).
% 1.33/1.50 tff(6188,plain,
% 1.33/1.50 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6187, 6186])).
% 1.33/1.50 tff(6189,plain,
% 1.33/1.50 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5650])).
% 1.33/1.50 tff(6190,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.33/1.50 tff(6191,plain,
% 1.33/1.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6190, 6189])).
% 1.33/1.50 tff(6192,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5611])).
% 1.33/1.50 tff(6193,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.33/1.50 inference(symmetry,[status(thm)],[6192])).
% 1.33/1.50 tff(6194,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5592])).
% 1.33/1.50 tff(6195,plain,
% 1.33/1.50 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.33/1.50 inference(symmetry,[status(thm)],[6194])).
% 1.33/1.50 tff(6196,plain,
% 1.33/1.50 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5611])).
% 1.33/1.50 tff(6197,plain,
% 1.33/1.50 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.33/1.50 inference(transitivity,[status(thm)],[6196, 6195, 6193])).
% 1.33/1.50 tff(6198,plain,
% 1.33/1.50 (~r(s(z), s(s(s(s(z)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[3144, 14, 17, 142])).
% 1.33/1.50 tff(6199,plain,
% 1.33/1.50 (b(s(z), s(s(s(s(z)))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[1653, 6198])).
% 1.33/1.50 tff(6200,plain,
% 1.33/1.50 (r(s(s(z)), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[138, 6190])).
% 1.33/1.50 tff(6201,plain,
% 1.33/1.50 (~r(s(z), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[3656, 6200, 17])).
% 1.33/1.50 tff(6202,plain,
% 1.33/1.50 (b(s(z), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[252, 6201])).
% 1.33/1.50 tff(6203,plain,
% 1.33/1.50 (~r(s(s(s(z))), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[2972, 6202, 14, 1283, 6199, 142, 140])).
% 1.33/1.50 tff(6204,plain,
% 1.33/1.50 (b(s(s(s(z))), z)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[169, 6203])).
% 1.33/1.50 tff(6205,plain,
% 1.33/1.50 (b(s(s(s(elem!1))), z)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6204, 6197])).
% 1.33/1.50 tff(6206,plain,
% 1.33/1.50 (b(s(s(s(z))), s(s(s(z)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5726])).
% 1.33/1.50 tff(6207,plain,
% 1.33/1.50 ((~b(s(s(s(z))), s(s(s(z))))) <=> (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6206])).
% 1.33/1.50 tff(6208,plain,
% 1.33/1.50 (b(s(elem!1), s(s(s(z))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6202, 5626])).
% 1.33/1.50 tff(6209,plain,
% 1.33/1.50 (b(s(s(s(z))), elem!1)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6204, 6196])).
% 1.33/1.50 tff(6210,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6211,plain,
% 1.33/1.50 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6212,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6211])).
% 1.33/1.50 tff(6213,plain,
% 1.33/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6212, 6210])).
% 1.33/1.50 tff(6214,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(6215,plain,
% 1.33/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6214, 6213])).
% 1.33/1.50 tff(6216,plain,
% 1.33/1.50 (~b(s(s(s(z))), s(s(s(z))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6215, 154, 6209, 6208])).
% 1.33/1.50 tff(6217,plain,
% 1.33/1.50 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6216, 6207])).
% 1.33/1.50 tff(6218,plain,
% 1.33/1.50 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.33/1.50 inference(commutativity,[status(thm)],[])).
% 1.33/1.50 tff(6219,plain,
% 1.33/1.50 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[6218])).
% 1.33/1.50 tff(6220,plain,
% 1.33/1.50 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.33/1.50 inference(monotonicity,[status(thm)],[5611])).
% 1.33/1.50 tff(6221,plain,
% 1.33/1.50 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.33/1.50 inference(transitivity,[status(thm)],[6220, 6219])).
% 1.33/1.50 tff(6222,plain,
% 1.33/1.50 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6221])).
% 1.33/1.50 tff(6223,plain,
% 1.33/1.50 (~(elem!1 = s(s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[434, 6222])).
% 1.33/1.50 tff(6224,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.50 tff(6225,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.50 tff(6226,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.33/1.50 tff(6227,plain,
% 1.33/1.50 (elem!1 = s(s(s(elem!1)))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6226, 6219])).
% 1.33/1.50 tff(6228,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6224, 6227])).
% 1.33/1.50 tff(6229,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(6230,plain,
% 1.33/1.50 (~(s(s(s(elem!1))) = elem!1)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6229, 6224])).
% 1.33/1.50 tff(6231,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.50 tff(6232,plain,
% 1.33/1.50 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[4030])).
% 1.33/1.50 tff(6233,plain,
% 1.33/1.50 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.33/1.50 inference(symmetry,[status(thm)],[6232])).
% 1.33/1.50 tff(6234,plain,
% 1.33/1.50 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[6233])).
% 1.33/1.50 tff(6235,plain,
% 1.33/1.50 (~b(elem!1, s(s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6225, 6234])).
% 1.33/1.50 tff(6236,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6231, 6235])).
% 1.33/1.50 tff(6237,plain,((~(elem!1 = s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(6238,plain,
% 1.33/1.50 (~(elem!1 = s(s(elem!1)))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6237, 6231, 6225])).
% 1.33/1.50 tff(6239,plain,
% 1.33/1.50 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[4028, 6238])).
% 1.33/1.50 tff(6240,plain,
% 1.33/1.50 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[4018, 6239])).
% 1.33/1.50 tff(6241,plain,
% 1.33/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(6242,plain,
% 1.33/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(6243,plain,
% 1.33/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[6242, 6241])).
% 1.33/1.50 tff(6244,plain,
% 1.33/1.50 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[6243, 60])).
% 1.33/1.51 tff(6245,plain,
% 1.33/1.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6244, 6240, 6225])).
% 1.33/1.51 tff(6246,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6247,plain,
% 1.33/1.51 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6248,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6247])).
% 1.33/1.51 tff(6249,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6248, 6246])).
% 1.33/1.51 tff(6250,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6251,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6250, 6249])).
% 1.33/1.51 tff(6252,plain,
% 1.33/1.51 (~r(z, s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6251, 28, 4132, 6245])).
% 1.33/1.51 tff(6253,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 1.33/1.51 tff(6254,plain,
% 1.33/1.51 (s(s(elem!1)) = z),
% 1.33/1.51 inference(symmetry,[status(thm)],[6253])).
% 1.33/1.51 tff(6255,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[366, 6254])).
% 1.33/1.51 tff(6256,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6257,plain,
% 1.33/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6258,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6259,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 1.33/1.51 tff(6260,plain,
% 1.33/1.51 (b(z, s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6259, 60, 6256, 6252])).
% 1.33/1.51 tff(6261,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6262,plain,
% 1.33/1.51 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6263,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6262])).
% 1.33/1.51 tff(6264,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6263, 6261])).
% 1.33/1.51 tff(6265,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6266,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6265, 6264])).
% 1.33/1.51 tff(6267,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6266, 28, 4132, 628, 4186])).
% 1.33/1.51 tff(6268,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6269,plain,
% 1.33/1.51 (~r(z, s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6268, 4186, 4132])).
% 1.33/1.51 tff(6270,plain,
% 1.33/1.51 (b(z, s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[648, 6269])).
% 1.33/1.51 tff(6271,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6272,plain,
% 1.33/1.51 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6273,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6272])).
% 1.33/1.51 tff(6274,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6273, 6271])).
% 1.33/1.51 tff(6275,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6276,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6275, 6274])).
% 1.33/1.51 tff(6277,plain,
% 1.33/1.51 (~r(s(s(s(z))), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6276, 28, 4132, 4186])).
% 1.33/1.51 tff(6278,plain,
% 1.33/1.51 (b(s(s(s(z))), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[169, 6277])).
% 1.33/1.51 tff(6279,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.51 tff(6280,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.33/1.51 tff(6281,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6282,plain,
% 1.33/1.51 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6283,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1)))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6282])).
% 1.33/1.51 tff(6284,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6283, 6281])).
% 1.33/1.51 tff(6285,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6286,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6285, 6284])).
% 1.33/1.51 tff(6287,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6286, 28, 6280, 4132, 6279])).
% 1.33/1.51 tff(6288,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,[]))).
% 1.33/1.51 tff(6289,plain,
% 1.33/1.51 (~r(s(s(elem!1)), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6288, 6245, 4132])).
% 1.33/1.51 tff(6290,plain,
% 1.33/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6291,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6292,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6291, 6290])).
% 1.33/1.51 tff(6293,plain,
% 1.33/1.51 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6292, 60, 366])).
% 1.33/1.51 tff(6294,plain,
% 1.33/1.51 (b(s(s(elem!1)), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6293, 6289])).
% 1.33/1.51 tff(6295,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6296,plain,
% 1.33/1.51 (((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6297,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6296])).
% 1.33/1.51 tff(6298,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6297, 6295])).
% 1.33/1.51 tff(6299,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6300,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6299, 6298])).
% 1.33/1.51 tff(6301,plain,
% 1.33/1.51 ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6300, 154, 6294, 6278, 6270])).
% 1.33/1.51 tff(6302,plain,
% 1.33/1.51 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6301, 6260])).
% 1.33/1.51 tff(6303,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.33/1.51 tff(6304,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6305,plain,
% 1.33/1.51 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6306,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6305])).
% 1.33/1.51 tff(6307,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.33/1.51 inference(transitivity,[status(thm)],[6306, 6304])).
% 1.33/1.51 tff(6308,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6309,plain,
% 1.33/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6308, 6307])).
% 1.33/1.51 tff(6310,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6309, 28, 6279, 6303, 4186])).
% 1.33/1.51 tff(6311,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6312,plain,
% 1.33/1.51 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6311, 6245, 4186])).
% 1.33/1.51 tff(6313,plain,
% 1.33/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6314,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6315,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6314, 6313])).
% 1.33/1.51 tff(6316,plain,
% 1.33/1.51 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6315, 60, 6312])).
% 1.33/1.51 tff(6317,plain,
% 1.33/1.51 (s(s(elem!1)) = s(s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6316, 6302])).
% 1.33/1.51 tff(6318,plain,
% 1.33/1.51 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6317])).
% 1.33/1.51 tff(6319,plain,
% 1.33/1.51 (s(elem!1) = s(s(z))),
% 1.33/1.51 inference(transitivity,[status(thm)],[486, 6318, 86])).
% 1.33/1.51 tff(6320,plain,
% 1.33/1.51 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6319])).
% 1.33/1.51 tff(6321,plain,
% 1.33/1.51 (elem!1 = s(z)),
% 1.33/1.51 inference(transitivity,[status(thm)],[4024, 6320, 81])).
% 1.33/1.51 tff(6322,plain,
% 1.33/1.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6317])).
% 1.33/1.51 tff(6323,plain,
% 1.33/1.51 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6322, 6321])).
% 1.33/1.51 tff(6324,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.33/1.51 tff(6325,plain,
% 1.33/1.51 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6320])).
% 1.33/1.51 tff(6326,plain,
% 1.33/1.51 (s(z) = elem!1),
% 1.33/1.51 inference(transitivity,[status(thm)],[289, 6325, 4023])).
% 1.33/1.51 tff(6327,plain,
% 1.33/1.51 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6322])).
% 1.33/1.51 tff(6328,plain,
% 1.33/1.51 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6327, 6326])).
% 1.33/1.51 tff(6329,plain,
% 1.33/1.51 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6328])).
% 1.33/1.51 tff(6330,plain,
% 1.33/1.51 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6327])).
% 1.33/1.51 tff(6331,plain,
% 1.33/1.51 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6330])).
% 1.33/1.51 tff(6332,plain,
% 1.33/1.51 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[4186, 6331])).
% 1.33/1.51 tff(6333,plain,
% 1.33/1.51 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), s(z))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6317, 6321])).
% 1.33/1.51 tff(6334,plain,
% 1.33/1.51 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[4028, 4026])).
% 1.33/1.51 tff(6335,plain,
% 1.33/1.51 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[4018, 6334])).
% 1.33/1.51 tff(6336,plain,
% 1.33/1.51 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6244, 6335, 6225])).
% 1.33/1.51 tff(6337,plain,
% 1.33/1.51 (~r(z, s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6251, 28, 4132, 6336])).
% 1.33/1.51 tff(6338,plain,
% 1.33/1.51 (b(z, s(s(elem!1)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6259, 60, 6256, 6337])).
% 1.33/1.51 tff(6339,plain,
% 1.33/1.51 (~r(s(s(elem!1)), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6288, 6336, 4132])).
% 1.33/1.51 tff(6340,plain,
% 1.33/1.51 (b(s(s(elem!1)), z)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6293, 6339])).
% 1.33/1.51 tff(6341,plain,
% 1.33/1.51 ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6300, 154, 6340, 6278, 6270])).
% 1.33/1.51 tff(6342,plain,
% 1.33/1.51 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6341, 6338])).
% 1.33/1.51 tff(6343,plain,
% 1.33/1.51 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6311, 6336, 4186])).
% 1.33/1.51 tff(6344,plain,
% 1.33/1.51 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6315, 60, 6343])).
% 1.33/1.51 tff(6345,plain,
% 1.33/1.51 (s(s(elem!1)) = s(s(s(z)))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6344, 6342])).
% 1.33/1.51 tff(6346,plain,
% 1.33/1.51 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6345])).
% 1.33/1.51 tff(6347,plain,
% 1.33/1.51 (s(elem!1) = s(s(z))),
% 1.33/1.51 inference(transitivity,[status(thm)],[486, 6346, 86])).
% 1.33/1.51 tff(6348,plain,
% 1.33/1.51 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6347])).
% 1.33/1.51 tff(6349,plain,
% 1.33/1.51 (elem!1 = s(z)),
% 1.33/1.51 inference(transitivity,[status(thm)],[4024, 6348, 81])).
% 1.33/1.51 tff(6350,plain,
% 1.33/1.51 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6345, 6349])).
% 1.33/1.51 tff(6351,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.33/1.51 tff(6352,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.33/1.51 tff(6353,plain,
% 1.33/1.51 (elem!1 = s(s(elem!1))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6352, 4055])).
% 1.33/1.51 tff(6354,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[4026, 6353])).
% 1.33/1.51 tff(6355,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6356,plain,
% 1.33/1.51 (~(s(s(elem!1)) = elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6355, 4026])).
% 1.33/1.51 tff(6357,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.33/1.51 tff(6358,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.33/1.51 tff(6359,plain,
% 1.33/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6360,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6361,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6360, 6359])).
% 1.33/1.51 tff(6362,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6361, 60, 6351, 6358, 6357])).
% 1.33/1.51 tff(6363,plain,(b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6364,plain,
% 1.33/1.51 (b(s(s(elem!1)), elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6363, 6356, 6351])).
% 1.33/1.51 tff(6365,plain,
% 1.33/1.51 (b(s(s(s(z))), s(z))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6364, 6350])).
% 1.33/1.51 tff(6366,plain,
% 1.33/1.51 (~b(s(z), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3091, 6365, 2604, 6278, 6270])).
% 1.33/1.51 tff(6367,plain,
% 1.33/1.51 (r(s(z), s(s(s(z))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[252, 6366])).
% 1.33/1.51 tff(6368,plain,
% 1.33/1.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6345])).
% 1.33/1.51 tff(6369,plain,
% 1.33/1.51 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6368])).
% 1.33/1.51 tff(6370,plain,
% 1.33/1.51 (r(z, s(s(s(s(z)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[4132, 6369])).
% 1.33/1.51 tff(6371,plain,
% 1.33/1.51 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6349, 6368])).
% 1.33/1.51 tff(6372,plain,
% 1.33/1.51 (b(s(z), s(s(s(s(z)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6231, 6371])).
% 1.33/1.51 tff(6373,plain,
% 1.33/1.51 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6368])).
% 1.33/1.51 tff(6374,plain,
% 1.33/1.51 (b(s(s(s(s(z)))), z)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[3852, 6373])).
% 1.33/1.51 tff(6375,plain,
% 1.33/1.51 (r(z, elem!1) <=> r(z, s(z))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6349])).
% 1.33/1.51 tff(6376,plain,
% 1.33/1.51 (r(z, s(z)) <=> r(z, elem!1)),
% 1.33/1.51 inference(symmetry,[status(thm)],[6375])).
% 1.33/1.51 tff(6377,plain,
% 1.33/1.51 (~b(z, s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[3217, 6365, 2604, 6278, 6270])).
% 1.33/1.51 tff(6378,plain,
% 1.33/1.51 (r(z, s(z))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[1181, 6377])).
% 1.33/1.51 tff(6379,plain,
% 1.33/1.51 (r(z, elem!1)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6378, 6376])).
% 1.33/1.51 tff(6380,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.33/1.51 tff(6381,plain,
% 1.33/1.51 ((elem!1 = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6380])).
% 1.33/1.51 tff(6382,plain,
% 1.33/1.51 ((s(elem!1) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6381])).
% 1.33/1.51 tff(6383,plain,
% 1.33/1.51 (s(elem!1) = elem!1),
% 1.33/1.51 inference(symmetry,[status(thm)],[6380])).
% 1.33/1.51 tff(6384,plain,
% 1.33/1.51 (s(s(elem!1)) = s(elem!1)),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6383])).
% 1.33/1.51 tff(6385,plain,
% 1.33/1.51 (s(elem!1) = s(s(elem!1))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6384])).
% 1.33/1.51 tff(6386,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.33/1.51 tff(6387,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6386, 6385])).
% 1.33/1.51 tff(6388,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6389,plain,
% 1.33/1.51 (s(elem!1) = s(s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6388, 6380])).
% 1.33/1.51 tff(6390,plain,
% 1.33/1.51 (elem!1 = s(s(elem!1))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6389, 6382])).
% 1.33/1.51 tff(6391,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[4026, 6390])).
% 1.33/1.51 tff(6392,plain,((~(elem!1 = s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6393,plain,
% 1.33/1.51 (~(elem!1 = s(elem!1))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6392, 4026])).
% 1.33/1.51 tff(6394,plain,
% 1.33/1.51 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.33/1.51 inference(commutativity,[status(thm)],[])).
% 1.33/1.51 tff(6395,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.33/1.51 tff(6396,plain,
% 1.33/1.51 (elem!1 = s(elem!1)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6395, 6394])).
% 1.33/1.51 tff(6397,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.33/1.51 tff(6398,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6397, 6396])).
% 1.33/1.51 tff(6399,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6400,plain,
% 1.33/1.51 (~(s(elem!1) = elem!1)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6399, 6393])).
% 1.33/1.51 tff(6401,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.33/1.51 tff(6402,plain,
% 1.33/1.51 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6401])).
% 1.33/1.51 tff(6403,plain,
% 1.33/1.51 (s(elem!1) = s(s(z))),
% 1.33/1.51 inference(transitivity,[status(thm)],[486, 6402, 86])).
% 1.33/1.51 tff(6404,plain,
% 1.33/1.51 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6403])).
% 1.33/1.51 tff(6405,plain,
% 1.33/1.51 (elem!1 = s(z)),
% 1.33/1.51 inference(transitivity,[status(thm)],[4024, 6404, 81])).
% 1.33/1.51 tff(6406,plain,
% 1.33/1.51 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6403, 6405])).
% 1.33/1.51 tff(6407,plain,
% 1.33/1.51 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 1.33/1.51 inference(symmetry,[status(thm)],[6406])).
% 1.33/1.51 tff(6408,plain,
% 1.33/1.51 ((~b(s(s(z)), s(z))) <=> (~b(s(elem!1), elem!1))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6407])).
% 1.33/1.51 tff(6409,plain,
% 1.33/1.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6401])).
% 1.33/1.51 tff(6410,plain,
% 1.33/1.51 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6403, 6409])).
% 1.33/1.51 tff(6411,plain,
% 1.33/1.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[913, 106, 172])).
% 1.33/1.51 tff(6412,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.33/1.51 tff(6413,plain,
% 1.33/1.51 (s(elem!1) = s(s(z))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6412])).
% 1.33/1.51 tff(6414,plain,
% 1.33/1.51 (s(s(elem!1)) = s(s(s(z)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6413])).
% 1.33/1.51 tff(6415,plain,
% 1.33/1.51 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6414])).
% 1.33/1.51 tff(6416,plain,
% 1.33/1.51 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6415])).
% 1.33/1.51 tff(6417,plain,
% 1.33/1.51 (s(s(z)) = s(elem!1)),
% 1.33/1.51 inference(symmetry,[status(thm)],[6413])).
% 1.33/1.51 tff(6418,plain,
% 1.33/1.51 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[6417, 6416])).
% 1.33/1.51 tff(6419,plain,
% 1.33/1.51 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.51 inference(symmetry,[status(thm)],[6418])).
% 1.33/1.51 tff(6420,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.51 tff(6421,plain,
% 1.33/1.51 (r(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6420, 6419])).
% 1.33/1.51 tff(6422,assumption,(~r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.33/1.51 tff(6423,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6422, 6421])).
% 1.33/1.51 tff(6424,plain,(r(s(s(z)), s(s(s(s(z))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(6425,plain,
% 1.33/1.51 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6424, 6411, 6405])).
% 1.33/1.51 tff(6426,plain,
% 1.33/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(6427,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(6428,plain,
% 1.33/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6427, 6426])).
% 1.33/1.51 tff(6429,plain,
% 1.33/1.51 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6428, 60])).
% 1.33/1.51 tff(6430,plain,
% 1.33/1.51 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[6429, 6425, 4016])).
% 1.33/1.51 tff(6431,plain,
% 1.33/1.51 (b(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[6430, 6410])).
% 1.33/1.51 tff(6432,plain,
% 1.33/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6433,plain,
% 1.33/1.52 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6434,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6433])).
% 1.33/1.52 tff(6435,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6434, 6432])).
% 1.33/1.52 tff(6436,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6437,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6436, 6435])).
% 1.33/1.52 tff(6438,plain,
% 1.33/1.52 (~b(s(s(z)), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6437, 154, 2604, 1299, 6431, 15])).
% 1.33/1.52 tff(6439,plain,
% 1.33/1.52 (~b(s(elem!1), elem!1)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6438, 6408])).
% 1.33/1.52 tff(6440,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.33/1.52 tff(6441,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.33/1.52 tff(6442,plain,
% 1.33/1.52 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6403])).
% 1.33/1.52 tff(6443,plain,
% 1.33/1.52 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.33/1.52 inference(symmetry,[status(thm)],[6442])).
% 1.33/1.52 tff(6444,plain,
% 1.33/1.52 (r(s(elem!1), z)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[106, 6443])).
% 1.33/1.52 tff(6445,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.33/1.52 tff(6446,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6447,plain,
% 1.33/1.52 (((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6448,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6447])).
% 1.33/1.52 tff(6449,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6448, 6446])).
% 1.33/1.52 tff(6450,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6451,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6450, 6449])).
% 1.33/1.52 tff(6452,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6451, 28, 5848, 6441, 6445])).
% 1.33/1.52 tff(6453,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6454,plain,
% 1.33/1.52 (~r(s(elem!1), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6453, 6444, 6441])).
% 1.33/1.52 tff(6455,plain,
% 1.33/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6456,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6457,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6456, 6455])).
% 1.33/1.52 tff(6458,plain,
% 1.33/1.52 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6457, 60])).
% 1.33/1.52 tff(6459,plain,
% 1.33/1.52 (b(s(elem!1), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6458, 6454, 6440])).
% 1.33/1.52 tff(6460,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6459, 6439])).
% 1.33/1.52 tff(6461,plain,((~r(s(s(z)), z)) | (~(s(s(elem!1)) = s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6462,plain,
% 1.33/1.52 (~r(s(s(z)), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6461, 6345, 6400, 6379, 2604, 6374, 6372, 6334, 6370])).
% 1.33/1.52 tff(6463,plain,
% 1.33/1.52 (b(s(s(z)), z)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[122, 6462])).
% 1.33/1.52 tff(6464,plain,
% 1.33/1.52 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6347, 6345])).
% 1.33/1.52 tff(6465,plain,
% 1.33/1.52 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6345])).
% 1.33/1.52 tff(6466,plain,
% 1.33/1.52 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.33/1.52 inference(symmetry,[status(thm)],[6465])).
% 1.33/1.52 tff(6467,plain,
% 1.33/1.52 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6349])).
% 1.33/1.52 tff(6468,plain,
% 1.33/1.52 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[6467])).
% 1.33/1.52 tff(6469,plain,
% 1.33/1.52 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6468, 6466])).
% 1.33/1.52 tff(6470,plain,
% 1.33/1.52 (r(elem!1, s(s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6367, 6469])).
% 1.33/1.52 tff(6471,plain,
% 1.33/1.52 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6347])).
% 1.33/1.52 tff(6472,plain,
% 1.33/1.52 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.33/1.52 inference(symmetry,[status(thm)],[6471])).
% 1.33/1.52 tff(6473,plain,
% 1.33/1.52 (b(s(elem!1), z)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6463, 6472])).
% 1.33/1.52 tff(6474,plain,
% 1.33/1.52 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.33/1.52 inference(symmetry,[status(thm)],[6368])).
% 1.33/1.52 tff(6475,plain,
% 1.33/1.52 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6474])).
% 1.33/1.52 tff(6476,plain,
% 1.33/1.52 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.33/1.52 inference(symmetry,[status(thm)],[6475])).
% 1.33/1.52 tff(6477,plain,
% 1.33/1.52 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[4186, 6476])).
% 1.33/1.52 tff(6478,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.33/1.52 tff(6479,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.33/1.52 tff(6480,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.33/1.52 tff(6481,plain,
% 1.33/1.52 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6480])).
% 1.33/1.52 tff(6482,plain,
% 1.33/1.52 (elem!1 = s(elem!1)),
% 1.33/1.52 inference(transitivity,[status(thm)],[4024, 6481, 485])).
% 1.33/1.52 tff(6483,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6397, 6482])).
% 1.33/1.52 tff(6484,plain,((~(s(elem!1) = s(s(elem!1)))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6485,plain,
% 1.33/1.52 (~(s(elem!1) = s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6484, 6397])).
% 1.33/1.52 tff(6486,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.33/1.52 tff(6487,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.33/1.52 tff(6488,plain,
% 1.33/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6489,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6490,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6489, 6488])).
% 1.33/1.52 tff(6491,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6490, 60, 6487, 6486, 6386])).
% 1.33/1.52 tff(6492,plain,(r(s(elem!1), s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6493,plain,
% 1.33/1.52 (r(s(elem!1), s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6492, 6486, 6485])).
% 1.33/1.52 tff(6494,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.33/1.52 tff(6495,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.33/1.52 tff(6496,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6497,plain,
% 1.33/1.52 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6498,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6497])).
% 1.33/1.52 tff(6499,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6498, 6496])).
% 1.33/1.52 tff(6500,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6501,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6500, 6499])).
% 1.33/1.52 tff(6502,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6501, 28, 6495, 6479, 6494])).
% 1.33/1.52 tff(6503,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6504,plain,
% 1.33/1.52 (~r(elem!1, s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6503, 6493, 6479])).
% 1.33/1.52 tff(6505,plain,
% 1.33/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6506,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6507,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6506, 6505])).
% 1.33/1.52 tff(6508,plain,
% 1.33/1.52 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6507, 60])).
% 1.33/1.52 tff(6509,plain,
% 1.33/1.52 (b(elem!1, s(elem!1))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6508, 6504, 6397])).
% 1.33/1.52 tff(6510,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.52 tff(6511,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.33/1.52 tff(6512,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6513,plain,
% 1.33/1.52 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6514,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6513])).
% 1.33/1.52 tff(6515,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6514, 6512])).
% 1.33/1.52 tff(6516,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6517,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6516, 6515])).
% 1.33/1.52 tff(6518,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6517, 154, 6511, 3852, 6231, 6510, 6478])).
% 1.33/1.52 tff(6519,plain,((~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6520,plain,
% 1.33/1.52 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6519, 6509, 6231, 6478, 3852])).
% 1.33/1.52 tff(6521,plain,
% 1.33/1.52 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6429, 6520, 4016])).
% 1.33/1.52 tff(6522,plain,
% 1.33/1.52 (r(s(s(z)), s(s(s(s(z)))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6424, 6521, 6412])).
% 1.33/1.52 tff(6523,plain,
% 1.33/1.52 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6413, 6414])).
% 1.33/1.52 tff(6524,plain,
% 1.33/1.52 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.33/1.52 inference(symmetry,[status(thm)],[6523])).
% 1.33/1.52 tff(6525,plain,
% 1.33/1.52 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[144, 6524])).
% 1.33/1.52 tff(6526,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6486, 6525])).
% 1.33/1.52 tff(6527,plain,((~b(s(s(z)), s(s(s(z))))) | b(s(elem!1), s(s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6528,plain,
% 1.33/1.52 (~b(s(s(z)), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6527, 6486, 6412])).
% 1.33/1.52 tff(6529,plain,
% 1.33/1.52 (r(s(s(z)), s(s(s(z))))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[138, 6528])).
% 1.33/1.52 tff(6530,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[130, 28, 6529, 66, 6522])).
% 1.33/1.52 tff(6531,plain,(b(s(elem!1), s(s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (elem!1 = s(elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6532,plain,
% 1.33/1.52 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6531, 6477, 6349, 6334, 6231, 6473, 3852, 6393, 6470])).
% 1.33/1.52 tff(6533,plain,
% 1.33/1.52 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6532, 6464])).
% 1.33/1.52 tff(6534,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6535,plain,
% 1.33/1.52 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6536,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6535])).
% 1.33/1.52 tff(6537,plain,
% 1.33/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(transitivity,[status(thm)],[6536, 6534])).
% 1.33/1.52 tff(6538,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6539,plain,
% 1.33/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6538, 6537])).
% 1.33/1.52 tff(6540,plain,
% 1.33/1.52 (~b(s(z), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6539, 154, 6533, 2604, 6270, 6463])).
% 1.33/1.52 tff(6541,plain,
% 1.33/1.52 (r(s(z), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[679, 6540, 675])).
% 1.33/1.52 tff(6542,plain,
% 1.33/1.52 (~b(s(s(s(z))), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[893, 154, 6533, 6278, 6270, 6463])).
% 1.33/1.52 tff(6543,plain,
% 1.33/1.52 (r(s(s(s(z))), s(s(z)))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[103, 6542, 99])).
% 1.33/1.52 tff(6544,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[597, 6543, 6541, 6367])).
% 1.33/1.52 tff(6545,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(6546,plain,
% 1.33/1.52 (r(s(s(elem!1)), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6545, 6238, 6231, 3852, 4186, 4132, 6225, 2604])).
% 1.33/1.52 tff(6547,plain,
% 1.33/1.52 (r(s(s(s(z))), s(z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6546, 6333])).
% 1.33/1.52 tff(6548,plain,
% 1.33/1.52 (~r(s(s(s(s(z)))), s(z))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[853, 6547, 6332])).
% 1.33/1.52 tff(6549,plain,
% 1.33/1.52 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6548, 6329])).
% 1.33/1.52 tff(6550,plain,
% 1.33/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(6551,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(6552,plain,
% 1.33/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6551, 6550])).
% 1.33/1.52 tff(6553,plain,
% 1.33/1.52 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6552, 60])).
% 1.33/1.52 tff(6554,plain,
% 1.33/1.52 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[6553, 6549, 6324])).
% 1.33/1.52 tff(6555,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), s(z))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[6554, 6323])).
% 1.33/1.52 tff(6556,plain,
% 1.33/1.52 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.33/1.52 inference(monotonicity,[status(thm)],[6322])).
% 1.33/1.52 tff(6557,plain,
% 1.33/1.52 (b(s(s(s(s(z)))), z)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[3852, 6556])).
% 1.33/1.52 tff(6558,plain,
% 1.33/1.52 (~b(s(z), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[3057, 6557, 2604, 6270, 6555])).
% 1.33/1.53 tff(6559,plain,
% 1.33/1.53 (r(s(z), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[252, 6558])).
% 1.33/1.53 tff(6560,plain,
% 1.33/1.53 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6322])).
% 1.33/1.53 tff(6561,plain,
% 1.33/1.53 (r(z, s(s(s(s(z)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[4132, 6560])).
% 1.33/1.53 tff(6562,plain,
% 1.33/1.53 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6321, 6322])).
% 1.33/1.53 tff(6563,plain,
% 1.33/1.53 (b(s(z), s(s(s(s(z)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6231, 6562])).
% 1.33/1.53 tff(6564,plain,
% 1.33/1.53 (~(elem!1 = s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6392, 6238])).
% 1.33/1.53 tff(6565,plain,
% 1.33/1.53 (~(s(elem!1) = elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6399, 6564])).
% 1.33/1.53 tff(6566,plain,
% 1.33/1.53 (r(z, elem!1) <=> r(z, s(z))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6321])).
% 1.33/1.53 tff(6567,plain,
% 1.33/1.53 (r(z, s(z)) <=> r(z, elem!1)),
% 1.33/1.53 inference(symmetry,[status(thm)],[6566])).
% 1.33/1.53 tff(6568,plain,
% 1.33/1.53 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6322])).
% 1.33/1.53 tff(6569,plain,
% 1.33/1.53 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.33/1.53 inference(symmetry,[status(thm)],[6568])).
% 1.33/1.53 tff(6570,plain,
% 1.33/1.53 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6562, 6569])).
% 1.33/1.53 tff(6571,plain,
% 1.33/1.53 (b(s(z), s(s(s(elem!1))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6231, 6570])).
% 1.33/1.53 tff(6572,plain,
% 1.33/1.53 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6322])).
% 1.33/1.53 tff(6573,plain,
% 1.33/1.53 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.33/1.53 inference(symmetry,[status(thm)],[6572])).
% 1.33/1.53 tff(6574,plain,
% 1.33/1.53 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6323, 6573])).
% 1.33/1.53 tff(6575,plain,
% 1.33/1.53 (b(s(s(s(elem!1))), s(z))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6554, 6574])).
% 1.33/1.53 tff(6576,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.33/1.53 tff(6577,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.53 tff(6578,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6579,plain,
% 1.33/1.53 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6580,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6579])).
% 1.33/1.53 tff(6581,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6580, 6578])).
% 1.33/1.53 tff(6582,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6583,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6582, 6581])).
% 1.33/1.53 tff(6584,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6583, 154, 3852, 1726, 2604, 6577, 6576])).
% 1.33/1.53 tff(6585,plain,((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6586,plain,
% 1.33/1.53 (~b(z, s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6585, 6575, 2604, 6571, 3852])).
% 1.33/1.53 tff(6587,plain,
% 1.33/1.53 (r(z, s(z))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[1181, 6586])).
% 1.33/1.53 tff(6588,plain,
% 1.33/1.53 (r(z, elem!1)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6587, 6567])).
% 1.33/1.53 tff(6589,plain,
% 1.33/1.53 (~r(s(s(z)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6461, 6588, 6565, 6317, 2604, 6557, 6563, 6239, 6561])).
% 1.33/1.53 tff(6590,plain,
% 1.33/1.53 (b(s(s(z)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[122, 6589])).
% 1.33/1.53 tff(6591,plain,
% 1.33/1.53 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6319])).
% 1.33/1.53 tff(6592,plain,
% 1.33/1.53 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.33/1.53 inference(symmetry,[status(thm)],[6591])).
% 1.33/1.53 tff(6593,plain,
% 1.33/1.53 (b(s(elem!1), z)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6590, 6592])).
% 1.33/1.53 tff(6594,plain,
% 1.33/1.53 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6317])).
% 1.33/1.53 tff(6595,plain,
% 1.33/1.53 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.33/1.53 inference(symmetry,[status(thm)],[6594])).
% 1.33/1.53 tff(6596,plain,
% 1.33/1.53 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6321])).
% 1.33/1.53 tff(6597,plain,
% 1.33/1.53 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.33/1.53 inference(symmetry,[status(thm)],[6596])).
% 1.33/1.53 tff(6598,plain,
% 1.33/1.53 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6597, 6595])).
% 1.33/1.53 tff(6599,plain,
% 1.33/1.53 (r(elem!1, s(s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6559, 6598])).
% 1.33/1.53 tff(6600,plain,
% 1.33/1.53 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6531, 6599, 6321, 6239, 6231, 6332, 3852, 6564, 6593])).
% 1.33/1.53 tff(6601,plain,
% 1.33/1.53 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6403, 6401])).
% 1.33/1.53 tff(6602,plain,
% 1.33/1.53 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.33/1.53 inference(symmetry,[status(thm)],[6601])).
% 1.33/1.53 tff(6603,plain,
% 1.33/1.53 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6602])).
% 1.33/1.53 tff(6604,plain,
% 1.33/1.53 (~b(s(elem!1), s(s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6190, 6603])).
% 1.33/1.53 tff(6605,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.33/1.53 tff(6606,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6605, 6604])).
% 1.33/1.53 tff(6607,plain,(b(s(s(z)), s(s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6608,plain,
% 1.33/1.53 (b(s(s(z)), s(s(s(z))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6607, 6600, 6317])).
% 1.33/1.53 tff(6609,plain,
% 1.33/1.53 (~b(s(z), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6539, 154, 6608, 2604, 6270, 6590])).
% 1.33/1.53 tff(6610,plain,
% 1.33/1.53 (r(s(z), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[679, 6609, 675])).
% 1.33/1.53 tff(6611,plain,
% 1.33/1.53 (~b(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[893, 154, 6608, 6278, 6270, 6590])).
% 1.33/1.53 tff(6612,plain,
% 1.33/1.53 (r(s(s(s(z))), s(s(z)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[103, 6611, 99])).
% 1.33/1.53 tff(6613,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[597, 6612, 6610, 6559])).
% 1.33/1.53 tff(6614,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6615,plain,
% 1.33/1.53 (~b(elem!1, s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6614, 4186, 3852, 6230, 2604, 4132, 6225])).
% 1.33/1.53 tff(6616,plain,
% 1.33/1.53 (r(elem!1, s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4311, 6615, 6224])).
% 1.33/1.53 tff(6617,plain,
% 1.33/1.53 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4018, 4016])).
% 1.33/1.53 tff(6618,plain,
% 1.33/1.53 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6244, 6617, 6225])).
% 1.33/1.53 tff(6619,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6620,plain,
% 1.33/1.53 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6621,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6620])).
% 1.33/1.53 tff(6622,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6621, 6619])).
% 1.33/1.53 tff(6623,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6624,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6623, 6622])).
% 1.33/1.53 tff(6625,plain,
% 1.33/1.53 (~r(elem!1, z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6624, 28, 4132, 4297])).
% 1.33/1.53 tff(6626,plain,
% 1.33/1.53 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4064, 4016])).
% 1.33/1.53 tff(6627,plain,
% 1.33/1.53 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4053, 6626])).
% 1.33/1.53 tff(6628,plain,
% 1.33/1.53 (~(elem!1 = s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4037, 6627])).
% 1.33/1.53 tff(6629,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6630,plain,
% 1.33/1.53 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6631,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6630])).
% 1.33/1.53 tff(6632,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6631, 6629])).
% 1.33/1.53 tff(6633,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6634,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6633, 6632])).
% 1.33/1.53 tff(6635,plain,
% 1.33/1.53 (~r(z, elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6634, 28, 4132, 4297])).
% 1.33/1.53 tff(6636,plain,
% 1.33/1.53 (~r(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6288, 6618, 4132])).
% 1.33/1.53 tff(6637,plain,
% 1.33/1.53 (b(s(s(elem!1)), z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6293, 6636])).
% 1.33/1.53 tff(6638,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.33/1.53 tff(6639,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.33/1.53 tff(6640,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.33/1.53 tff(6641,plain,
% 1.33/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6642,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6643,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6642, 6641])).
% 1.33/1.53 tff(6644,plain,
% 1.33/1.53 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6643, 60])).
% 1.33/1.53 tff(6645,plain,
% 1.33/1.53 (r(elem!1, s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6644, 4026, 6640])).
% 1.33/1.53 tff(6646,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6647,plain,
% 1.33/1.53 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6648,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6647])).
% 1.33/1.53 tff(6649,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6648, 6646])).
% 1.33/1.53 tff(6650,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6651,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6650, 6649])).
% 1.33/1.53 tff(6652,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6651, 28, 6645, 4297, 6336])).
% 1.33/1.53 tff(6653,plain,((elem!1 = s(s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6654,plain,
% 1.33/1.53 (b(elem!1, s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6653, 4026, 6225, 4297])).
% 1.33/1.53 tff(6655,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.33/1.53 tff(6656,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.33/1.53 tff(6657,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.33/1.53 tff(6658,plain,
% 1.33/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6659,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6660,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6659, 6658])).
% 1.33/1.53 tff(6661,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6660, 60, 6657, 6638, 4357])).
% 1.33/1.53 tff(6662,plain,(b(elem!1, z) | r(elem!1, z) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6663,plain,
% 1.33/1.53 (b(elem!1, z)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6662, 4357, 6638])).
% 1.33/1.53 tff(6664,plain,
% 1.33/1.53 (~(z = elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4359, 4357])).
% 1.33/1.53 tff(6665,plain,
% 1.33/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6666,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6667,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6666, 6665])).
% 1.33/1.53 tff(6668,plain,
% 1.33/1.53 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6667, 60])).
% 1.33/1.53 tff(6669,plain,
% 1.33/1.53 (b(z, elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6668, 6664, 6639])).
% 1.33/1.53 tff(6670,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.33/1.53 tff(6671,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.33/1.53 tff(6672,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6673,plain,
% 1.33/1.53 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6674,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6673])).
% 1.33/1.53 tff(6675,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6674, 6672])).
% 1.33/1.53 tff(6676,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6677,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6676, 6675])).
% 1.33/1.53 tff(6678,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6677, 154, 6655, 6656, 5702, 6671, 6670])).
% 1.33/1.53 tff(6679,plain,((~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6680,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6679, 6669, 6663, 5702, 6656, 6655])).
% 1.33/1.53 tff(6681,plain,((elem!1 = z) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6682,plain,
% 1.33/1.53 (elem!1 = z),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6681, 6654, 6639, 5702, 6364, 6638])).
% 1.33/1.53 tff(6683,plain,
% 1.33/1.53 (s(elem!1) = s(z)),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6682])).
% 1.33/1.53 tff(6684,plain,
% 1.33/1.53 (s(s(elem!1)) = s(s(z))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6683])).
% 1.33/1.53 tff(6685,plain,
% 1.33/1.53 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6684])).
% 1.33/1.53 tff(6686,plain,
% 1.33/1.53 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6684, 6685])).
% 1.33/1.53 tff(6687,plain,
% 1.33/1.53 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.53 inference(symmetry,[status(thm)],[6686])).
% 1.33/1.53 tff(6688,plain,
% 1.33/1.53 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6687])).
% 1.33/1.53 tff(6689,plain,
% 1.33/1.53 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6684])).
% 1.33/1.53 tff(6690,plain,
% 1.33/1.53 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6689])).
% 1.33/1.53 tff(6691,plain,
% 1.33/1.53 (~r(s(s(z)), s(s(s(z))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6343, 6690])).
% 1.33/1.53 tff(6692,plain,
% 1.33/1.53 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6691, 6688])).
% 1.33/1.53 tff(6693,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6336, 6692])).
% 1.33/1.53 tff(6694,plain,((elem!1 = s(s(elem!1))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(z, elem!1) | (~b(s(s(elem!1)), z)) | r(elem!1, z) | r(s(s(elem!1)), elem!1) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6695,plain,
% 1.33/1.53 (r(s(s(elem!1)), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6694, 6637, 6225, 4297, 4186, 6635, 6628, 6625])).
% 1.33/1.53 tff(6696,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6697,plain,
% 1.33/1.53 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6698,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6697])).
% 1.33/1.53 tff(6699,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6698, 6696])).
% 1.33/1.53 tff(6700,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6701,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6700, 6699])).
% 1.33/1.53 tff(6702,plain,
% 1.33/1.53 ($false),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6701, 28, 6695, 4297, 6618])).
% 1.33/1.53 tff(6703,plain,((s(elem!1) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.53 tff(6704,plain,
% 1.33/1.53 (s(elem!1) = s(s(s(elem!1)))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6703, 6616, 6225, 4186, 4132])).
% 1.33/1.53 tff(6705,plain,
% 1.33/1.53 (elem!1 = s(s(elem!1))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4028, 6704])).
% 1.33/1.53 tff(6706,plain,
% 1.33/1.53 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6705])).
% 1.33/1.53 tff(6707,plain,
% 1.33/1.53 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.33/1.53 inference(commutativity,[status(thm)],[])).
% 1.33/1.53 tff(6708,plain,
% 1.33/1.53 (s(s(elem!1)) = elem!1),
% 1.33/1.53 inference(symmetry,[status(thm)],[6705])).
% 1.33/1.53 tff(6709,plain,
% 1.33/1.53 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6708])).
% 1.33/1.53 tff(6710,plain,
% 1.33/1.53 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.33/1.53 inference(transitivity,[status(thm)],[6709, 6707])).
% 1.33/1.53 tff(6711,plain,
% 1.33/1.53 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.33/1.53 inference(commutativity,[status(thm)],[])).
% 1.33/1.53 tff(6712,plain,
% 1.33/1.53 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[4037, 6705])).
% 1.33/1.53 tff(6713,plain,
% 1.33/1.53 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.33/1.53 inference(symmetry,[status(thm)],[6712])).
% 1.33/1.53 tff(6714,plain,
% 1.33/1.53 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6713])).
% 1.33/1.53 tff(6715,plain,
% 1.33/1.53 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6714, 6711])).
% 1.33/1.53 tff(6716,plain,
% 1.33/1.53 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 1.33/1.53 inference(transitivity,[status(thm)],[6715, 6710])).
% 1.33/1.53 tff(6717,plain,
% 1.33/1.53 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6716])).
% 1.33/1.53 tff(6718,plain,
% 1.33/1.53 (~(s(s(s(z))) = elem!1)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[984, 6717])).
% 1.33/1.53 tff(6719,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6720,plain,
% 1.33/1.53 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6721,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[6720])).
% 1.33/1.53 tff(6722,plain,
% 1.33/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[6721, 6719])).
% 1.33/1.53 tff(6723,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6724,plain,
% 1.33/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), elem!1))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[6723, 6722])).
% 1.33/1.53 tff(6725,plain,
% 1.33/1.53 (~r(s(s(s(z))), elem!1)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[6724, 28, 6616, 4186])).
% 1.33/1.53 tff(6726,plain,
% 1.33/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(6727,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(6728,plain,
% 1.33/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6727, 6726])).
% 1.33/1.54 tff(6729,plain,
% 1.33/1.54 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6728, 60, 6725])).
% 1.33/1.54 tff(6730,plain,
% 1.33/1.54 (b(s(s(s(z))), elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6729, 6718])).
% 1.33/1.54 tff(6731,plain,
% 1.33/1.54 (b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6730, 6706])).
% 1.33/1.54 tff(6732,plain,
% 1.33/1.54 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6705])).
% 1.33/1.54 tff(6733,plain,
% 1.33/1.54 ((~r(z, elem!1)) <=> (~r(z, s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6732])).
% 1.33/1.54 tff(6734,plain,
% 1.33/1.54 (~r(z, elem!1)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6634, 28, 4132, 6616])).
% 1.33/1.54 tff(6735,plain,
% 1.33/1.54 (~r(z, s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6734, 6733])).
% 1.33/1.54 tff(6736,plain,
% 1.33/1.54 (b(z, s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6259, 60, 6256, 6735])).
% 1.33/1.54 tff(6737,plain,
% 1.33/1.54 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6705])).
% 1.33/1.54 tff(6738,plain,
% 1.33/1.54 ((~r(elem!1, z)) <=> (~r(s(s(elem!1)), z))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6737])).
% 1.33/1.54 tff(6739,plain,
% 1.33/1.54 (~r(elem!1, z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6624, 28, 4132, 6616])).
% 1.33/1.54 tff(6740,plain,
% 1.33/1.54 (~r(s(s(elem!1)), z)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6739, 6738])).
% 1.33/1.54 tff(6741,plain,
% 1.33/1.54 (b(s(s(elem!1)), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6293, 6740])).
% 1.33/1.54 tff(6742,plain,
% 1.33/1.54 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6715])).
% 1.33/1.54 tff(6743,plain,
% 1.33/1.54 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[984, 6742])).
% 1.33/1.54 tff(6744,plain,
% 1.33/1.54 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6705])).
% 1.33/1.54 tff(6745,plain,
% 1.33/1.54 ((~r(elem!1, s(s(s(z))))) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6744])).
% 1.33/1.54 tff(6746,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6747,plain,
% 1.33/1.54 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6748,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6747])).
% 1.33/1.54 tff(6749,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6748, 6746])).
% 1.33/1.54 tff(6750,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6751,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(z)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6750, 6749])).
% 1.33/1.54 tff(6752,plain,
% 1.33/1.54 (~r(elem!1, s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6751, 28, 6616, 4186])).
% 1.33/1.54 tff(6753,plain,
% 1.33/1.54 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6752, 6745])).
% 1.33/1.54 tff(6754,plain,
% 1.33/1.54 (b(s(s(elem!1)), s(s(s(z))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6315, 60, 6753, 6743])).
% 1.33/1.54 tff(6755,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6756,plain,
% 1.33/1.54 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6757,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6756])).
% 1.33/1.54 tff(6758,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6757, 6755])).
% 1.33/1.54 tff(6759,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6760,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6759, 6758])).
% 1.33/1.54 tff(6761,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6760, 154, 5702, 5701, 5700, 5699, 143])).
% 1.33/1.54 tff(6762,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6763,plain,
% 1.33/1.54 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6762, 6754, 6278, 6741, 6736])).
% 1.33/1.54 tff(6764,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6763, 6731])).
% 1.33/1.54 tff(6765,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6766,plain,
% 1.33/1.54 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6765, 2604, 4132, 6224, 3852, 6225])).
% 1.33/1.54 tff(6767,plain,
% 1.33/1.54 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[4202, 6766, 4197])).
% 1.33/1.54 tff(6768,plain,
% 1.33/1.54 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6767])).
% 1.33/1.54 tff(6769,plain,
% 1.33/1.54 (s(s(z)) = s(s(elem!1))),
% 1.33/1.54 inference(transitivity,[status(thm)],[87, 6768, 362])).
% 1.33/1.54 tff(6770,plain,
% 1.33/1.54 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6769])).
% 1.33/1.54 tff(6771,plain,
% 1.33/1.54 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6770])).
% 1.33/1.54 tff(6772,plain,
% 1.33/1.54 (s(elem!1) = s(z)),
% 1.33/1.54 inference(transitivity,[status(thm)],[486, 6771, 81])).
% 1.33/1.54 tff(6773,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6772])).
% 1.33/1.54 tff(6774,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6773])).
% 1.33/1.54 tff(6775,plain,
% 1.33/1.54 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6767])).
% 1.33/1.54 tff(6776,plain,
% 1.33/1.54 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6767])).
% 1.33/1.54 tff(6777,plain,
% 1.33/1.54 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6776])).
% 1.33/1.54 tff(6778,plain,
% 1.33/1.54 (r(z, s(s(s(z))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[4132, 6777])).
% 1.33/1.54 tff(6779,plain,
% 1.33/1.54 (s(z) = s(elem!1)),
% 1.33/1.54 inference(transitivity,[status(thm)],[289, 6770, 485])).
% 1.33/1.54 tff(6780,plain,
% 1.33/1.54 (r(z, s(z)) <=> r(z, s(elem!1))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6779])).
% 1.33/1.54 tff(6781,plain,
% 1.33/1.54 (r(z, s(elem!1)) <=> r(z, s(z))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6780])).
% 1.33/1.54 tff(6782,plain,
% 1.33/1.54 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6779])).
% 1.33/1.54 tff(6783,plain,
% 1.33/1.54 (z = elem!1),
% 1.33/1.54 inference(transitivity,[status(thm)],[4229, 6782, 4023])).
% 1.33/1.54 tff(6784,plain,
% 1.33/1.54 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6783])).
% 1.33/1.54 tff(6785,plain,
% 1.33/1.54 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6784])).
% 1.33/1.54 tff(6786,plain,
% 1.33/1.54 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6785, 6781])).
% 1.33/1.54 tff(6787,plain,
% 1.33/1.54 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6783])).
% 1.33/1.54 tff(6788,plain,
% 1.33/1.54 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6787, 6394])).
% 1.33/1.54 tff(6789,plain,
% 1.33/1.54 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6788])).
% 1.33/1.54 tff(6790,plain,
% 1.33/1.54 (~(elem!1 = s(elem!1))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[489, 6789])).
% 1.33/1.54 tff(6791,plain,
% 1.33/1.54 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6783])).
% 1.33/1.54 tff(6792,plain,
% 1.33/1.54 (b(s(z), z) <=> b(s(elem!1), z)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6779])).
% 1.33/1.54 tff(6793,plain,
% 1.33/1.54 (b(s(elem!1), z)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2604, 6792])).
% 1.33/1.54 tff(6794,plain,
% 1.33/1.54 (b(s(elem!1), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6793, 6791])).
% 1.33/1.54 tff(6795,plain,
% 1.33/1.54 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6782])).
% 1.33/1.54 tff(6796,plain,
% 1.33/1.54 (elem!1 = z),
% 1.33/1.54 inference(transitivity,[status(thm)],[4024, 6795, 91])).
% 1.33/1.54 tff(6797,plain,
% 1.33/1.54 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6796])).
% 1.33/1.54 tff(6798,plain,
% 1.33/1.54 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(symmetry,[status(thm)],[6797])).
% 1.33/1.54 tff(6799,plain,
% 1.33/1.54 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6768])).
% 1.33/1.54 tff(6800,plain,
% 1.33/1.54 (s(s(elem!1)) = s(s(z))),
% 1.33/1.54 inference(transitivity,[status(thm)],[363, 6799, 86])).
% 1.33/1.54 tff(6801,plain,
% 1.33/1.54 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6800])).
% 1.33/1.54 tff(6802,plain,
% 1.33/1.54 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6801])).
% 1.33/1.54 tff(6803,plain,
% 1.33/1.54 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6802])).
% 1.33/1.54 tff(6804,plain,
% 1.33/1.54 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3906, 6803])).
% 1.33/1.54 tff(6805,plain,
% 1.33/1.54 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6244, 6804, 6225])).
% 1.33/1.54 tff(6806,plain,
% 1.33/1.54 (~r(s(s(elem!1)), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6288, 6805, 4132])).
% 1.33/1.54 tff(6807,plain,
% 1.33/1.54 (b(s(s(elem!1)), z)),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6293, 6806])).
% 1.33/1.54 tff(6808,plain,
% 1.33/1.54 (b(s(s(elem!1)), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6807, 6798])).
% 1.33/1.54 tff(6809,plain,
% 1.33/1.54 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6783])).
% 1.33/1.54 tff(6810,plain,
% 1.33/1.54 (r(elem!1, s(s(s(elem!1))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[4132, 6809])).
% 1.33/1.54 tff(6811,plain,
% 1.33/1.54 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.33/1.54 inference(commutativity,[status(thm)],[])).
% 1.33/1.54 tff(6812,plain,
% 1.33/1.54 ((elem!1 = s(s(elem!1))) <=> (z = s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6796])).
% 1.33/1.54 tff(6813,plain,
% 1.33/1.54 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.33/1.54 inference(transitivity,[status(thm)],[6812, 6811])).
% 1.33/1.54 tff(6814,plain,
% 1.33/1.54 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6813])).
% 1.33/1.54 tff(6815,plain,
% 1.33/1.54 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6814])).
% 1.33/1.54 tff(6816,plain,
% 1.33/1.54 (~(elem!1 = s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[366, 6815])).
% 1.33/1.54 tff(6817,plain,
% 1.33/1.54 (b(elem!1, s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6653, 6816, 6225, 6810])).
% 1.33/1.54 tff(6818,plain,
% 1.33/1.54 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6772])).
% 1.33/1.54 tff(6819,plain,
% 1.33/1.54 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6818, 3896])).
% 1.33/1.54 tff(6820,plain,
% 1.33/1.54 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6819])).
% 1.33/1.54 tff(6821,plain,
% 1.33/1.54 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6820])).
% 1.33/1.54 tff(6822,plain,
% 1.33/1.54 (~(s(elem!1) = s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3904, 6821])).
% 1.33/1.54 tff(6823,plain,
% 1.33/1.54 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.33/1.54 inference(symmetry,[status(thm)],[4213])).
% 1.33/1.54 tff(6824,plain,
% 1.33/1.54 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6823])).
% 1.33/1.54 tff(6825,plain,
% 1.33/1.54 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6824])).
% 1.33/1.54 tff(6826,plain,
% 1.33/1.54 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[4213])).
% 1.33/1.54 tff(6827,plain,
% 1.33/1.54 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6826])).
% 1.33/1.54 tff(6828,plain,
% 1.33/1.54 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6827])).
% 1.33/1.54 tff(6829,plain,
% 1.33/1.54 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[4215])).
% 1.33/1.54 tff(6830,plain,
% 1.33/1.54 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6829])).
% 1.33/1.54 tff(6831,plain,
% 1.33/1.54 (s(elem!1) = s(z)),
% 1.33/1.54 inference(transitivity,[status(thm)],[486, 6830, 81])).
% 1.33/1.54 tff(6832,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6831])).
% 1.33/1.54 tff(6833,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6832])).
% 1.33/1.54 tff(6834,plain,
% 1.33/1.54 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[4213])).
% 1.33/1.54 tff(6835,plain,
% 1.33/1.54 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6823, 6831])).
% 1.33/1.54 tff(6836,plain,
% 1.33/1.54 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6835])).
% 1.33/1.54 tff(6837,plain,
% 1.33/1.54 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[4213, 4215])).
% 1.33/1.54 tff(6838,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.33/1.54 inference(symmetry,[status(thm)],[4386])).
% 1.33/1.54 tff(6839,plain,
% 1.33/1.54 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(z))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6838])).
% 1.33/1.54 tff(6840,plain,
% 1.33/1.54 (s(z) = s(elem!1)),
% 1.33/1.54 inference(transitivity,[status(thm)],[289, 6829, 485])).
% 1.33/1.54 tff(6841,plain,
% 1.33/1.54 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6840])).
% 1.33/1.54 tff(6842,plain,
% 1.33/1.54 (z = elem!1),
% 1.33/1.54 inference(transitivity,[status(thm)],[4229, 6841, 4023])).
% 1.33/1.54 tff(6843,plain,
% 1.33/1.54 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6842])).
% 1.33/1.54 tff(6844,plain,
% 1.33/1.54 (b(s(z), z) <=> b(s(elem!1), z)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6840])).
% 1.33/1.54 tff(6845,plain,
% 1.33/1.54 (b(s(elem!1), z)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[2604, 6844])).
% 1.33/1.54 tff(6846,plain,
% 1.33/1.54 (b(s(elem!1), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6845, 6843])).
% 1.33/1.54 tff(6847,plain,
% 1.33/1.54 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6841])).
% 1.33/1.54 tff(6848,plain,
% 1.33/1.54 (elem!1 = z),
% 1.33/1.54 inference(transitivity,[status(thm)],[4024, 6847, 91])).
% 1.33/1.54 tff(6849,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6848])).
% 1.33/1.54 tff(6850,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.33/1.54 inference(symmetry,[status(thm)],[6849])).
% 1.33/1.54 tff(6851,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[3852, 6850])).
% 1.33/1.54 tff(6852,plain,
% 1.33/1.54 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6831])).
% 1.33/1.54 tff(6853,plain,
% 1.33/1.54 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.54 inference(symmetry,[status(thm)],[6852])).
% 1.33/1.54 tff(6854,plain,
% 1.33/1.54 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6853])).
% 1.33/1.54 tff(6855,plain,
% 1.33/1.54 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[368, 6854])).
% 1.33/1.54 tff(6856,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6857,plain,
% 1.33/1.54 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6858,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6857])).
% 1.33/1.54 tff(6859,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6858, 6856])).
% 1.33/1.54 tff(6860,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6861,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6860, 6859])).
% 1.33/1.54 tff(6862,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6861, 28, 6494, 6420, 6279])).
% 1.33/1.54 tff(6863,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6864,plain,
% 1.33/1.54 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6863, 6494, 6279])).
% 1.33/1.54 tff(6865,plain,
% 1.33/1.54 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6429, 6864, 6855])).
% 1.33/1.54 tff(6866,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.33/1.54 tff(6867,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.33/1.54 tff(6868,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.33/1.54 tff(6869,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6870,plain,
% 1.33/1.54 (((~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(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6871,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6870])).
% 1.33/1.54 tff(6872,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6871, 6869])).
% 1.33/1.54 tff(6873,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6874,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6873, 6872])).
% 1.33/1.54 tff(6875,plain,
% 1.33/1.54 ($false),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6874, 154, 6868, 6655, 6867, 6510, 6866])).
% 1.33/1.54 tff(6876,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.54 tff(6877,plain,
% 1.33/1.54 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6876, 6865, 6655, 6851, 6846])).
% 1.33/1.54 tff(6878,plain,
% 1.33/1.54 (~b(s(s(s(z))), s(s(z)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6877, 6839])).
% 1.33/1.54 tff(6879,plain,
% 1.33/1.54 (r(s(s(s(z))), s(s(z)))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[103, 6878, 99])).
% 1.33/1.54 tff(6880,plain,
% 1.33/1.54 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6879, 6837])).
% 1.33/1.54 tff(6881,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6882,plain,
% 1.33/1.54 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.54 inference(rewrite,[status(thm)],[])).
% 1.33/1.54 tff(6883,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.33/1.54 inference(monotonicity,[status(thm)],[6882])).
% 1.33/1.54 tff(6884,plain,
% 1.33/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.54 inference(transitivity,[status(thm)],[6883, 6881])).
% 1.33/1.54 tff(6885,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.54 inference(quant_inst,[status(thm)],[])).
% 1.33/1.54 tff(6886,plain,
% 1.33/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6885, 6884])).
% 1.33/1.54 tff(6887,plain,
% 1.33/1.54 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[6886, 28, 6494, 6880])).
% 1.33/1.54 tff(6888,plain,
% 1.33/1.54 (~r(s(s(s(z))), s(z))),
% 1.33/1.54 inference(modus_ponens,[status(thm)],[6887, 6836])).
% 1.33/1.54 tff(6889,plain,
% 1.33/1.54 (b(s(s(s(z))), s(z))),
% 1.33/1.54 inference(unit_resolution,[status(thm)],[818, 6888])).
% 1.33/1.54 tff(6890,plain,
% 1.33/1.54 (b(s(s(s(elem!1))), s(z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6889, 6834])).
% 1.33/1.55 tff(6891,plain,
% 1.33/1.55 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6890, 6833])).
% 1.33/1.55 tff(6892,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6831])).
% 1.33/1.55 tff(6893,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(symmetry,[status(thm)],[6892])).
% 1.33/1.55 tff(6894,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6831])).
% 1.33/1.55 tff(6895,plain,
% 1.33/1.55 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6894])).
% 1.33/1.55 tff(6896,plain,
% 1.33/1.55 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6842])).
% 1.33/1.55 tff(6897,plain,
% 1.33/1.55 (r(z, s(z)) <=> r(z, s(elem!1))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6840])).
% 1.33/1.55 tff(6898,plain,
% 1.33/1.55 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6897, 6896])).
% 1.33/1.55 tff(6899,plain,
% 1.33/1.55 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6831])).
% 1.33/1.55 tff(6900,plain,
% 1.33/1.55 (b(s(z), s(s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6865, 6899])).
% 1.33/1.55 tff(6901,plain,
% 1.33/1.55 (~b(z, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6585, 6890, 2604, 6900, 3852])).
% 1.33/1.55 tff(6902,plain,
% 1.33/1.55 (r(z, s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[1181, 6901])).
% 1.33/1.55 tff(6903,plain,
% 1.33/1.55 (r(elem!1, s(elem!1))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6902, 6898])).
% 1.33/1.55 tff(6904,plain,
% 1.33/1.55 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6848])).
% 1.33/1.55 tff(6905,plain,
% 1.33/1.55 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.33/1.55 inference(symmetry,[status(thm)],[6904])).
% 1.33/1.55 tff(6906,plain,
% 1.33/1.55 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6905, 4255])).
% 1.33/1.55 tff(6907,plain,
% 1.33/1.55 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6906])).
% 1.33/1.55 tff(6908,plain,
% 1.33/1.55 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[388, 6907])).
% 1.33/1.55 tff(6909,plain,
% 1.33/1.55 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6905])).
% 1.33/1.55 tff(6910,plain,
% 1.33/1.55 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[388, 6909])).
% 1.33/1.55 tff(6911,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(symmetry,[status(thm)],[6894])).
% 1.33/1.55 tff(6912,plain,
% 1.33/1.55 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6892])).
% 1.33/1.55 tff(6913,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.33/1.55 tff(6914,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[780, 6825])).
% 1.33/1.55 tff(6915,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6916,plain,
% 1.33/1.55 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6917,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6916])).
% 1.33/1.55 tff(6918,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6917, 6915])).
% 1.33/1.55 tff(6919,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6920,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6919, 6918])).
% 1.33/1.55 tff(6921,plain,
% 1.33/1.55 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6920, 28, 6495, 6913, 4297])).
% 1.33/1.55 tff(6922,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6921, 6914])).
% 1.33/1.55 tff(6923,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6924,plain,
% 1.33/1.55 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6923, 6913, 6495, 4213, 4297])).
% 1.33/1.55 tff(6925,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[496, 6924])).
% 1.33/1.55 tff(6926,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6925, 6826])).
% 1.33/1.55 tff(6927,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6928,plain,
% 1.33/1.55 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6929,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6928])).
% 1.33/1.55 tff(6930,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6929, 6927])).
% 1.33/1.55 tff(6931,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6932,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6931, 6930])).
% 1.33/1.55 tff(6933,plain,
% 1.33/1.55 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6932, 154, 6868, 6867, 6510, 6926])).
% 1.33/1.55 tff(6934,plain,
% 1.33/1.55 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6933, 6912])).
% 1.33/1.55 tff(6935,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[441, 6934])).
% 1.33/1.55 tff(6936,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6935, 6911])).
% 1.33/1.55 tff(6937,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6938,plain,
% 1.33/1.55 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6939,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6938])).
% 1.33/1.55 tff(6940,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6939, 6937])).
% 1.33/1.55 tff(6941,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6942,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6941, 6940])).
% 1.33/1.55 tff(6943,plain,
% 1.33/1.55 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6942, 28, 6495, 6913])).
% 1.33/1.55 tff(6944,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6943, 6936])).
% 1.33/1.55 tff(6945,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6946,plain,
% 1.33/1.55 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6945, 6903, 4213, 6846, 6851, 6865, 4297])).
% 1.33/1.55 tff(6947,plain,
% 1.33/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6948,plain,
% 1.33/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6949,plain,
% 1.33/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6948, 6947])).
% 1.33/1.55 tff(6950,plain,
% 1.33/1.55 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6949, 60])).
% 1.33/1.55 tff(6951,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6950, 6946, 6910])).
% 1.33/1.55 tff(6952,plain,
% 1.33/1.55 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[4064, 6855])).
% 1.33/1.55 tff(6953,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.33/1.55 tff(6954,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6955,plain,
% 1.33/1.55 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6956,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6955])).
% 1.33/1.55 tff(6957,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6956, 6954])).
% 1.33/1.55 tff(6958,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6959,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6958, 6957])).
% 1.33/1.55 tff(6960,plain,
% 1.33/1.55 ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6959, 28, 6495])).
% 1.33/1.55 tff(6961,plain,
% 1.33/1.55 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6960, 6953])).
% 1.33/1.55 tff(6962,plain,
% 1.33/1.55 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[4286, 6961, 4279])).
% 1.33/1.55 tff(6963,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.33/1.55 tff(6964,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6965,plain,
% 1.33/1.55 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6966,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6965])).
% 1.33/1.55 tff(6967,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6966, 6964])).
% 1.33/1.55 tff(6968,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6969,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6968, 6967])).
% 1.33/1.55 tff(6970,plain,
% 1.33/1.55 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6969, 154, 6655, 6963, 6656])).
% 1.33/1.55 tff(6971,plain,
% 1.33/1.55 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6970, 6962])).
% 1.33/1.55 tff(6972,plain,
% 1.33/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6973,plain,
% 1.33/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6974,plain,
% 1.33/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6973, 6972])).
% 1.33/1.55 tff(6975,plain,
% 1.33/1.55 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6974, 60])).
% 1.33/1.55 tff(6976,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6975, 6971, 4051])).
% 1.33/1.55 tff(6977,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6978,plain,
% 1.33/1.55 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6979,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6978])).
% 1.33/1.55 tff(6980,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(transitivity,[status(thm)],[6979, 6977])).
% 1.33/1.55 tff(6981,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6982,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6981, 6980])).
% 1.33/1.55 tff(6983,plain,
% 1.33/1.55 ($false),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6982, 28, 6494, 6976, 6953])).
% 1.33/1.55 tff(6984,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.55 tff(6985,plain,
% 1.33/1.55 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6984, 6494, 6952, 6655, 6951, 6656, 6908, 6903])).
% 1.33/1.55 tff(6986,plain,
% 1.33/1.55 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6985, 6895])).
% 1.33/1.55 tff(6987,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), s(z))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[441, 6986])).
% 1.33/1.55 tff(6988,plain,
% 1.33/1.55 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6987, 6893])).
% 1.33/1.55 tff(6989,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(6990,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.33/1.55 inference(quant_inst,[status(thm)],[])).
% 1.33/1.55 tff(6991,plain,
% 1.33/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6990, 6989])).
% 1.33/1.55 tff(6992,plain,
% 1.33/1.55 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[6991, 154, 6846, 6851, 6988, 6891])).
% 1.33/1.55 tff(6993,plain,
% 1.33/1.55 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6992, 6828])).
% 1.33/1.55 tff(6994,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.33/1.55 inference(unit_resolution,[status(thm)],[496, 6993])).
% 1.33/1.55 tff(6995,plain,
% 1.33/1.55 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.33/1.55 inference(modus_ponens,[status(thm)],[6994, 6825])).
% 1.33/1.55 tff(6996,plain,
% 1.33/1.55 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[4213])).
% 1.33/1.55 tff(6997,plain,
% 1.33/1.55 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[4213])).
% 1.33/1.55 tff(6998,plain,
% 1.33/1.55 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.55 inference(symmetry,[status(thm)],[6997])).
% 1.33/1.55 tff(6999,plain,
% 1.33/1.55 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.33/1.55 inference(monotonicity,[status(thm)],[6998])).
% 1.33/1.55 tff(7000,plain,
% 1.33/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.55 inference(rewrite,[status(thm)],[])).
% 1.33/1.55 tff(7001,plain,
% 1.33/1.55 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7002,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7001])).
% 1.33/1.56 tff(7003,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[7002, 7000])).
% 1.33/1.56 tff(7004,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7005,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7004, 7003])).
% 1.33/1.56 tff(7006,plain,
% 1.33/1.56 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7005, 154, 6846, 6951])).
% 1.33/1.56 tff(7007,plain,
% 1.33/1.56 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7006, 6988, 6891])).
% 1.33/1.56 tff(7008,plain,
% 1.33/1.56 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7007, 6999])).
% 1.33/1.56 tff(7009,plain,
% 1.33/1.56 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[989, 7008])).
% 1.33/1.56 tff(7010,plain,
% 1.33/1.56 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7009, 6996])).
% 1.33/1.56 tff(7011,plain,
% 1.33/1.56 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4306, 6994, 4297, 6842])).
% 1.33/1.56 tff(7012,plain,
% 1.33/1.56 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4286, 7011, 6908])).
% 1.33/1.56 tff(7013,plain,
% 1.33/1.56 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6969, 154, 6655, 6951, 6656])).
% 1.33/1.56 tff(7014,plain,
% 1.33/1.56 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7013, 7012])).
% 1.33/1.56 tff(7015,plain,
% 1.33/1.56 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6975, 7014, 6952])).
% 1.33/1.56 tff(7016,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7017,plain,
% 1.33/1.56 (((~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(s(elem!1)))), 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(s(elem!1)))), s(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)))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7018,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7017])).
% 1.33/1.56 tff(7019,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[7018, 7016])).
% 1.33/1.56 tff(7020,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7021,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7020, 7019])).
% 1.33/1.56 tff(7022,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7021, 28, 7015, 6880, 7010, 6995])).
% 1.33/1.56 tff(7023,plain,((~r(s(elem!1), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(7024,plain,
% 1.33/1.56 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7023, 6767, 6817, 6808, 6810, 2604, 3852, 6805])).
% 1.33/1.56 tff(7025,plain,
% 1.33/1.56 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6492, 7024, 6822])).
% 1.33/1.56 tff(7026,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7027,plain,
% 1.33/1.56 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7028,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7027])).
% 1.33/1.56 tff(7029,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[7028, 7026])).
% 1.33/1.56 tff(7030,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7031,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7030, 7029])).
% 1.33/1.56 tff(7032,plain,
% 1.33/1.56 ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7031, 154])).
% 1.33/1.56 tff(7033,plain,
% 1.33/1.56 (~b(elem!1, s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7032, 7025, 6817, 6808, 6794])).
% 1.33/1.56 tff(7034,plain,
% 1.33/1.56 (r(elem!1, s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6508, 7033, 6790])).
% 1.33/1.56 tff(7035,plain,
% 1.33/1.56 (r(z, s(z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7034, 6786])).
% 1.33/1.56 tff(7036,plain,
% 1.33/1.56 (~r(s(s(s(z))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[838, 7035, 6778])).
% 1.33/1.56 tff(7037,plain,
% 1.33/1.56 (b(s(s(s(z))), s(z))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[818, 7036])).
% 1.33/1.56 tff(7038,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), s(z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7037, 6775])).
% 1.33/1.56 tff(7039,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7038, 6774])).
% 1.33/1.56 tff(7040,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.33/1.56 inference(monotonicity,[status(thm)],[6796])).
% 1.33/1.56 tff(7041,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.33/1.56 inference(symmetry,[status(thm)],[7040])).
% 1.33/1.56 tff(7042,plain,
% 1.33/1.56 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[3852, 7041])).
% 1.33/1.56 tff(7043,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7044,plain,
% 1.33/1.56 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7045,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7044])).
% 1.33/1.56 tff(7046,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.56 inference(transitivity,[status(thm)],[7045, 7043])).
% 1.33/1.56 tff(7047,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7048,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7047, 7046])).
% 1.33/1.56 tff(7049,plain,
% 1.33/1.56 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7048, 154, 6794, 6817, 7025, 7042])).
% 1.33/1.56 tff(7050,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7049, 7039])).
% 1.33/1.56 tff(7051,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(7052,plain,
% 1.33/1.56 (~b(s(z), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7051, 3852, 4132, 6225, 4197, 6224])).
% 1.33/1.56 tff(7053,plain,
% 1.33/1.56 (r(s(z), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[271, 7052])).
% 1.33/1.56 tff(7054,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.33/1.56 tff(7055,plain,
% 1.33/1.56 (b(elem!1, s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4311, 7054, 6224])).
% 1.33/1.56 tff(7056,plain,
% 1.33/1.56 (~(elem!1 = s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6237, 7055, 6225])).
% 1.33/1.56 tff(7057,plain,
% 1.33/1.56 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4028, 7056])).
% 1.33/1.56 tff(7058,plain,
% 1.33/1.56 (~(elem!1 = s(elem!1))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6392, 7056])).
% 1.33/1.56 tff(7059,plain,
% 1.33/1.56 (~(s(elem!1) = elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6399, 7058])).
% 1.33/1.56 tff(7060,plain,
% 1.33/1.56 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4018, 7057])).
% 1.33/1.56 tff(7061,plain,
% 1.33/1.56 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6244, 7060, 6225])).
% 1.33/1.56 tff(7062,plain,
% 1.33/1.56 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[4361])).
% 1.33/1.56 tff(7063,plain,
% 1.33/1.56 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.33/1.56 inference(symmetry,[status(thm)],[7062])).
% 1.33/1.56 tff(7064,plain,
% 1.33/1.56 (r(elem!1, s(s(s(elem!1))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[4132, 7063])).
% 1.33/1.56 tff(7065,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7054, 7064])).
% 1.33/1.56 tff(7066,plain,((~(elem!1 = z)) | r(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(7067,plain,
% 1.33/1.56 (~(elem!1 = z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7066, 7054, 4132])).
% 1.33/1.56 tff(7068,plain,
% 1.33/1.56 (~(z = elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[4359, 7067])).
% 1.33/1.56 tff(7069,plain,
% 1.33/1.56 (~r(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6251, 28, 4132, 6279])).
% 1.33/1.56 tff(7070,plain,
% 1.33/1.56 (b(z, s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6259, 60, 6256, 7069])).
% 1.33/1.56 tff(7071,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.33/1.56 tff(7072,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7073,plain,
% 1.33/1.56 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7074,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7073])).
% 1.33/1.56 tff(7075,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.56 inference(transitivity,[status(thm)],[7074, 7072])).
% 1.33/1.56 tff(7076,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7077,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7076, 7075])).
% 1.33/1.56 tff(7078,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7077, 28, 6441, 7071, 4132])).
% 1.33/1.56 tff(7079,plain,((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(7080,plain,
% 1.33/1.56 (~r(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7079, 7071, 4132])).
% 1.33/1.56 tff(7081,plain,
% 1.33/1.56 (b(z, elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6668, 7080, 4231])).
% 1.33/1.56 tff(7082,plain,
% 1.33/1.56 (~r(s(s(elem!1)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6288, 6279, 4132])).
% 1.33/1.56 tff(7083,plain,
% 1.33/1.56 (b(s(s(elem!1)), z)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6293, 7082])).
% 1.33/1.56 tff(7084,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.33/1.56 tff(7085,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7086,plain,
% 1.33/1.56 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7087,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7086])).
% 1.33/1.56 tff(7088,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.56 inference(transitivity,[status(thm)],[7087, 7085])).
% 1.33/1.56 tff(7089,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7090,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7089, 7088])).
% 1.33/1.56 tff(7091,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7090, 28, 7084, 7071, 6279])).
% 1.33/1.56 tff(7092,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(7093,plain,
% 1.33/1.56 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7092, 7071, 6279])).
% 1.33/1.56 tff(7094,plain,
% 1.33/1.56 (b(s(s(elem!1)), elem!1)),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[6363, 7093, 6356])).
% 1.33/1.56 tff(7095,plain,
% 1.33/1.56 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.33/1.56 inference(commutativity,[status(thm)],[])).
% 1.33/1.56 tff(7096,plain,
% 1.33/1.56 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.33/1.56 inference(symmetry,[status(thm)],[7095])).
% 1.33/1.56 tff(7097,plain,
% 1.33/1.56 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7096])).
% 1.33/1.56 tff(7098,plain,
% 1.33/1.56 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[6335, 7097])).
% 1.33/1.56 tff(7099,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7100,plain,
% 1.33/1.56 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7101,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 1.33/1.56 inference(monotonicity,[status(thm)],[7100])).
% 1.33/1.56 tff(7102,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.56 inference(transitivity,[status(thm)],[7101, 7099])).
% 1.33/1.56 tff(7103,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7104,plain,
% 1.33/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7103, 7102])).
% 1.33/1.56 tff(7105,plain,
% 1.33/1.56 ($false),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7104, 154, 3852, 6656, 6671, 6866, 5699])).
% 1.33/1.56 tff(7106,plain,((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.56 tff(7107,plain,
% 1.33/1.56 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7106, 7081, 7094, 3852, 7070])).
% 1.33/1.56 tff(7108,plain,
% 1.33/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7109,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.33/1.56 inference(quant_inst,[status(thm)],[])).
% 1.33/1.56 tff(7110,plain,
% 1.33/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.56 inference(modus_ponens,[status(thm)],[7109, 7108])).
% 1.33/1.56 tff(7111,plain,
% 1.33/1.56 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7110, 60, 7107])).
% 1.33/1.56 tff(7112,plain,
% 1.33/1.56 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.56 inference(unit_resolution,[status(thm)],[7111, 7098])).
% 1.33/1.56 tff(7113,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.33/1.56 tff(7114,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7115,plain,
% 1.33/1.56 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.33/1.56 inference(rewrite,[status(thm)],[])).
% 1.33/1.56 tff(7116,plain,
% 1.33/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7115])).
% 1.33/1.57 tff(7117,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7116, 7114])).
% 1.33/1.57 tff(7118,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7119,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7118, 7117])).
% 1.33/1.57 tff(7120,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7119, 28, 6479, 7071, 7113])).
% 1.33/1.57 tff(7121,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7122,plain,
% 1.33/1.57 (~r(elem!1, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7121, 7112, 7071])).
% 1.33/1.57 tff(7123,plain,
% 1.33/1.57 (b(elem!1, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6644, 7122, 4026])).
% 1.33/1.57 tff(7124,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7125,plain,
% 1.33/1.57 (((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7126,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7125])).
% 1.33/1.57 tff(7127,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7126, 7124])).
% 1.33/1.57 tff(7128,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7129,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7128, 7127])).
% 1.33/1.57 tff(7130,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7129, 154, 7123, 7094, 7083, 7081, 7070])).
% 1.33/1.57 tff(7131,plain,((~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (z = elem!1) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7132,plain,
% 1.33/1.57 (~r(s(s(s(elem!1))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7131, 7056, 3852, 7068, 4132, 7061])).
% 1.33/1.57 tff(7133,plain,
% 1.33/1.57 (b(s(s(s(elem!1))), elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6553, 7132, 6230])).
% 1.33/1.57 tff(7134,plain,
% 1.33/1.57 (~r(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6288, 7061, 4132])).
% 1.33/1.57 tff(7135,plain,
% 1.33/1.57 (b(s(s(elem!1)), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6293, 7134])).
% 1.33/1.57 tff(7136,plain,
% 1.33/1.57 (~r(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6251, 28, 4132, 7061])).
% 1.33/1.57 tff(7137,plain,
% 1.33/1.57 (b(z, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6259, 60, 6256, 7136])).
% 1.33/1.57 tff(7138,plain,
% 1.33/1.57 (~(s(elem!1) = s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6484, 7058])).
% 1.33/1.57 tff(7139,plain,
% 1.33/1.57 (~(s(s(elem!1)) = elem!1)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6355, 7056])).
% 1.33/1.57 tff(7140,assumption,(z = s(elem!1)), introduced(assumption)).
% 1.33/1.57 tff(7141,plain,
% 1.33/1.57 (s(elem!1) = z),
% 1.33/1.57 inference(symmetry,[status(thm)],[7140])).
% 1.33/1.57 tff(7142,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[489, 7141])).
% 1.33/1.57 tff(7143,plain,(~(z = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7144,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.33/1.57 tff(7145,plain,
% 1.33/1.57 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7144])).
% 1.33/1.57 tff(7146,plain,
% 1.33/1.57 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.33/1.57 inference(symmetry,[status(thm)],[7145])).
% 1.33/1.57 tff(7147,plain,
% 1.33/1.57 (s(elem!1) = s(s(elem!1))),
% 1.33/1.57 inference(symmetry,[status(thm)],[7144])).
% 1.33/1.57 tff(7148,plain,
% 1.33/1.57 (s(elem!1) = s(s(s(elem!1)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7147, 7146])).
% 1.33/1.57 tff(7149,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[4016, 7148])).
% 1.33/1.57 tff(7150,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7151,plain,
% 1.33/1.57 (~(s(s(elem!1)) = s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7150, 6334])).
% 1.33/1.57 tff(7152,plain,
% 1.33/1.57 (~(s(z) = s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[4233, 6664])).
% 1.33/1.57 tff(7153,plain,
% 1.33/1.57 (~(s(elem!1) = s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6484, 6393])).
% 1.33/1.57 tff(7154,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7155,plain,
% 1.33/1.57 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7156,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7155])).
% 1.33/1.57 tff(7157,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7156, 7154])).
% 1.33/1.57 tff(7158,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7159,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7158, 7157])).
% 1.33/1.57 tff(7160,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7159, 154, 3852, 6671, 6867, 6231, 6670])).
% 1.33/1.57 tff(7161,plain,((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7162,plain,
% 1.33/1.57 (~b(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7161, 6671, 3852, 6867, 6231])).
% 1.33/1.57 tff(7163,plain,
% 1.33/1.57 (r(elem!1, z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6662, 7162, 4357])).
% 1.33/1.57 tff(7164,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7165,plain,
% 1.33/1.57 (((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7166,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7165])).
% 1.33/1.57 tff(7167,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7166, 7164])).
% 1.33/1.57 tff(7168,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7169,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7168, 7167])).
% 1.33/1.57 tff(7170,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7169, 154, 6655, 3852, 6671, 6867, 5699])).
% 1.33/1.57 tff(7171,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7172,plain,
% 1.33/1.57 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7171, 6671, 3852, 6867, 7070])).
% 1.33/1.57 tff(7173,plain,
% 1.33/1.57 (r(elem!1, s(s(elem!1)))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[6644, 7172, 4026])).
% 1.33/1.57 tff(7174,plain,
% 1.33/1.57 (~(s(s(elem!1)) = s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7150, 4016])).
% 1.33/1.57 tff(7175,plain,
% 1.33/1.57 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.33/1.57 inference(commutativity,[status(thm)],[])).
% 1.33/1.57 tff(7176,plain,
% 1.33/1.57 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.33/1.57 inference(symmetry,[status(thm)],[7175])).
% 1.33/1.57 tff(7177,plain,
% 1.33/1.57 ((~(s(z) = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7176])).
% 1.33/1.57 tff(7178,plain,
% 1.33/1.57 (~(s(elem!1) = s(z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[4223, 7177])).
% 1.33/1.57 tff(7179,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.33/1.57 tff(7180,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7181,plain,
% 1.33/1.57 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7182,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7181])).
% 1.33/1.57 tff(7183,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7182, 7180])).
% 1.33/1.57 tff(7184,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7185,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7184, 7183])).
% 1.33/1.57 tff(7186,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7185, 28, 5848, 7084, 7179])).
% 1.33/1.57 tff(7187,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7188,plain,
% 1.33/1.57 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7187, 5848, 7084])).
% 1.33/1.57 tff(7189,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.33/1.57 tff(7190,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.33/1.57 tff(7191,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.33/1.57 tff(7192,plain,
% 1.33/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7193,plain,
% 1.33/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7194,plain,
% 1.33/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7193, 7192])).
% 1.33/1.57 tff(7195,plain,
% 1.33/1.57 ($false),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7194, 60, 7191, 7190, 7189])).
% 1.33/1.57 tff(7196,plain,(b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.57 tff(7197,plain,
% 1.33/1.57 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7196, 7188, 7174])).
% 1.33/1.57 tff(7198,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7199,plain,
% 1.33/1.57 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7200,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7199])).
% 1.33/1.57 tff(7201,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7200, 7198])).
% 1.33/1.57 tff(7202,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7203,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7202, 7201])).
% 1.33/1.57 tff(7204,plain,
% 1.33/1.57 (~b(s(elem!1), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7203, 154, 6605, 7197, 5702, 5699])).
% 1.33/1.57 tff(7205,plain,
% 1.33/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7206,plain,
% 1.33/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7207,plain,
% 1.33/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7206, 7205])).
% 1.33/1.57 tff(7208,plain,
% 1.33/1.57 (b(s(elem!1), z) | r(s(elem!1), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7207, 60, 489])).
% 1.33/1.57 tff(7209,plain,
% 1.33/1.57 (r(s(elem!1), z)),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7208, 7204])).
% 1.33/1.57 tff(7210,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7211,plain,
% 1.33/1.57 (((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7212,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z))))),
% 1.33/1.57 inference(monotonicity,[status(thm)],[7211])).
% 1.33/1.57 tff(7213,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.33/1.57 inference(transitivity,[status(thm)],[7212, 7210])).
% 1.33/1.57 tff(7214,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7215,plain,
% 1.33/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7214, 7213])).
% 1.33/1.57 tff(7216,plain,
% 1.33/1.57 (~r(s(elem!1), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7215, 28, 7209, 13])).
% 1.33/1.57 tff(7217,plain,
% 1.33/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.33/1.57 inference(rewrite,[status(thm)],[])).
% 1.33/1.57 tff(7218,plain,
% 1.33/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.33/1.57 inference(quant_inst,[status(thm)],[])).
% 1.33/1.57 tff(7219,plain,
% 1.33/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.33/1.57 inference(modus_ponens,[status(thm)],[7218, 7217])).
% 1.33/1.57 tff(7220,plain,
% 1.33/1.57 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7219, 60, 7216])).
% 1.33/1.57 tff(7221,plain,
% 1.33/1.57 (b(s(elem!1), s(z))),
% 1.33/1.57 inference(unit_resolution,[status(thm)],[7220, 7178])).
% 1.33/1.57 tff(7222,plain,
% 1.33/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7223,plain,
% 1.33/1.58 (((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7224,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7223])).
% 1.33/1.58 tff(7225,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7224, 7222])).
% 1.33/1.58 tff(7226,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7227,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7226, 7225])).
% 1.33/1.58 tff(7228,plain,
% 1.33/1.58 (~r(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7227, 28, 7209, 13])).
% 1.33/1.58 tff(7229,plain,
% 1.33/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7230,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7231,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7230, 7229])).
% 1.33/1.58 tff(7232,plain,
% 1.33/1.58 (b(s(z), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7231, 60, 4223, 7228])).
% 1.33/1.58 tff(7233,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7234,plain,
% 1.33/1.58 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7235,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7234])).
% 1.33/1.58 tff(7236,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7235, 7233])).
% 1.33/1.58 tff(7237,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7238,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7237, 7236])).
% 1.33/1.58 tff(7239,plain,
% 1.33/1.58 ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7238, 154, 6605, 7197, 7232])).
% 1.33/1.58 tff(7240,plain,
% 1.33/1.58 (~b(s(z), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7239, 7221])).
% 1.33/1.58 tff(7241,plain,
% 1.33/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7242,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7243,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7242, 7241])).
% 1.33/1.58 tff(7244,plain,
% 1.33/1.58 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7243, 60])).
% 1.33/1.58 tff(7245,plain,
% 1.33/1.58 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7244, 3903])).
% 1.33/1.58 tff(7246,plain,
% 1.33/1.58 (r(s(z), s(s(elem!1)))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7245, 7240])).
% 1.33/1.58 tff(7247,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7248,plain,
% 1.33/1.58 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7249,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7248])).
% 1.33/1.58 tff(7250,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7249, 7247])).
% 1.33/1.58 tff(7251,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7252,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7251, 7250])).
% 1.33/1.58 tff(7253,plain,
% 1.33/1.58 (~r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7252, 28, 6479, 7246])).
% 1.33/1.58 tff(7254,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7255,plain,
% 1.33/1.58 (((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7256,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7255])).
% 1.33/1.58 tff(7257,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7256, 7254])).
% 1.33/1.58 tff(7258,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7259,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7258, 7257])).
% 1.33/1.58 tff(7260,plain,
% 1.33/1.58 (~b(z, s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7259, 154, 6605, 7197, 5702, 5699])).
% 1.33/1.58 tff(7261,plain,
% 1.33/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7262,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7263,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7262, 7261])).
% 1.33/1.58 tff(7264,plain,
% 1.33/1.58 (r(z, s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7263, 60, 7260, 7143])).
% 1.33/1.58 tff(7265,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.33/1.58 tff(7266,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7267,plain,
% 1.33/1.58 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7268,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7267])).
% 1.33/1.58 tff(7269,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7268, 7266])).
% 1.33/1.58 tff(7270,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7271,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(s(s(elem!1)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7270, 7269])).
% 1.33/1.58 tff(7272,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7271, 28, 5848, 4132, 6420, 7265])).
% 1.33/1.58 tff(7273,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(7274,plain,
% 1.33/1.58 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7273, 7264, 5848, 4132])).
% 1.33/1.58 tff(7275,plain,
% 1.33/1.58 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6429, 7274, 4016])).
% 1.33/1.58 tff(7276,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7277,plain,
% 1.33/1.58 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7278,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7277])).
% 1.33/1.58 tff(7279,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7278, 7276])).
% 1.33/1.58 tff(7280,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7281,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7280, 7279])).
% 1.33/1.58 tff(7282,plain,
% 1.33/1.58 (~b(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7281, 154, 6511, 6231, 7275, 7232])).
% 1.33/1.58 tff(7283,plain,
% 1.33/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7284,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7285,plain,
% 1.33/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7284, 7283])).
% 1.33/1.58 tff(7286,plain,
% 1.33/1.58 ((s(z) = elem!1) | r(s(z), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7285, 60, 7282])).
% 1.33/1.58 tff(7287,plain,
% 1.33/1.58 (s(z) = elem!1),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7286, 7253])).
% 1.33/1.58 tff(7288,plain,
% 1.33/1.58 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7287])).
% 1.33/1.58 tff(7289,plain,
% 1.33/1.58 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.33/1.58 inference(symmetry,[status(thm)],[7288])).
% 1.33/1.58 tff(7290,plain,
% 1.33/1.58 (r(s(elem!1), s(z))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[5848, 7289])).
% 1.33/1.58 tff(7291,plain,
% 1.33/1.58 ($false),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7216, 7290])).
% 1.33/1.58 tff(7292,plain,((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.58 tff(7293,plain,
% 1.33/1.58 (~r(s(elem!1), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7292, 6605, 6479, 6511, 6231, 4223, 4016, 4132, 13, 7083, 7070, 7084])).
% 1.33/1.58 tff(7294,plain,
% 1.33/1.58 (b(s(elem!1), elem!1)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6458, 7293, 6440])).
% 1.33/1.58 tff(7295,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7296,plain,
% 1.33/1.58 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7297,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7296])).
% 1.33/1.58 tff(7298,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7297, 7295])).
% 1.33/1.58 tff(7299,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7300,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7299, 7298])).
% 1.33/1.58 tff(7301,plain,
% 1.33/1.58 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7300, 154, 6511, 7294, 6867, 6231])).
% 1.33/1.58 tff(7302,plain,
% 1.33/1.58 (r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[6429, 7301, 4016])).
% 1.33/1.58 tff(7303,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7304,plain,
% 1.33/1.58 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7305,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7304])).
% 1.33/1.58 tff(7306,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7305, 7303])).
% 1.33/1.58 tff(7307,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7308,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7307, 7306])).
% 1.33/1.58 tff(7309,plain,
% 1.33/1.58 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7308, 28, 7302, 6279])).
% 1.33/1.58 tff(7310,plain,
% 1.33/1.58 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7196, 7309, 7174])).
% 1.33/1.58 tff(7311,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7312,plain,
% 1.33/1.58 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.58 inference(rewrite,[status(thm)],[])).
% 1.33/1.58 tff(7313,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))))),
% 1.33/1.58 inference(monotonicity,[status(thm)],[7312])).
% 1.33/1.58 tff(7314,plain,
% 1.33/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))))),
% 1.33/1.58 inference(transitivity,[status(thm)],[7313, 7311])).
% 1.33/1.58 tff(7315,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), z)))),
% 1.33/1.58 inference(quant_inst,[status(thm)],[])).
% 1.33/1.58 tff(7316,plain,
% 1.33/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1)))))),
% 1.33/1.58 inference(modus_ponens,[status(thm)],[7315, 7314])).
% 1.33/1.58 tff(7317,plain,
% 1.33/1.58 (~r(s(elem!1), z)),
% 1.33/1.58 inference(unit_resolution,[status(thm)],[7316, 28, 4132, 7302])).
% 1.33/1.58 tff(7318,plain,
% 1.33/1.58 (b(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7208, 7317])).
% 1.33/1.59 tff(7319,plain,
% 1.33/1.59 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7203, 154, 6605, 7083, 7070])).
% 1.33/1.59 tff(7320,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7319, 7318, 7310])).
% 1.33/1.59 tff(7321,plain,((~b(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7322,plain,
% 1.33/1.59 (~b(s(elem!1), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7321, 6511, 6279, 4016, 4132, 6867, 6231, 6440, 6479, 4223, 13, 7084])).
% 1.33/1.59 tff(7323,plain,
% 1.33/1.59 (r(s(elem!1), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6492, 7322, 6386])).
% 1.33/1.59 tff(7324,plain,
% 1.33/1.59 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6863, 7323, 6279])).
% 1.33/1.59 tff(7325,plain,
% 1.33/1.59 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6429, 7324, 4016])).
% 1.33/1.59 tff(7326,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7327,plain,
% 1.33/1.59 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7328,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7327])).
% 1.33/1.59 tff(7329,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7328, 7326])).
% 1.33/1.59 tff(7330,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7331,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7330, 7329])).
% 1.33/1.59 tff(7332,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7331, 28, 5848, 7084, 6494])).
% 1.33/1.59 tff(7333,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7334,plain,
% 1.33/1.59 (~r(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7333, 7323, 7084])).
% 1.33/1.59 tff(7335,plain,
% 1.33/1.59 (b(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6458, 7334, 6440])).
% 1.33/1.59 tff(7336,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7300, 154, 6511, 7335, 6867, 6231, 7325])).
% 1.33/1.59 tff(7337,plain,((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | (s(elem!1) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (s(z) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7338,plain,
% 1.33/1.59 (~b(elem!1, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7337, 7173, 6231, 6334, 6400, 6279, 7084, 7153, 4132, 6867, 7152, 13])).
% 1.33/1.59 tff(7339,plain,
% 1.33/1.59 (r(elem!1, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6508, 7338, 6393])).
% 1.33/1.59 tff(7340,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7341,plain,
% 1.33/1.59 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7342,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7341])).
% 1.33/1.59 tff(7343,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7342, 7340])).
% 1.33/1.59 tff(7344,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7345,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7344, 7343])).
% 1.33/1.59 tff(7346,plain,
% 1.33/1.59 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7345, 28])).
% 1.33/1.59 tff(7347,plain,
% 1.33/1.59 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7346, 7339, 7084])).
% 1.33/1.59 tff(7348,plain,
% 1.33/1.59 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7196, 7347, 7151])).
% 1.33/1.59 tff(7349,plain,
% 1.33/1.59 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6503, 7339, 7173])).
% 1.33/1.59 tff(7350,plain,
% 1.33/1.59 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6492, 7349, 7153])).
% 1.33/1.59 tff(7351,plain,
% 1.33/1.59 (~b(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7203, 154, 7350, 7348, 7083, 7070])).
% 1.33/1.59 tff(7352,plain,
% 1.33/1.59 (r(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7208, 7351])).
% 1.33/1.59 tff(7353,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7354,plain,
% 1.33/1.59 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7355,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7354])).
% 1.33/1.59 tff(7356,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7355, 7353])).
% 1.33/1.59 tff(7357,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7358,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(s(elem!1), z))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7357, 7356])).
% 1.33/1.59 tff(7359,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7358, 28, 7339, 7352, 7163])).
% 1.33/1.59 tff(7360,plain,((~b(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7361,plain,
% 1.33/1.59 (~b(z, elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7360, 7084, 6231, 6279, 4132, 6867, 13, 4026, 3852, 4357])).
% 1.33/1.59 tff(7362,plain,
% 1.33/1.59 (r(z, elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6668, 7361, 6664])).
% 1.33/1.59 tff(7363,plain,
% 1.33/1.59 (~(s(elem!1) = elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6399, 6397])).
% 1.33/1.59 tff(7364,plain,
% 1.33/1.59 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[6617, 7097])).
% 1.33/1.59 tff(7365,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7366,plain,
% 1.33/1.59 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7367,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7366])).
% 1.33/1.59 tff(7368,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7367, 7365])).
% 1.33/1.59 tff(7369,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7370,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7369, 7368])).
% 1.33/1.59 tff(7371,plain,
% 1.33/1.59 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7370, 154, 6655, 3852, 7083, 6231])).
% 1.33/1.59 tff(7372,plain,
% 1.33/1.59 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7110, 60, 7371])).
% 1.33/1.59 tff(7373,plain,
% 1.33/1.59 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7372, 7364])).
% 1.33/1.59 tff(7374,plain,
% 1.33/1.59 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.33/1.59 inference(commutativity,[status(thm)],[])).
% 1.33/1.59 tff(7375,plain,
% 1.33/1.59 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.59 inference(symmetry,[status(thm)],[7374])).
% 1.33/1.59 tff(7376,plain,
% 1.33/1.59 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7375])).
% 1.33/1.59 tff(7377,plain,
% 1.33/1.59 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[4016, 7376])).
% 1.33/1.59 tff(7378,plain,
% 1.33/1.59 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6429, 6864, 4016])).
% 1.33/1.59 tff(7379,plain,
% 1.33/1.59 (~r(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7333, 6494, 7084])).
% 1.33/1.59 tff(7380,plain,
% 1.33/1.59 (b(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6458, 7379, 6440])).
% 1.33/1.59 tff(7381,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7382,plain,
% 1.33/1.59 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7383,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7382])).
% 1.33/1.59 tff(7384,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7383, 7381])).
% 1.33/1.59 tff(7385,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7386,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7385, 7384])).
% 1.33/1.59 tff(7387,plain,
% 1.33/1.59 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7386, 154, 7380, 6867, 6231, 7378])).
% 1.33/1.59 tff(7388,plain,
% 1.33/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7389,plain,
% 1.33/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7390,plain,
% 1.33/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7389, 7388])).
% 1.33/1.59 tff(7391,plain,
% 1.33/1.59 ((s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7390, 60, 7387])).
% 1.33/1.59 tff(7392,plain,
% 1.33/1.59 (r(s(s(s(elem!1))), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7391, 7377])).
% 1.33/1.59 tff(7393,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6886, 28, 6494, 7113, 7392])).
% 1.33/1.59 tff(7394,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7395,plain,
% 1.33/1.59 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7394, 7373, 4016, 6867, 6231, 7363, 6279, 7084])).
% 1.33/1.59 tff(7396,plain,
% 1.33/1.59 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6492, 7395, 6485])).
% 1.33/1.59 tff(7397,plain,
% 1.33/1.59 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7308, 28, 6420, 6279])).
% 1.33/1.59 tff(7398,plain,
% 1.33/1.59 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7196, 7397, 7189])).
% 1.33/1.59 tff(7399,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7400,plain,
% 1.33/1.59 (((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7401,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7400])).
% 1.33/1.59 tff(7402,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7401, 7399])).
% 1.33/1.59 tff(7403,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7404,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7403, 7402])).
% 1.33/1.59 tff(7405,plain,
% 1.33/1.59 (~r(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7404, 28, 6441, 4132, 6420])).
% 1.33/1.59 tff(7406,plain,
% 1.33/1.59 (b(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7208, 7405])).
% 1.33/1.59 tff(7407,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7319, 7406, 7398])).
% 1.33/1.59 tff(7408,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7409,plain,
% 1.33/1.59 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7408, 7396, 7174, 6441, 4132, 6279])).
% 1.33/1.59 tff(7410,plain,
% 1.33/1.59 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6429, 7409, 4016])).
% 1.33/1.59 tff(7411,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7412,plain,
% 1.33/1.59 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.59 inference(rewrite,[status(thm)],[])).
% 1.33/1.59 tff(7413,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.33/1.59 inference(monotonicity,[status(thm)],[7412])).
% 1.33/1.59 tff(7414,plain,
% 1.33/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.59 inference(transitivity,[status(thm)],[7413, 7411])).
% 1.33/1.59 tff(7415,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.33/1.59 inference(quant_inst,[status(thm)],[])).
% 1.33/1.59 tff(7416,plain,
% 1.33/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.33/1.59 inference(modus_ponens,[status(thm)],[7415, 7414])).
% 1.33/1.59 tff(7417,plain,
% 1.33/1.59 (~b(elem!1, z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7416, 154, 6655, 3852, 6867, 7070])).
% 1.33/1.59 tff(7418,plain,
% 1.33/1.59 (r(elem!1, z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6662, 7417, 4357])).
% 1.33/1.59 tff(7419,plain,
% 1.33/1.59 (~r(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6453, 6445, 6441])).
% 1.33/1.59 tff(7420,plain,
% 1.33/1.59 (b(s(elem!1), elem!1)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6458, 7419, 7363])).
% 1.33/1.59 tff(7421,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.33/1.59 tff(7422,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7358, 28, 6495, 6445, 7421])).
% 1.33/1.59 tff(7423,plain,((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7424,plain,
% 1.33/1.59 (~r(elem!1, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7423, 6445, 7421])).
% 1.33/1.59 tff(7425,plain,
% 1.33/1.59 (b(elem!1, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6508, 7424, 6397])).
% 1.33/1.59 tff(7426,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7300, 154, 7425, 7420, 6867, 6231, 6510])).
% 1.33/1.59 tff(7427,plain,((~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (elem!1 = s(elem!1)) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7428,plain,
% 1.33/1.59 (~r(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7427, 7410, 6231, 6867, 6397, 7418, 6441])).
% 1.33/1.59 tff(7429,plain,
% 1.33/1.59 (b(s(elem!1), z)),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7208, 7428])).
% 1.33/1.59 tff(7430,plain,
% 1.33/1.59 (~b(elem!1, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6519, 7429, 6231, 7410, 3852])).
% 1.33/1.59 tff(7431,plain,
% 1.33/1.59 (r(elem!1, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6508, 7430, 6397])).
% 1.33/1.59 tff(7432,plain,
% 1.33/1.59 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7203, 154, 7396, 7083, 7070])).
% 1.33/1.59 tff(7433,plain,
% 1.33/1.59 (~b(s(s(elem!1)), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7432, 7429])).
% 1.33/1.59 tff(7434,plain,
% 1.33/1.59 (r(s(s(elem!1)), s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7196, 7433, 7174])).
% 1.33/1.59 tff(7435,plain,
% 1.33/1.59 ($false),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7346, 7434, 7431, 7084])).
% 1.33/1.59 tff(7436,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.59 tff(7437,plain,
% 1.33/1.59 (~b(elem!1, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7436, 7084, 6393, 6231, 3852, 6867, 7362, 6334, 4132, 6279, 4357])).
% 1.33/1.59 tff(7438,plain,
% 1.33/1.59 (r(elem!1, s(s(elem!1)))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[6644, 7437, 4026])).
% 1.33/1.59 tff(7439,plain,
% 1.33/1.59 (~b(elem!1, s(elem!1))),
% 1.33/1.59 inference(unit_resolution,[status(thm)],[7337, 7438, 6231, 6334, 6400, 6279, 7084, 7153, 4132, 6867, 7152, 13])).
% 1.33/1.60 tff(7440,plain,
% 1.33/1.60 (r(elem!1, s(elem!1))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[6508, 7439, 6393])).
% 1.33/1.60 tff(7441,plain,
% 1.33/1.60 (~r(s(s(elem!1)), s(elem!1))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7346, 7440, 7084])).
% 1.33/1.60 tff(7442,plain,
% 1.33/1.60 (b(s(s(elem!1)), s(elem!1))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7196, 7441, 7151])).
% 1.33/1.60 tff(7443,plain,
% 1.33/1.60 (~r(s(elem!1), s(s(elem!1)))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[6503, 7440, 7438])).
% 1.33/1.60 tff(7444,plain,
% 1.33/1.60 (b(s(elem!1), s(s(elem!1)))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[6492, 7443, 7153])).
% 1.33/1.60 tff(7445,plain,
% 1.33/1.60 (~b(z, s(elem!1))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7259, 154, 7444, 7442, 7083, 7070])).
% 1.33/1.60 tff(7446,plain,
% 1.33/1.60 (r(z, s(elem!1))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7263, 60, 7445, 7143])).
% 1.33/1.60 tff(7447,plain,
% 1.33/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(7448,plain,
% 1.33/1.60 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.33/1.60 inference(rewrite,[status(thm)],[])).
% 1.33/1.60 tff(7449,plain,
% 1.33/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))))),
% 1.33/1.60 inference(monotonicity,[status(thm)],[7448])).
% 1.33/1.60 tff(7450,plain,
% 1.33/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.33/1.60 inference(transitivity,[status(thm)],[7449, 7447])).
% 1.33/1.60 tff(7451,plain,
% 1.33/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))),
% 1.33/1.60 inference(quant_inst,[status(thm)],[])).
% 1.33/1.60 tff(7452,plain,
% 1.33/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, elem!1))),
% 1.33/1.60 inference(modus_ponens,[status(thm)],[7451, 7450])).
% 1.33/1.60 tff(7453,plain,
% 1.33/1.60 ($false),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7452, 28, 7440, 7362, 7446])).
% 1.33/1.60 tff(7454,plain,((~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.60 tff(7455,plain,
% 1.33/1.60 (~r(s(s(elem!1)), elem!1)),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7454, 7055, 7061, 4132, 7133, 13, 7056, 3852, 7067])).
% 1.33/1.60 tff(7456,plain,
% 1.33/1.60 (b(s(s(elem!1)), elem!1)),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[6363, 7455, 7139])).
% 1.33/1.60 tff(7457,plain,
% 1.33/1.60 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.33/1.60 inference(modus_ponens,[status(thm)],[6334, 7376])).
% 1.33/1.60 tff(7458,plain,
% 1.33/1.60 (b(s(elem!1), s(s(s(elem!1))))),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[6429, 6864, 6334])).
% 1.33/1.60 tff(7459,plain,
% 1.33/1.60 (~b(s(elem!1), z)),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[6519, 6511, 6231, 6510, 3852])).
% 1.33/1.60 tff(7460,plain,
% 1.33/1.60 (r(s(elem!1), z)),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7208, 7459])).
% 1.33/1.60 tff(7461,plain,
% 1.33/1.60 ($false),
% 1.33/1.60 inference(unit_resolution,[status(thm)],[7300, 154, 6511, 6868, 6867, 6231, 6510])).
% 1.43/1.60 tff(7462,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7463,plain,
% 1.43/1.60 (~b(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7462, 6511, 6867, 6231, 6510])).
% 1.43/1.60 tff(7464,plain,
% 1.43/1.60 (r(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6458, 7463, 6440])).
% 1.43/1.60 tff(7465,plain,
% 1.43/1.60 (~r(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6453, 7464, 7460])).
% 1.43/1.60 tff(7466,plain,
% 1.43/1.60 (b(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6668, 7465, 6664])).
% 1.43/1.60 tff(7467,plain,
% 1.43/1.60 (~b(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7161, 7466, 3852, 6867, 6231])).
% 1.43/1.60 tff(7468,plain,
% 1.43/1.60 (r(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6662, 7467, 4357])).
% 1.43/1.60 tff(7469,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7470,plain,
% 1.43/1.60 (((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7471,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7470])).
% 1.43/1.60 tff(7472,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7471, 7469])).
% 1.43/1.60 tff(7473,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7474,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7473, 7472])).
% 1.43/1.60 tff(7475,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7474, 28, 7421, 13, 4468])).
% 1.43/1.60 tff(7476,plain,((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7477,plain,
% 1.43/1.60 (~r(s(z), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7476, 7468, 13])).
% 1.43/1.60 tff(7478,plain,
% 1.43/1.60 (~r(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7227, 28, 7460, 13])).
% 1.43/1.60 tff(7479,plain,
% 1.43/1.60 (b(s(z), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7231, 60, 7152, 7478])).
% 1.43/1.60 tff(7480,plain,
% 1.43/1.60 (~b(s(z), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7281, 154, 6511, 6231, 6510, 7479])).
% 1.43/1.60 tff(7481,plain,
% 1.43/1.60 ((s(z) = elem!1) | r(s(z), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7285, 60, 7480])).
% 1.43/1.60 tff(7482,plain,
% 1.43/1.60 (s(z) = elem!1),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7481, 7477])).
% 1.43/1.60 tff(7483,plain,
% 1.43/1.60 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7482])).
% 1.43/1.60 tff(7484,plain,
% 1.43/1.60 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.43/1.60 inference(symmetry,[status(thm)],[7483])).
% 1.43/1.60 tff(7485,plain,
% 1.43/1.60 (r(s(elem!1), s(z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7464, 7484])).
% 1.43/1.60 tff(7486,plain,
% 1.43/1.60 (~r(s(elem!1), s(z))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7215, 28, 7460, 13])).
% 1.43/1.60 tff(7487,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7486, 7485])).
% 1.43/1.60 tff(7488,plain,((~b(elem!1, s(elem!1))) | (~r(s(z), z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7489,plain,
% 1.43/1.60 (~b(elem!1, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7488, 7458, 4357, 3852, 6867, 6231, 6400, 13])).
% 1.43/1.60 tff(7490,plain,
% 1.43/1.60 (r(elem!1, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6508, 7489, 6393])).
% 1.43/1.60 tff(7491,plain,
% 1.43/1.60 (~r(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6503, 7490, 6494])).
% 1.43/1.60 tff(7492,plain,
% 1.43/1.60 (b(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6644, 7491, 4026])).
% 1.43/1.60 tff(7493,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7494,plain,
% 1.43/1.60 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7495,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7494])).
% 1.43/1.60 tff(7496,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7495, 7493])).
% 1.43/1.60 tff(7497,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7498,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7497, 7496])).
% 1.43/1.60 tff(7499,plain,
% 1.43/1.60 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7498, 154, 7492, 6656, 6867, 6231])).
% 1.43/1.60 tff(7500,plain,
% 1.43/1.60 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7110, 60, 7499])).
% 1.43/1.60 tff(7501,plain,
% 1.43/1.60 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7500, 7098])).
% 1.43/1.60 tff(7502,plain,
% 1.43/1.60 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6886, 28, 6494, 7501])).
% 1.43/1.60 tff(7503,plain,
% 1.43/1.60 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7390, 60, 7502])).
% 1.43/1.60 tff(7504,plain,
% 1.43/1.60 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7503, 7457])).
% 1.43/1.60 tff(7505,plain,
% 1.43/1.60 (~b(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7171, 7492, 3852, 6867, 5699])).
% 1.43/1.60 tff(7506,plain,
% 1.43/1.60 (r(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6668, 7505, 6664])).
% 1.43/1.60 tff(7507,plain,
% 1.43/1.60 ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7386, 154, 6867, 6231, 7458])).
% 1.43/1.60 tff(7508,plain,
% 1.43/1.60 (~b(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7507, 7504])).
% 1.43/1.60 tff(7509,plain,
% 1.43/1.60 (r(s(elem!1), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6458, 7508, 6400])).
% 1.43/1.60 tff(7510,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7511,plain,
% 1.43/1.60 (((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7512,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, elem!1))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7511])).
% 1.43/1.60 tff(7513,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7512, 7510])).
% 1.43/1.60 tff(7514,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7515,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(z, elem!1))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7514, 7513])).
% 1.43/1.60 tff(7516,plain,
% 1.43/1.60 (~r(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7515, 28, 7509, 7506])).
% 1.43/1.60 tff(7517,plain,
% 1.43/1.60 (b(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7263, 60, 7143, 7516])).
% 1.43/1.60 tff(7518,plain,
% 1.43/1.60 (~b(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7416, 154, 7492, 3852, 6867, 5699])).
% 1.43/1.60 tff(7519,plain,
% 1.43/1.60 (r(elem!1, z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6662, 7518, 4357])).
% 1.43/1.60 tff(7520,plain,
% 1.43/1.60 (~r(s(elem!1), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7423, 7519, 7490])).
% 1.43/1.60 tff(7521,plain,
% 1.43/1.60 (b(s(elem!1), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7208, 7520])).
% 1.43/1.60 tff(7522,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7523,plain,
% 1.43/1.60 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7524,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7523])).
% 1.43/1.60 tff(7525,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7524, 7522])).
% 1.43/1.60 tff(7526,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7527,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7526, 7525])).
% 1.43/1.60 tff(7528,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7527, 154, 3852, 7458, 7521, 7517, 7504])).
% 1.43/1.60 tff(7529,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = z) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7530,plain,
% 1.43/1.60 (~r(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7529, 7133, 3852, 7055, 7067, 7137, 7456, 7056, 13, 7061])).
% 1.43/1.60 tff(7531,plain,
% 1.43/1.60 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6492, 7530, 7138])).
% 1.43/1.60 tff(7532,plain,
% 1.43/1.60 (~r(s(elem!1), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7423, 7163, 6495])).
% 1.43/1.60 tff(7533,plain,
% 1.43/1.60 (b(s(elem!1), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7208, 7532])).
% 1.43/1.60 tff(7534,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7535,plain,
% 1.43/1.60 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7536,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[7535])).
% 1.43/1.60 tff(7537,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[7536, 7534])).
% 1.43/1.60 tff(7538,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(7539,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[7538, 7537])).
% 1.43/1.60 tff(7540,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7539, 154, 6656, 6605, 6671, 7533, 5699])).
% 1.43/1.60 tff(7541,plain,((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (elem!1 = z) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7542,plain,
% 1.43/1.60 (~b(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7541, 6495, 6605, 5699, 6656, 4357, 3852, 6867, 6231])).
% 1.43/1.60 tff(7543,plain,
% 1.43/1.60 (r(z, elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[6668, 7542, 6664])).
% 1.43/1.60 tff(7544,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7452, 28, 6495, 6441, 7265])).
% 1.43/1.60 tff(7545,plain,((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(7546,plain,
% 1.43/1.60 (~r(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7545, 6495, 7543])).
% 1.43/1.60 tff(7547,plain,
% 1.43/1.60 (b(z, s(elem!1))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[7263, 60, 7143, 7546])).
% 1.43/1.60 tff(7548,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.43/1.60 tff(7549,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7550,plain,
% 1.43/1.60 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(7551,plain,
% 1.43/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7550])).
% 1.43/1.61 tff(7552,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7551, 7549])).
% 1.43/1.61 tff(7553,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7554,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7553, 7552])).
% 1.43/1.61 tff(7555,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7554, 154, 6605, 5702, 6478, 7548, 5699])).
% 1.43/1.61 tff(7556,plain,((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7557,plain,
% 1.43/1.61 (~b(s(elem!1), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7556, 7547, 5702, 6605, 5699])).
% 1.43/1.61 tff(7558,plain,
% 1.43/1.61 (r(s(elem!1), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7208, 7557])).
% 1.43/1.61 tff(7559,plain,
% 1.43/1.61 (~r(s(elem!1), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6453, 7558, 7543])).
% 1.43/1.61 tff(7560,plain,
% 1.43/1.61 (b(s(elem!1), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6458, 7559, 6440])).
% 1.43/1.61 tff(7561,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7562,plain,
% 1.43/1.61 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7563,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7562])).
% 1.43/1.61 tff(7564,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7563, 7561])).
% 1.43/1.61 tff(7565,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7566,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7565, 7564])).
% 1.43/1.61 tff(7567,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7566, 154, 7560, 6656, 6605, 7547, 5699])).
% 1.43/1.61 tff(7568,plain,((~r(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7569,plain,
% 1.43/1.61 (~r(elem!1, s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7568, 7456, 7531, 7137, 7059, 7135, 7067, 3852, 7133, 7055])).
% 1.43/1.61 tff(7570,plain,
% 1.43/1.61 (b(elem!1, s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6508, 7569, 7058])).
% 1.43/1.61 tff(7571,plain,
% 1.43/1.61 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7488, 7570, 7067, 3852, 7133, 7055, 7059, 13])).
% 1.43/1.61 tff(7572,plain,
% 1.43/1.61 (r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6429, 7571, 7057])).
% 1.43/1.61 tff(7573,plain,
% 1.43/1.61 (~r(s(elem!1), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7316, 28, 4132, 7572])).
% 1.43/1.61 tff(7574,plain,
% 1.43/1.61 (~(s(s(elem!1)) = s(elem!1))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7150, 7057])).
% 1.43/1.61 tff(7575,plain,
% 1.43/1.61 (~r(z, elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7408, 7572, 7574, 7531, 4132, 7061])).
% 1.43/1.61 tff(7576,plain,
% 1.43/1.61 (b(z, elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6668, 7575, 7068])).
% 1.43/1.61 tff(7577,plain,
% 1.43/1.61 (~b(s(elem!1), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7539, 154, 7456, 7531, 7576, 7137])).
% 1.43/1.61 tff(7578,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7208, 7577, 7573])).
% 1.43/1.61 tff(7579,plain,(r(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7580,plain,
% 1.43/1.61 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7579, 3852, 4132, 7053, 6225, 6224])).
% 1.43/1.61 tff(7581,plain,
% 1.43/1.61 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4037, 4030])).
% 1.43/1.61 tff(7582,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7581])).
% 1.43/1.61 tff(7583,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.61 inference(symmetry,[status(thm)],[7582])).
% 1.43/1.61 tff(7584,plain,
% 1.43/1.61 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.43/1.61 inference(symmetry,[status(thm)],[7581])).
% 1.43/1.61 tff(7585,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7584])).
% 1.43/1.61 tff(7586,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[7585])).
% 1.43/1.61 tff(7587,plain,
% 1.43/1.61 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7586])).
% 1.43/1.61 tff(7588,plain,
% 1.43/1.61 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.43/1.61 inference(commutativity,[status(thm)],[])).
% 1.43/1.61 tff(7589,plain,
% 1.43/1.61 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[7588])).
% 1.43/1.61 tff(7590,plain,
% 1.43/1.61 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7584])).
% 1.43/1.61 tff(7591,plain,
% 1.43/1.61 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7590])).
% 1.43/1.61 tff(7592,plain,
% 1.43/1.61 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7591, 7589])).
% 1.43/1.61 tff(7593,plain,
% 1.43/1.61 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7592])).
% 1.43/1.61 tff(7594,plain,
% 1.43/1.61 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[5882, 7593])).
% 1.43/1.61 tff(7595,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4202, 7594, 4197])).
% 1.43/1.61 tff(7596,plain,
% 1.43/1.61 (~r(z, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6268, 7595, 4132])).
% 1.43/1.61 tff(7597,plain,
% 1.43/1.61 (b(z, s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[648, 7596])).
% 1.43/1.61 tff(7598,plain,
% 1.43/1.61 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[4030])).
% 1.43/1.61 tff(7599,plain,
% 1.43/1.61 ((~r(z, elem!1)) <=> (~r(z, s(s(elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7598])).
% 1.43/1.61 tff(7600,plain,
% 1.43/1.61 (~r(z, s(s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[6635, 7599])).
% 1.43/1.61 tff(7601,plain,
% 1.43/1.61 (b(z, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6259, 60, 6256, 7600])).
% 1.43/1.61 tff(7602,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7584])).
% 1.43/1.61 tff(7603,plain,
% 1.43/1.61 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[4030])).
% 1.43/1.61 tff(7604,plain,
% 1.43/1.61 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[4297, 7603])).
% 1.43/1.61 tff(7605,plain,
% 1.43/1.61 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6311, 7595, 7604])).
% 1.43/1.61 tff(7606,plain,
% 1.43/1.61 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4123, 7605, 4030])).
% 1.43/1.61 tff(7607,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[496, 7606])).
% 1.43/1.61 tff(7608,plain,
% 1.43/1.61 (b(s(s(elem!1)), s(s(s(z))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7607, 7602])).
% 1.43/1.61 tff(7609,plain,
% 1.43/1.61 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[4030])).
% 1.43/1.61 tff(7610,plain,
% 1.43/1.61 ((~r(elem!1, z)) <=> (~r(s(s(elem!1)), z))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7609])).
% 1.43/1.61 tff(7611,plain,
% 1.43/1.61 (~r(s(s(elem!1)), z)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[6625, 7610])).
% 1.43/1.61 tff(7612,plain,
% 1.43/1.61 (b(s(s(elem!1)), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6293, 7611])).
% 1.43/1.61 tff(7613,plain,
% 1.43/1.61 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[5710, 7612, 7608, 7601, 7597])).
% 1.43/1.61 tff(7614,plain,
% 1.43/1.61 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7613, 7587])).
% 1.43/1.61 tff(7615,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[989, 7614])).
% 1.43/1.61 tff(7616,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7615, 7583])).
% 1.43/1.61 tff(7617,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7618,plain,
% 1.43/1.61 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7619,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7618])).
% 1.43/1.61 tff(7620,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7619, 7617])).
% 1.43/1.61 tff(7621,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7622,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7621, 7620])).
% 1.43/1.61 tff(7623,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7622, 28, 7604, 7595, 7616])).
% 1.43/1.61 tff(7624,plain,((~(elem!1 = s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7625,plain,
% 1.43/1.61 (~(elem!1 = s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7624, 7580, 4197, 4132])).
% 1.43/1.61 tff(7626,plain,
% 1.43/1.61 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4028, 7625])).
% 1.43/1.61 tff(7627,plain,
% 1.43/1.61 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6703, 7626, 6225, 7580, 4132])).
% 1.43/1.61 tff(7628,plain,
% 1.43/1.61 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4202, 7627, 4197])).
% 1.43/1.61 tff(7629,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7628])).
% 1.43/1.61 tff(7630,plain,
% 1.43/1.61 (b(elem!1, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6653, 7625, 6225, 7580])).
% 1.43/1.61 tff(7631,plain,
% 1.43/1.61 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4018, 7626])).
% 1.43/1.61 tff(7632,plain,
% 1.43/1.61 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6244, 7631, 6225])).
% 1.43/1.61 tff(7633,plain,
% 1.43/1.61 (~(s(s(elem!1)) = elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6355, 7625])).
% 1.43/1.61 tff(7634,plain,
% 1.43/1.61 (~r(s(s(elem!1)), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6701, 28, 7580, 7632])).
% 1.43/1.61 tff(7635,plain,
% 1.43/1.61 (b(s(s(elem!1)), elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6363, 7634, 7633])).
% 1.43/1.61 tff(7636,plain,
% 1.43/1.61 ((~(z = elem!1)) <=> (~(elem!1 = z))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[4355])).
% 1.43/1.61 tff(7637,plain,
% 1.43/1.61 (~(elem!1 = z)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[4231, 7636])).
% 1.43/1.61 tff(7638,plain,
% 1.43/1.61 ((elem!1 = z) | b(elem!1, z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6660, 60, 6625])).
% 1.43/1.61 tff(7639,plain,
% 1.43/1.61 (b(elem!1, z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7638, 7637])).
% 1.43/1.61 tff(7640,plain,
% 1.43/1.61 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.43/1.61 inference(symmetry,[status(thm)],[6811])).
% 1.43/1.61 tff(7641,plain,
% 1.43/1.61 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7640])).
% 1.43/1.61 tff(7642,plain,
% 1.43/1.61 (~(z = s(s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[366, 7641])).
% 1.43/1.61 tff(7643,plain,
% 1.43/1.61 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6259, 60, 7069])).
% 1.43/1.61 tff(7644,plain,
% 1.43/1.61 (b(z, s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7643, 7642])).
% 1.43/1.61 tff(7645,plain,
% 1.43/1.61 (b(z, elem!1)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6668, 6635, 4231])).
% 1.43/1.61 tff(7646,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7647,plain,
% 1.43/1.61 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7648,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7647])).
% 1.43/1.61 tff(7649,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7648, 7646])).
% 1.43/1.61 tff(7650,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7651,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7650, 7649])).
% 1.43/1.61 tff(7652,plain,
% 1.43/1.61 ((~b(z, s(s(elem!1)))) | (~b(elem!1, z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7651, 154, 6655, 6656, 7645])).
% 1.43/1.61 tff(7653,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7652, 7644, 7639])).
% 1.43/1.61 tff(7654,plain,((~r(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (z = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7655,plain,
% 1.43/1.61 (z = elem!1),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7654, 7635, 4132, 7580, 7632, 7630])).
% 1.43/1.61 tff(7656,plain,
% 1.43/1.61 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4064, 7626])).
% 1.43/1.61 tff(7657,plain,
% 1.43/1.61 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4053, 4051])).
% 1.43/1.61 tff(7658,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7659,plain,
% 1.43/1.61 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7660,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7659])).
% 1.43/1.61 tff(7661,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7660, 7658])).
% 1.43/1.61 tff(7662,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7663,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7662, 7661])).
% 1.43/1.61 tff(7664,plain,
% 1.43/1.61 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7663, 28, 6279, 6914])).
% 1.43/1.61 tff(7665,plain,
% 1.43/1.61 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7666,plain,
% 1.43/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7667,plain,
% 1.43/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7666, 7665])).
% 1.43/1.61 tff(7668,plain,
% 1.43/1.61 ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7667, 60])).
% 1.43/1.61 tff(7669,plain,
% 1.43/1.61 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7668, 7664, 7657])).
% 1.43/1.61 tff(7670,plain,
% 1.43/1.61 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[4288])).
% 1.43/1.61 tff(7671,plain,
% 1.43/1.61 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7670, 4255])).
% 1.43/1.61 tff(7672,plain,
% 1.43/1.61 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7671])).
% 1.43/1.61 tff(7673,plain,
% 1.43/1.61 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[388, 7672])).
% 1.43/1.61 tff(7674,plain,
% 1.43/1.61 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4306, 780, 4297, 4288])).
% 1.43/1.61 tff(7675,plain,
% 1.43/1.61 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4286, 7674, 7673])).
% 1.43/1.61 tff(7676,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7677,plain,
% 1.43/1.61 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7678,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7677])).
% 1.43/1.61 tff(7679,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7678, 7676])).
% 1.43/1.61 tff(7680,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7681,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7680, 7679])).
% 1.43/1.61 tff(7682,plain,
% 1.43/1.61 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7681, 28, 6279, 6914])).
% 1.43/1.61 tff(7683,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[6975, 7682, 4051])).
% 1.43/1.61 tff(7684,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7685,plain,
% 1.43/1.61 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(7686,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7685])).
% 1.43/1.61 tff(7687,plain,
% 1.43/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[7686, 7684])).
% 1.43/1.61 tff(7688,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(7689,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7688, 7687])).
% 1.43/1.61 tff(7690,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7689, 154, 6655, 6656, 7683, 7675, 7669])).
% 1.43/1.61 tff(7691,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7692,plain,
% 1.43/1.61 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7691, 7630, 7635, 7656, 7632, 7628, 7580, 7655])).
% 1.43/1.61 tff(7693,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[496, 7692])).
% 1.43/1.61 tff(7694,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[7693, 7629])).
% 1.43/1.61 tff(7695,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7628])).
% 1.43/1.61 tff(7696,plain,
% 1.43/1.61 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7628])).
% 1.43/1.61 tff(7697,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[7696])).
% 1.43/1.61 tff(7698,plain,
% 1.43/1.61 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[7697])).
% 1.43/1.61 tff(7699,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.43/1.61 tff(7700,plain,
% 1.43/1.61 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.43/1.61 inference(symmetry,[status(thm)],[7699])).
% 1.43/1.61 tff(7701,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[4009, 7700])).
% 1.43/1.61 tff(7702,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(7703,plain,
% 1.43/1.61 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[7702, 7631])).
% 1.43/1.61 tff(7704,plain,
% 1.43/1.61 (elem!1 = z),
% 1.43/1.61 inference(symmetry,[status(thm)],[7655])).
% 1.43/1.61 tff(7705,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7704])).
% 1.43/1.62 tff(7706,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.43/1.62 inference(symmetry,[status(thm)],[7705])).
% 1.43/1.62 tff(7707,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[3852, 7706])).
% 1.43/1.62 tff(7708,plain,
% 1.43/1.62 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7655])).
% 1.43/1.62 tff(7709,plain,
% 1.43/1.62 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7708])).
% 1.43/1.62 tff(7710,plain,
% 1.43/1.62 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[388, 7709])).
% 1.43/1.62 tff(7711,plain,
% 1.43/1.62 (s(z) = s(elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7655])).
% 1.43/1.62 tff(7712,plain,
% 1.43/1.62 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7711])).
% 1.43/1.62 tff(7713,plain,
% 1.43/1.62 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7655])).
% 1.43/1.62 tff(7714,plain,
% 1.43/1.62 (r(s(z), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7053, 7713])).
% 1.43/1.62 tff(7715,plain,
% 1.43/1.62 (r(s(elem!1), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7714, 7712])).
% 1.43/1.62 tff(7716,plain,
% 1.43/1.62 (s(elem!1) = s(z)),
% 1.43/1.62 inference(symmetry,[status(thm)],[7711])).
% 1.43/1.62 tff(7717,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7716])).
% 1.43/1.62 tff(7718,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7717])).
% 1.43/1.62 tff(7719,plain,
% 1.43/1.62 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7628])).
% 1.43/1.62 tff(7720,plain,
% 1.43/1.62 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7628])).
% 1.43/1.62 tff(7721,plain,
% 1.43/1.62 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7720])).
% 1.43/1.62 tff(7722,plain,
% 1.43/1.62 (r(z, s(s(s(z))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[4132, 7721])).
% 1.43/1.62 tff(7723,plain,
% 1.43/1.62 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7655])).
% 1.43/1.62 tff(7724,plain,
% 1.43/1.62 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7723])).
% 1.43/1.62 tff(7725,plain,
% 1.43/1.62 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7711])).
% 1.43/1.62 tff(7726,plain,
% 1.43/1.62 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7725])).
% 1.43/1.62 tff(7727,plain,
% 1.43/1.62 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7726, 7724])).
% 1.43/1.62 tff(7728,plain,
% 1.43/1.62 (~(elem!1 = s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[6392, 7625])).
% 1.43/1.62 tff(7729,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7730,plain,
% 1.43/1.62 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7731,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7730])).
% 1.43/1.62 tff(7732,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7731, 7729])).
% 1.43/1.62 tff(7733,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7734,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7733, 7732])).
% 1.43/1.62 tff(7735,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7734, 28, 5848, 4297, 6420])).
% 1.43/1.62 tff(7736,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(7737,plain,
% 1.43/1.62 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7736, 7715, 7580])).
% 1.43/1.62 tff(7738,plain,
% 1.43/1.62 (b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[6429, 7737, 7626])).
% 1.43/1.62 tff(7739,plain,
% 1.43/1.62 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4053, 7656])).
% 1.43/1.62 tff(7740,plain,
% 1.43/1.62 (~(s(elem!1) = s(s(elem!1)))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[6484, 7728])).
% 1.43/1.62 tff(7741,plain,
% 1.43/1.62 (s(elem!1) = s(z)),
% 1.43/1.62 inference(symmetry,[status(thm)],[4289])).
% 1.43/1.62 tff(7742,plain,
% 1.43/1.62 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7741])).
% 1.43/1.62 tff(7743,plain,
% 1.43/1.62 ((~b(s(elem!1), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7742])).
% 1.43/1.62 tff(7744,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.62 tff(7745,plain,
% 1.43/1.62 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7670])).
% 1.43/1.62 tff(7746,plain,
% 1.43/1.62 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[388, 7745])).
% 1.43/1.62 tff(7747,plain,
% 1.43/1.62 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7742])).
% 1.43/1.62 tff(7748,plain,
% 1.43/1.62 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4288])).
% 1.43/1.62 tff(7749,plain,
% 1.43/1.62 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 1.43/1.62 inference(symmetry,[status(thm)],[7748])).
% 1.43/1.62 tff(7750,plain,
% 1.43/1.62 (r(s(s(s(s(elem!1)))), z)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[6913, 7749])).
% 1.43/1.62 tff(7751,plain,
% 1.43/1.62 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1016, 7750, 13])).
% 1.43/1.62 tff(7752,plain,
% 1.43/1.62 (b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[467, 7751])).
% 1.43/1.62 tff(7753,plain,
% 1.43/1.62 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7752, 7747])).
% 1.43/1.62 tff(7754,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7741])).
% 1.43/1.62 tff(7755,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7754])).
% 1.43/1.62 tff(7756,plain,
% 1.43/1.62 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7741])).
% 1.43/1.62 tff(7757,plain,
% 1.43/1.62 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7756])).
% 1.43/1.62 tff(7758,plain,
% 1.43/1.62 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4289])).
% 1.43/1.62 tff(7759,plain,
% 1.43/1.62 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4288])).
% 1.43/1.62 tff(7760,plain,
% 1.43/1.62 (r(s(z), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[13, 7759])).
% 1.43/1.62 tff(7761,plain,
% 1.43/1.62 (r(s(elem!1), elem!1)),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7760, 7758])).
% 1.43/1.62 tff(7762,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7763,plain,
% 1.43/1.62 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7764,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7763])).
% 1.43/1.62 tff(7765,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7764, 7762])).
% 1.43/1.62 tff(7766,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7767,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 1.43/1.62 tff(7768,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7767, 28, 7761, 6913])).
% 1.43/1.62 tff(7769,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7768, 7757])).
% 1.43/1.62 tff(7770,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[441, 7769])).
% 1.43/1.62 tff(7771,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7770, 7755])).
% 1.43/1.62 tff(7772,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7773,plain,
% 1.43/1.62 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7774,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7773])).
% 1.43/1.62 tff(7775,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7774, 7772])).
% 1.43/1.62 tff(7776,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7777,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7776, 7775])).
% 1.43/1.62 tff(7778,plain,
% 1.43/1.62 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7777, 154, 6511, 6510, 7744])).
% 1.43/1.62 tff(7779,plain,
% 1.43/1.62 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7778, 7771])).
% 1.43/1.62 tff(7780,plain,
% 1.43/1.62 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[4286, 7779, 7673])).
% 1.43/1.62 tff(7781,plain,
% 1.43/1.62 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[4292])).
% 1.43/1.62 tff(7782,plain,
% 1.43/1.62 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7781])).
% 1.43/1.62 tff(7783,plain,
% 1.43/1.62 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1019, 7782])).
% 1.43/1.62 tff(7784,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7785,plain,
% 1.43/1.62 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7786,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7785])).
% 1.43/1.62 tff(7787,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7786, 7784])).
% 1.43/1.62 tff(7788,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7789,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7788, 7787])).
% 1.43/1.62 tff(7790,plain,
% 1.43/1.62 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7789, 28, 4297, 4296])).
% 1.43/1.62 tff(7791,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7790, 7783])).
% 1.43/1.62 tff(7792,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(7793,plain,
% 1.43/1.62 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7792, 7780, 4297, 4288])).
% 1.43/1.62 tff(7794,plain,
% 1.43/1.62 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[989, 7793])).
% 1.43/1.62 tff(7795,plain,
% 1.43/1.62 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7794, 6997])).
% 1.43/1.62 tff(7796,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7797,plain,
% 1.43/1.62 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7798,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7797])).
% 1.43/1.62 tff(7799,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7798, 7796])).
% 1.43/1.62 tff(7800,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7801,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7800, 7799])).
% 1.43/1.62 tff(7802,plain,
% 1.43/1.62 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7801, 154, 6510, 7795, 7744, 7771])).
% 1.43/1.62 tff(7803,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7802, 7753])).
% 1.43/1.62 tff(7804,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(7805,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7804, 6511, 6510, 7744, 4213, 4297, 4288, 13])).
% 1.43/1.62 tff(7806,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[6950, 7805, 7746])).
% 1.43/1.62 tff(7807,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7808,plain,
% 1.43/1.62 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(7809,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7808])).
% 1.43/1.62 tff(7810,plain,
% 1.43/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[7809, 7807])).
% 1.43/1.62 tff(7811,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(7812,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7811, 7810])).
% 1.43/1.62 tff(7813,plain,
% 1.43/1.62 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7812, 154, 7806, 6867, 6510, 7744])).
% 1.43/1.62 tff(7814,plain,
% 1.43/1.62 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[7813, 7743])).
% 1.43/1.62 tff(7815,plain,
% 1.43/1.62 (r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[467, 7814])).
% 1.43/1.62 tff(7816,plain,
% 1.43/1.62 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[7741])).
% 1.43/1.62 tff(7817,plain,
% 1.43/1.62 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[7816])).
% 1.43/1.62 tff(7818,plain,
% 1.43/1.62 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[535, 7817])).
% 1.43/1.62 tff(7819,assumption,(~r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.62 tff(7820,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[7819, 7818])).
% 1.43/1.63 tff(7821,plain,(r(s(elem!1), s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7822,plain,
% 1.43/1.63 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7821, 7815, 4288])).
% 1.43/1.63 tff(7823,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.63 tff(7824,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7825,plain,
% 1.43/1.63 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7826,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7825])).
% 1.43/1.63 tff(7827,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7826, 7824])).
% 1.43/1.63 tff(7828,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7829,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7828, 7827])).
% 1.43/1.63 tff(7830,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7829, 28, 5848, 4296, 7823])).
% 1.43/1.63 tff(7831,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7832,plain,
% 1.43/1.63 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7831, 7822, 7761])).
% 1.43/1.63 tff(7833,plain,
% 1.43/1.63 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[4286, 7832, 7673])).
% 1.43/1.63 tff(7834,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7835,plain,
% 1.43/1.63 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7836,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7835])).
% 1.43/1.63 tff(7837,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7836, 7834])).
% 1.43/1.63 tff(7838,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7839,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7838, 7837])).
% 1.43/1.63 tff(7840,plain,
% 1.43/1.63 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7839, 154, 6655, 7806, 6656, 7833])).
% 1.43/1.63 tff(7841,plain,
% 1.43/1.63 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7668, 7840, 4035])).
% 1.43/1.63 tff(7842,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7843,plain,
% 1.43/1.63 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7844,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7843])).
% 1.43/1.63 tff(7845,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7844, 7842])).
% 1.43/1.63 tff(7846,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7847,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7846, 7845])).
% 1.43/1.63 tff(7848,plain,
% 1.43/1.63 (~r(s(elem!1), s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7847, 28, 7841, 7822])).
% 1.43/1.63 tff(7849,plain,
% 1.43/1.63 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7741])).
% 1.43/1.63 tff(7850,plain,
% 1.43/1.63 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.43/1.63 inference(symmetry,[status(thm)],[7849])).
% 1.43/1.63 tff(7851,plain,
% 1.43/1.63 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7754])).
% 1.43/1.63 tff(7852,plain,
% 1.43/1.63 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7778, 7833])).
% 1.43/1.63 tff(7853,plain,
% 1.43/1.63 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7852, 7851])).
% 1.43/1.63 tff(7854,plain,
% 1.43/1.63 (r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[441, 7853])).
% 1.43/1.63 tff(7855,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.63 tff(7856,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.43/1.63 tff(7857,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7858,plain,
% 1.43/1.63 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~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))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7859,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7858])).
% 1.43/1.63 tff(7860,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7859, 7857])).
% 1.43/1.63 tff(7861,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7862,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7861, 7860])).
% 1.43/1.63 tff(7863,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7862, 28, 345, 7856, 7855])).
% 1.43/1.63 tff(7864,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7865,plain,
% 1.43/1.63 (~r(s(s(elem!1)), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7864, 7841, 7854])).
% 1.43/1.63 tff(7866,plain,
% 1.43/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7867,plain,
% 1.43/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7868,plain,
% 1.43/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7867, 7866])).
% 1.43/1.63 tff(7869,plain,
% 1.43/1.63 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7868, 60])).
% 1.43/1.63 tff(7870,plain,
% 1.43/1.63 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7869, 3904])).
% 1.43/1.63 tff(7871,plain,
% 1.43/1.63 (b(s(s(elem!1)), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7870, 7865])).
% 1.43/1.63 tff(7872,plain,
% 1.43/1.63 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7871, 7850])).
% 1.43/1.63 tff(7873,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.43/1.63 tff(7874,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7875,plain,
% 1.43/1.63 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7876,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7875])).
% 1.43/1.63 tff(7877,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7876, 7874])).
% 1.43/1.63 tff(7878,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7879,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7878, 7877])).
% 1.43/1.63 tff(7880,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7879, 154, 6511, 6655, 6656, 6605, 7873])).
% 1.43/1.63 tff(7881,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7882,plain,
% 1.43/1.63 (~b(s(elem!1), s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7881, 7872, 6655, 6656, 6511])).
% 1.43/1.63 tff(7883,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[6492, 7882, 7848, 6386])).
% 1.43/1.63 tff(7884,plain,((~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7885,plain,
% 1.43/1.63 (~b(elem!1, s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7884, 7740, 7630, 7635, 7655, 7739, 7738, 7694, 7707, 7628, 7580, 7053])).
% 1.43/1.63 tff(7886,plain,
% 1.43/1.63 (r(elem!1, s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[6508, 7885, 7728])).
% 1.43/1.63 tff(7887,plain,
% 1.43/1.63 (r(z, s(z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7886, 7727])).
% 1.43/1.63 tff(7888,plain,
% 1.43/1.63 (~r(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[838, 7887, 7722])).
% 1.43/1.63 tff(7889,plain,
% 1.43/1.63 (b(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[818, 7888])).
% 1.43/1.63 tff(7890,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), s(z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7889, 7719])).
% 1.43/1.63 tff(7891,plain,
% 1.43/1.63 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7890, 7718])).
% 1.43/1.63 tff(7892,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.43/1.63 tff(7893,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7812, 154, 6963, 6867, 6510, 7744, 5842])).
% 1.43/1.63 tff(7894,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7895,plain,
% 1.43/1.63 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7894, 5842, 6510, 7744, 6867])).
% 1.43/1.63 tff(7896,plain,
% 1.43/1.63 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[6950, 7895, 7746])).
% 1.43/1.63 tff(7897,plain,
% 1.43/1.63 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7767, 28, 5848, 7896])).
% 1.43/1.63 tff(7898,plain,
% 1.43/1.63 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7897, 7757])).
% 1.43/1.63 tff(7899,plain,
% 1.43/1.63 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[441, 7898])).
% 1.43/1.63 tff(7900,plain,
% 1.43/1.63 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7899, 7755])).
% 1.43/1.63 tff(7901,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7902,plain,
% 1.43/1.63 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7903,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[7902])).
% 1.43/1.63 tff(7904,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[7903, 7901])).
% 1.43/1.63 tff(7905,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(7906,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[7905, 7904])).
% 1.43/1.63 tff(7907,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7906, 154, 6510, 7744, 7900, 7892, 5842])).
% 1.43/1.63 tff(7908,plain,((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7909,plain,
% 1.43/1.63 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7908, 7738, 7694, 7891, 7655, 7715, 7707])).
% 1.43/1.63 tff(7910,plain,
% 1.43/1.63 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[505, 7747])).
% 1.43/1.63 tff(7911,assumption,(~b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.63 tff(7912,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7911, 7910])).
% 1.43/1.63 tff(7913,plain,(b(s(elem!1), s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7914,plain,
% 1.43/1.63 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7913, 7909, 7655])).
% 1.43/1.63 tff(7915,plain,
% 1.43/1.63 (r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[467, 7914])).
% 1.43/1.63 tff(7916,plain,
% 1.43/1.63 (~r(s(s(s(s(elem!1)))), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1016, 7915, 7053])).
% 1.43/1.63 tff(7917,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[412, 7750])).
% 1.43/1.63 tff(7918,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | r(s(s(s(s(elem!1)))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(7919,plain,
% 1.43/1.63 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[7918, 7916, 7655])).
% 1.43/1.63 tff(7920,plain,
% 1.43/1.63 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[6950, 7919, 7710])).
% 1.43/1.63 tff(7921,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7922,plain,
% 1.43/1.63 (((~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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(7923,plain,
% 1.43/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7922])).
% 1.43/1.64 tff(7924,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7923, 7921])).
% 1.43/1.64 tff(7925,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7926,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7925, 7924])).
% 1.43/1.64 tff(7927,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7926, 154, 6655, 6963, 6867, 6866, 7744])).
% 1.43/1.64 tff(7928,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(7929,plain,
% 1.43/1.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7928, 7920, 7707, 7694, 7630])).
% 1.43/1.64 tff(7930,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 1.43/1.64 tff(7931,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.64 tff(7932,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.64 tff(7933,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7110, 60, 7932, 7931, 7930])).
% 1.43/1.64 tff(7934,plain,(b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(7935,plain,
% 1.43/1.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7934, 7929, 7703])).
% 1.43/1.64 tff(7936,plain,
% 1.43/1.64 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7708, 4255])).
% 1.43/1.64 tff(7937,plain,
% 1.43/1.64 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7936])).
% 1.43/1.64 tff(7938,plain,
% 1.43/1.64 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[388, 7937])).
% 1.43/1.64 tff(7939,plain,
% 1.43/1.64 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7821, 7915, 7655])).
% 1.43/1.64 tff(7940,plain,
% 1.43/1.64 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7831, 7939, 7715])).
% 1.43/1.64 tff(7941,plain,
% 1.43/1.64 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[4286, 7940, 7938])).
% 1.43/1.64 tff(7942,plain,
% 1.43/1.64 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[6969, 154, 7630, 7920, 7635, 7941])).
% 1.43/1.64 tff(7943,plain,
% 1.43/1.64 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[6975, 7942, 7656])).
% 1.43/1.64 tff(7944,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.64 tff(7945,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.64 tff(7946,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7947,plain,
% 1.43/1.64 (((~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(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)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7948,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7947])).
% 1.43/1.64 tff(7949,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~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)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7948, 7946])).
% 1.43/1.64 tff(7950,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7951,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7950, 7949])).
% 1.43/1.64 tff(7952,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7951, 28, 7945, 7113, 7944])).
% 1.43/1.64 tff(7953,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(7954,plain,
% 1.43/1.64 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7953, 7943, 7935])).
% 1.43/1.64 tff(7955,plain,
% 1.43/1.64 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7954, 7698])).
% 1.43/1.64 tff(7956,plain,
% 1.43/1.64 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[989, 7955])).
% 1.43/1.64 tff(7957,plain,
% 1.43/1.64 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7956, 7695])).
% 1.43/1.64 tff(7958,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7959,plain,
% 1.43/1.64 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7960,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7959])).
% 1.43/1.64 tff(7961,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7960, 7958])).
% 1.43/1.64 tff(7962,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7963,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7962, 7961])).
% 1.43/1.64 tff(7964,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7963, 154, 7920, 7707, 7941, 7957, 7694])).
% 1.43/1.64 tff(7965,plain,((~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(7966,plain,
% 1.43/1.64 ((~b(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7965, 6223])).
% 1.43/1.64 tff(7967,plain,
% 1.43/1.64 (~r(z, s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7966, 6217, 6205, 6191])).
% 1.43/1.64 tff(7968,plain,
% 1.43/1.64 (b(z, s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[3977, 7967])).
% 1.43/1.64 tff(7969,plain,
% 1.43/1.64 (b(elem!1, s(s(s(z))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7968, 6188])).
% 1.43/1.64 tff(7970,plain,
% 1.43/1.64 (b(elem!1, s(s(z)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[140, 5689])).
% 1.43/1.64 tff(7971,plain,
% 1.43/1.64 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[5621])).
% 1.43/1.64 tff(7972,plain,
% 1.43/1.64 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[5611])).
% 1.43/1.64 tff(7973,plain,
% 1.43/1.64 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7972, 7971])).
% 1.43/1.64 tff(7974,plain,
% 1.43/1.64 (r(elem!1, s(elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[14, 7973])).
% 1.43/1.64 tff(7975,plain,
% 1.43/1.64 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[5672])).
% 1.43/1.64 tff(7976,plain,
% 1.43/1.64 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[6199, 5632])).
% 1.43/1.64 tff(7977,plain,
% 1.43/1.64 (b(s(elem!1), s(s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7976, 5630])).
% 1.43/1.64 tff(7978,plain,
% 1.43/1.64 (~r(s(s(s(s(z)))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1323, 1283, 140, 14, 142])).
% 1.43/1.64 tff(7979,plain,
% 1.43/1.64 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[318, 7978])).
% 1.43/1.64 tff(7980,plain,
% 1.43/1.64 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7979, 5624])).
% 1.43/1.64 tff(7981,plain,
% 1.43/1.64 (b(s(s(s(s(z)))), s(elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7980, 5620])).
% 1.43/1.64 tff(7982,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.43/1.64 tff(7983,plain,
% 1.43/1.64 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[5739, 154, 6208, 7982, 7981, 7977])).
% 1.43/1.64 tff(7984,plain,
% 1.43/1.64 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[343, 7983])).
% 1.43/1.64 tff(7985,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))), introduced(assumption)).
% 1.43/1.64 tff(7986,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7987,plain,
% 1.43/1.64 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(7988,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7987])).
% 1.43/1.64 tff(7989,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[7988, 7986])).
% 1.43/1.64 tff(7990,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(7991,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[7990, 7989])).
% 1.43/1.64 tff(7992,plain,
% 1.43/1.64 (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[7991, 28, 124, 7985])).
% 1.43/1.64 tff(7993,assumption,(s(s(z)) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.64 tff(7994,plain,
% 1.43/1.64 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7993])).
% 1.43/1.64 tff(7995,plain,
% 1.43/1.64 (s(z) = s(s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[289, 7994, 5821])).
% 1.43/1.64 tff(7996,plain,
% 1.43/1.64 (inj_0(s(z)) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[7995])).
% 1.43/1.64 tff(7997,plain,
% 1.43/1.64 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 1.43/1.64 inference(symmetry,[status(thm)],[7996])).
% 1.43/1.64 tff(7998,plain,
% 1.43/1.64 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[4244])).
% 1.43/1.64 tff(7999,plain,
% 1.43/1.64 (s(s(s(s(elem!1)))) = z),
% 1.43/1.64 inference(transitivity,[status(thm)],[7998, 7997, 91])).
% 1.43/1.64 tff(8000,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[388, 7999])).
% 1.43/1.64 tff(8001,plain,(~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(8002,plain,
% 1.43/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(8003,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(8004,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[8003, 8002])).
% 1.43/1.64 tff(8005,plain,
% 1.43/1.64 (b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[8004, 60, 8001, 7992])).
% 1.43/1.64 tff(8006,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(8007,plain,
% 1.43/1.64 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(8008,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[8007])).
% 1.43/1.64 tff(8009,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[8008, 8006])).
% 1.43/1.64 tff(8010,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(8011,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[8010, 8009])).
% 1.43/1.64 tff(8012,plain,
% 1.43/1.64 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[8011, 28, 604, 7985])).
% 1.43/1.64 tff(8013,plain,
% 1.43/1.64 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[5911, 8012, 5884])).
% 1.43/1.64 tff(8014,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(8015,plain,
% 1.43/1.64 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(8016,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[8015])).
% 1.43/1.64 tff(8017,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[8016, 8014])).
% 1.43/1.64 tff(8018,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(8019,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[8018, 8017])).
% 1.43/1.64 tff(8020,plain,
% 1.43/1.64 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[8019, 28, 604, 7985])).
% 1.43/1.64 tff(8021,plain,
% 1.43/1.64 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[6124, 8020, 6109])).
% 1.43/1.64 tff(8022,plain,
% 1.43/1.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[612, 604, 124])).
% 1.43/1.64 tff(8023,plain,
% 1.43/1.64 (b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1259, 8022])).
% 1.43/1.64 tff(8024,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(8025,plain,
% 1.43/1.64 (((~b(s(s(s(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(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(8026,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[8025])).
% 1.43/1.64 tff(8027,plain,
% 1.43/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[8026, 8024])).
% 1.43/1.64 tff(8028,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(8029,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[8028, 8027])).
% 1.43/1.64 tff(8030,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[8029, 154, 8023, 2121, 8021, 8013, 8005])).
% 1.43/1.64 tff(8031,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(8032,plain,
% 1.43/1.64 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[8031, 7984, 6200])).
% 1.43/1.64 tff(8033,plain,
% 1.43/1.64 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(commutativity,[status(thm)],[])).
% 1.43/1.64 tff(8034,plain,
% 1.43/1.64 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[8033])).
% 1.43/1.64 tff(8035,plain,
% 1.43/1.64 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[5932])).
% 1.43/1.64 tff(8036,plain,
% 1.43/1.64 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[8035, 8033])).
% 1.43/1.64 tff(8037,plain,
% 1.43/1.64 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[8036, 8034])).
% 1.43/1.64 tff(8038,plain,
% 1.43/1.64 ((~(s(s(s(s(s(s(z)))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8037])).
% 1.43/1.65 tff(8039,plain,
% 1.43/1.65 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[5955, 8038])).
% 1.43/1.65 tff(8040,plain,
% 1.43/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8041,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(8042,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8041, 8040])).
% 1.43/1.65 tff(8043,plain,
% 1.43/1.65 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8042, 60])).
% 1.43/1.65 tff(8044,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8043, 8039])).
% 1.43/1.65 tff(8045,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8044, 8032])).
% 1.43/1.65 tff(8046,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8045, 7975])).
% 1.43/1.65 tff(8047,plain,
% 1.43/1.65 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1427, 28, 6200, 7984])).
% 1.43/1.65 tff(8048,plain,
% 1.43/1.65 (b(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[229, 8047])).
% 1.43/1.65 tff(8049,plain,
% 1.43/1.65 (b(s(s(z)), elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[142, 5751])).
% 1.43/1.65 tff(8050,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8051,plain,
% 1.43/1.65 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8052,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8051])).
% 1.43/1.65 tff(8053,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[8052, 8050])).
% 1.43/1.65 tff(8054,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(8055,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8054, 8053])).
% 1.43/1.65 tff(8056,plain,
% 1.43/1.65 (~b(elem!1, s(s(s(s(z)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8055, 154, 1283, 7970, 8049, 8048])).
% 1.43/1.65 tff(8057,plain,
% 1.43/1.65 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.43/1.65 inference(commutativity,[status(thm)],[])).
% 1.43/1.65 tff(8058,plain,
% 1.43/1.65 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[5611])).
% 1.43/1.65 tff(8059,plain,
% 1.43/1.65 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[8058, 8057])).
% 1.43/1.65 tff(8060,plain,
% 1.43/1.65 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8059])).
% 1.43/1.65 tff(8061,plain,
% 1.43/1.65 (~(elem!1 = s(s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[185, 8060])).
% 1.43/1.65 tff(8062,plain,
% 1.43/1.65 (b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[4102, 8061])).
% 1.43/1.65 tff(8063,plain,
% 1.43/1.65 (r(elem!1, s(s(s(s(z)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8062, 8056])).
% 1.43/1.65 tff(8064,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[5763])).
% 1.43/1.65 tff(8065,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[8064])).
% 1.43/1.65 tff(8066,plain,
% 1.43/1.65 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[5763])).
% 1.43/1.65 tff(8067,plain,
% 1.43/1.65 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8066])).
% 1.43/1.65 tff(8068,plain,
% 1.43/1.65 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[6008])).
% 1.43/1.65 tff(8069,plain,
% 1.43/1.65 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[6012, 8068])).
% 1.43/1.65 tff(8070,plain,
% 1.43/1.65 (b(elem!1, s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[5763])).
% 1.43/1.65 tff(8071,plain,
% 1.43/1.65 ((~b(elem!1, s(s(s(s(s(s(z)))))))) <=> (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8070])).
% 1.43/1.65 tff(8072,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.43/1.65 tff(8073,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.43/1.65 tff(8074,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.43/1.65 inference(symmetry,[status(thm)],[6014])).
% 1.43/1.65 tff(8075,plain,
% 1.43/1.65 ((~r(s(s(s(s(s(s(z)))))), elem!1)) <=> (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[6003])).
% 1.43/1.65 tff(8076,plain,
% 1.43/1.65 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[8066])).
% 1.43/1.65 tff(8077,plain,
% 1.43/1.65 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8064])).
% 1.43/1.65 tff(8078,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.43/1.65 tff(8079,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8080,plain,
% 1.43/1.65 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8081,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8080])).
% 1.43/1.65 tff(8082,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[8081, 8079])).
% 1.43/1.65 tff(8083,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(8084,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8083, 8082])).
% 1.43/1.65 tff(8085,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8084, 154, 1283, 6019, 5964, 8078, 6103])).
% 1.43/1.65 tff(8086,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(8087,plain,
% 1.43/1.65 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8086, 6103, 6019, 5964, 1283])).
% 1.43/1.65 tff(8088,plain,
% 1.43/1.65 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8087, 8077])).
% 1.43/1.65 tff(8089,plain,
% 1.43/1.65 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[6124, 8088, 6109])).
% 1.43/1.65 tff(8090,plain,
% 1.43/1.65 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8089, 8076])).
% 1.43/1.65 tff(8091,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8092,plain,
% 1.43/1.65 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8093,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8092])).
% 1.43/1.65 tff(8094,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.43/1.65 inference(transitivity,[status(thm)],[8093, 8091])).
% 1.43/1.65 tff(8095,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(8096,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8095, 8094])).
% 1.43/1.65 tff(8097,plain,
% 1.43/1.65 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8096, 28, 6495, 4111])).
% 1.43/1.65 tff(8098,plain,
% 1.43/1.65 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8097, 8090])).
% 1.43/1.65 tff(8099,plain,
% 1.43/1.65 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8098, 8075])).
% 1.43/1.65 tff(8100,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[6032, 8099, 6013])).
% 1.43/1.65 tff(8101,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8100, 8074])).
% 1.43/1.65 tff(8102,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8103,plain,
% 1.43/1.65 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8104,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8103])).
% 1.43/1.65 tff(8105,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[8104, 8102])).
% 1.43/1.65 tff(8106,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(8107,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8106, 8105])).
% 1.43/1.65 tff(8108,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8107, 154, 4455, 8073, 8072, 8101, 6103])).
% 1.43/1.65 tff(8109,plain,((~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(8110,plain,
% 1.43/1.65 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8109, 5964, 8073, 8072, 5601, 6495, 4111, 6019, 4455, 1283])).
% 1.43/1.65 tff(8111,plain,
% 1.43/1.65 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8110, 8071])).
% 1.43/1.65 tff(8112,plain,
% 1.43/1.65 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[6093, 8111, 8069])).
% 1.43/1.65 tff(8113,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.43/1.65 tff(8114,plain,
% 1.43/1.65 (r(elem!1, s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[5763])).
% 1.43/1.65 tff(8115,plain,
% 1.43/1.65 (r(elem!1, s(s(s(s(s(s(elem!1))))))) <=> r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[8114])).
% 1.43/1.65 tff(8116,plain,
% 1.43/1.65 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[6073, 8115])).
% 1.43/1.65 tff(8117,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8118,plain,
% 1.43/1.65 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8119,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[8118])).
% 1.43/1.65 tff(8120,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[8119, 8117])).
% 1.43/1.65 tff(8121,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(8122,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8121, 8120])).
% 1.43/1.65 tff(8123,plain,
% 1.43/1.65 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8122, 28, 4111])).
% 1.43/1.65 tff(8124,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8123, 8116, 8113])).
% 1.43/1.65 tff(8125,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(8126,plain,
% 1.43/1.65 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[8125, 8112, 4111, 5601])).
% 1.43/1.65 tff(8127,plain,
% 1.43/1.65 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8126, 8067])).
% 1.43/1.65 tff(8128,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[6124, 8127, 6109])).
% 1.43/1.65 tff(8129,plain,
% 1.43/1.65 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[8128, 8065])).
% 1.43/1.65 tff(8130,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8131,plain,
% 1.43/1.65 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(8132,plain,
% 1.43/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8131])).
% 1.43/1.66 tff(8133,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[8132, 8130])).
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% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(8135,plain,
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% 1.43/1.66 inference(modus_ponens,[status(thm)],[8134, 8133])).
% 1.43/1.66 tff(8136,plain,
% 1.43/1.66 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8135, 154, 1283, 1603, 5964, 8129])).
% 1.43/1.66 tff(8137,plain,
% 1.43/1.66 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8136, 6150])).
% 1.43/1.66 tff(8138,plain,
% 1.43/1.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5911, 8137, 5884])).
% 1.43/1.66 tff(8139,plain,
% 1.43/1.66 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8138, 5901])).
% 1.43/1.66 tff(8140,plain,
% 1.43/1.66 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8112, 8115])).
% 1.43/1.66 tff(8141,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8142,plain,
% 1.43/1.66 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8143,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8142])).
% 1.43/1.66 tff(8144,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[8143, 8141])).
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% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
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% 1.43/1.66 inference(modus_ponens,[status(thm)],[8145, 8144])).
% 1.43/1.66 tff(8147,plain,
% 1.43/1.66 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8146, 28, 4111])).
% 1.43/1.66 tff(8148,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8147, 8140, 8139])).
% 1.43/1.66 tff(8149,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(8150,plain,
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% 1.43/1.66 inference(unit_resolution,[status(thm)],[8149, 5590])).
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% 1.43/1.66 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8150, 8063, 1283, 8048, 6209, 8046, 7974, 7970, 7969])).
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% 1.43/1.66 inference(unit_resolution,[status(thm)],[5800, 5590])).
% 1.43/1.66 tff(8153,plain,
% 1.43/1.66 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8152, 8151])).
% 1.43/1.66 tff(8154,plain,
% 1.43/1.66 (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)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5805, 5974])).
% 1.43/1.66 tff(8155,plain,
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% 1.43/1.66 inference(unit_resolution,[status(thm)],[8154, 8153])).
% 1.43/1.66 tff(8156,plain,
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% 1.43/1.66 inference(modus_ponens,[status(thm)],[8155, 6185])).
% 1.43/1.66 tff(8157,plain,
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% 1.43/1.66 inference(unit_resolution,[status(thm)],[5854, 28, 5848, 8156])).
% 1.43/1.66 tff(8158,plain,
% 1.43/1.66 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8157, 6184])).
% 1.43/1.66 tff(8159,plain,
% 1.43/1.66 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8158, 6181])).
% 1.43/1.66 tff(8160,plain,
% 1.43/1.66 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[5866, 8159])).
% 1.43/1.66 tff(8161,plain,
% 1.43/1.66 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8160, 6179])).
% 1.43/1.66 tff(8162,plain,
% 1.43/1.66 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[5932])).
% 1.43/1.66 tff(8163,plain,
% 1.43/1.66 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[8162])).
% 1.43/1.66 tff(8164,plain,
% 1.43/1.66 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[5932])).
% 1.43/1.66 tff(8165,plain,
% 1.43/1.66 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8164])).
% 1.43/1.66 tff(8166,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8167,plain,
% 1.43/1.66 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8168,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8167])).
% 1.43/1.66 tff(8169,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[8168, 8166])).
% 1.43/1.66 tff(8170,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(8171,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8170, 8169])).
% 1.43/1.66 tff(8172,plain,
% 1.43/1.66 ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8171, 154, 6209, 7970, 8049])).
% 1.43/1.66 tff(8173,plain,
% 1.43/1.66 (~b(s(s(s(z))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8172, 7969])).
% 1.43/1.66 tff(8174,plain,
% 1.43/1.66 (r(s(s(s(z))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[104, 8173])).
% 1.43/1.66 tff(8175,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8176,plain,
% 1.43/1.66 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8177,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(s(s(s(s(z))))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8176])).
% 1.43/1.66 tff(8178,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[8177, 8175])).
% 1.43/1.66 tff(8179,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(8180,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(s(s(s(s(z))))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8179, 8178])).
% 1.43/1.66 tff(8181,plain,
% 1.43/1.66 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8180, 28, 8174, 8156])).
% 1.43/1.66 tff(8182,plain,
% 1.43/1.66 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8181, 8165])).
% 1.43/1.66 tff(8183,plain,
% 1.43/1.66 ((~(s(s(s(s(s(s(z)))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8036])).
% 1.43/1.66 tff(8184,plain,
% 1.43/1.66 (~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[5955, 8183])).
% 1.43/1.66 tff(8185,plain,
% 1.43/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8186,plain,
% 1.43/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(8187,plain,
% 1.43/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8186, 8185])).
% 1.43/1.66 tff(8188,plain,
% 1.43/1.66 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8187, 60])).
% 1.43/1.66 tff(8189,plain,
% 1.43/1.66 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8188, 8184])).
% 1.43/1.66 tff(8190,plain,
% 1.43/1.66 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8189, 8182])).
% 1.43/1.66 tff(8191,plain,
% 1.43/1.66 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8190, 8163])).
% 1.43/1.66 tff(8192,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8193,plain,
% 1.43/1.66 (((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8194,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8193])).
% 1.43/1.66 tff(8195,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[8194, 8192])).
% 1.43/1.66 tff(8196,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(8197,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8196, 8195])).
% 1.43/1.66 tff(8198,plain,
% 1.43/1.66 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8197, 154, 8046, 6208, 7982])).
% 1.43/1.66 tff(8199,plain,
% 1.43/1.66 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8198, 8191])).
% 1.43/1.66 tff(8200,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8199, 8161])).
% 1.43/1.66 tff(8201,plain,(b(s(s(z)), s(s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(8202,plain,
% 1.43/1.66 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8201, 5732, 5655, 17, 6177, 5670, 2205, 65])).
% 1.43/1.66 tff(8203,plain,
% 1.43/1.66 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8202, 5650])).
% 1.43/1.66 tff(8204,plain,
% 1.43/1.66 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[5689, 5688])).
% 1.43/1.66 tff(8205,plain,
% 1.43/1.66 (b(elem!1, s(s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[65, 8204])).
% 1.43/1.66 tff(8206,plain,
% 1.43/1.66 (~r(s(s(s(s(z)))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1323, 6177, 65, 5670, 2205])).
% 1.43/1.66 tff(8207,plain,
% 1.43/1.66 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[318, 8206])).
% 1.43/1.66 tff(8208,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8207, 5624])).
% 1.43/1.66 tff(8209,plain,
% 1.43/1.66 (b(s(s(s(s(z)))), s(elem!1))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8208, 5620])).
% 1.43/1.66 tff(8210,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8211,plain,
% 1.43/1.66 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(8212,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[8211])).
% 1.43/1.66 tff(8213,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[8212, 8210])).
% 1.43/1.66 tff(8214,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(8215,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8214, 8213])).
% 1.43/1.66 tff(8216,plain,
% 1.43/1.66 ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8215, 154, 6177])).
% 1.43/1.66 tff(8217,plain,
% 1.43/1.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[8216, 8202, 5732, 8209])).
% 1.43/1.66 tff(8218,plain,
% 1.43/1.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[564, 8217])).
% 1.43/1.66 tff(8219,plain,
% 1.43/1.66 (~r(s(s(s(z))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[2207, 8218, 13, 17, 6177])).
% 1.43/1.66 tff(8220,plain,
% 1.43/1.66 (b(s(s(s(z))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[169, 8219])).
% 1.43/1.66 tff(8221,plain,
% 1.43/1.66 (b(s(s(s(elem!1))), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[8220, 6197])).
% 1.43/1.66 tff(8222,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.66 tff(8223,plain,
% 1.43/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8224,plain,
% 1.43/1.67 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~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(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8225,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8224])).
% 1.43/1.67 tff(8226,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8225, 8223])).
% 1.43/1.67 tff(8227,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8228,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8227, 8226])).
% 1.43/1.67 tff(8229,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8228, 154, 6655, 3852, 5702, 6231, 8222])).
% 1.43/1.67 tff(8230,plain,((~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8231,plain,
% 1.43/1.67 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8230, 8221, 8205, 5684, 8203])).
% 1.43/1.67 tff(8232,plain,
% 1.43/1.67 (b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4311, 6223])).
% 1.43/1.67 tff(8233,plain,
% 1.43/1.67 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8232, 8231])).
% 1.43/1.67 tff(8234,plain,
% 1.43/1.67 (r(z, s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8233, 5662])).
% 1.43/1.67 tff(8235,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5590])).
% 1.43/1.67 tff(8236,plain,
% 1.43/1.67 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8235])).
% 1.43/1.67 tff(8237,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8207, 8236])).
% 1.43/1.67 tff(8238,plain,
% 1.43/1.67 (~b(s(s(s(z))), s(s(z)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[162, 8220, 65, 2205, 8202])).
% 1.43/1.67 tff(8239,plain,
% 1.43/1.67 (r(s(s(s(z))), s(s(z)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[104, 8238])).
% 1.43/1.67 tff(8240,plain,
% 1.43/1.67 (~r(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[597, 8239, 17])).
% 1.43/1.67 tff(8241,plain,
% 1.43/1.67 (b(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[252, 8240])).
% 1.43/1.67 tff(8242,plain,
% 1.43/1.67 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[476, 8241, 5668, 17, 8237, 8202])).
% 1.43/1.67 tff(8243,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[496, 8242])).
% 1.43/1.67 tff(8244,plain,
% 1.43/1.67 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8243, 5924])).
% 1.43/1.67 tff(8245,plain,
% 1.43/1.67 (~r(z, s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1471, 8244, 65, 2205, 6177])).
% 1.43/1.67 tff(8246,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8245, 8234])).
% 1.43/1.67 tff(8247,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8248,plain,
% 1.43/1.67 (~r(s(z), s(s(z)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8247, 13])).
% 1.43/1.67 tff(8249,plain,
% 1.43/1.67 (b(s(z), s(s(z)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[680, 8248])).
% 1.43/1.67 tff(8250,plain,
% 1.43/1.67 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8249, 5658])).
% 1.43/1.67 tff(8251,plain,
% 1.43/1.67 (r(s(elem!1), z) <=> r(s(elem!1), elem!1)),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5611])).
% 1.43/1.67 tff(8252,plain,
% 1.43/1.67 (r(s(elem!1), elem!1) <=> r(s(elem!1), z)),
% 1.43/1.67 inference(symmetry,[status(thm)],[8251])).
% 1.43/1.67 tff(8253,plain,
% 1.43/1.67 (r(s(z), z) <=> r(s(elem!1), z)),
% 1.43/1.67 inference(transitivity,[status(thm)],[5653, 5652, 8252])).
% 1.43/1.67 tff(8254,plain,
% 1.43/1.67 (r(s(elem!1), z)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[13, 8253])).
% 1.43/1.67 tff(8255,plain,
% 1.43/1.67 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5657, 5621])).
% 1.43/1.67 tff(8256,plain,
% 1.43/1.67 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5590])).
% 1.43/1.67 tff(8257,plain,
% 1.43/1.67 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8256])).
% 1.43/1.67 tff(8258,plain,
% 1.43/1.67 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[16, 8257])).
% 1.43/1.67 tff(8259,plain,
% 1.43/1.67 (~r(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3823, 8258, 535])).
% 1.43/1.67 tff(8260,plain,
% 1.43/1.67 (b(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[296, 8259])).
% 1.43/1.67 tff(8261,plain,
% 1.43/1.67 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8260, 8255])).
% 1.43/1.67 tff(8262,plain,
% 1.43/1.67 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.43/1.67 inference(commutativity,[status(thm)],[])).
% 1.43/1.67 tff(8263,plain,
% 1.43/1.67 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5622, 5592])).
% 1.43/1.67 tff(8264,plain,
% 1.43/1.67 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(z))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8263, 8262])).
% 1.43/1.67 tff(8265,plain,
% 1.43/1.67 ((s(s(s(z))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8264])).
% 1.43/1.67 tff(8266,plain,
% 1.43/1.67 ((~(s(s(s(z))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8265])).
% 1.43/1.67 tff(8267,plain,
% 1.43/1.67 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[96, 8266])).
% 1.43/1.67 tff(8268,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8269,plain,
% 1.43/1.67 (((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8270,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8269])).
% 1.43/1.67 tff(8271,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8270, 8268])).
% 1.43/1.67 tff(8272,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8273,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8272, 8271])).
% 1.43/1.67 tff(8274,plain,
% 1.43/1.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8273, 28, 5848, 4161, 6445])).
% 1.43/1.67 tff(8275,plain,
% 1.43/1.67 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[7390, 60, 8274])).
% 1.43/1.67 tff(8276,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), s(elem!1))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8275, 7377])).
% 1.43/1.67 tff(8277,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8278,plain,
% 1.43/1.67 (((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8279,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8278])).
% 1.43/1.67 tff(8280,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8279, 8277])).
% 1.43/1.67 tff(8281,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8282,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8281, 8280])).
% 1.43/1.67 tff(8283,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8282, 28, 4161, 6420, 6445])).
% 1.43/1.67 tff(8284,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8285,plain,
% 1.43/1.67 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8284, 4161, 6445])).
% 1.43/1.67 tff(8286,plain,
% 1.43/1.67 (b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[6429, 8285, 4016])).
% 1.43/1.67 tff(8287,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8288,plain,
% 1.43/1.67 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8289,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8288])).
% 1.43/1.67 tff(8290,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8289, 8287])).
% 1.43/1.67 tff(8291,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8292,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8291, 8290])).
% 1.43/1.67 tff(8293,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8292, 154, 6605, 7873, 8286, 8222, 8276])).
% 1.43/1.67 tff(8294,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8295,plain,
% 1.43/1.67 ((~r(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8294, 8267])).
% 1.43/1.67 tff(8296,plain,
% 1.43/1.67 (~r(s(s(s(elem!1))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8295, 8261, 8254, 8250, 5655, 5651])).
% 1.43/1.67 tff(8297,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4159, 8296])).
% 1.43/1.67 tff(8298,plain,
% 1.43/1.67 ((~b(s(s(s(elem!1))), z)) | b(s(s(s(z))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[3865, 5592])).
% 1.43/1.67 tff(8299,plain,
% 1.43/1.67 (b(s(s(s(z))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8298, 8297])).
% 1.43/1.67 tff(8300,plain,
% 1.43/1.67 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), elem!1)),
% 1.43/1.67 inference(transitivity,[status(thm)],[6192, 6194])).
% 1.43/1.67 tff(8301,plain,
% 1.43/1.67 (b(s(s(s(z))), elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8297, 8300])).
% 1.43/1.67 tff(8302,plain,
% 1.43/1.67 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5622])).
% 1.43/1.67 tff(8303,plain,
% 1.43/1.67 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8302])).
% 1.43/1.67 tff(8304,plain,
% 1.43/1.67 (b(s(elem!1), s(s(z)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[684, 8303])).
% 1.43/1.67 tff(8305,assumption,(~b(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.43/1.67 tff(8306,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8305, 8304])).
% 1.43/1.67 tff(8307,plain,(b(s(elem!1), s(s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8308,plain,
% 1.43/1.67 (b(s(elem!1), s(s(z)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8307, 8249])).
% 1.43/1.67 tff(8309,plain,
% 1.43/1.67 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5622])).
% 1.43/1.67 tff(8310,plain,
% 1.43/1.67 (b(s(s(z)), s(z)) <=> b(s(s(z)), s(elem!1))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8309])).
% 1.43/1.67 tff(8311,plain,
% 1.43/1.67 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[4953, 66, 8249, 1655])).
% 1.43/1.67 tff(8312,plain,
% 1.43/1.67 (b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1259, 8311])).
% 1.43/1.67 tff(8313,plain,
% 1.43/1.67 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[5590])).
% 1.43/1.67 tff(8314,plain,
% 1.43/1.67 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[8313])).
% 1.43/1.67 tff(8315,plain,
% 1.43/1.67 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[66, 8314])).
% 1.43/1.67 tff(8316,plain,
% 1.43/1.67 (~r(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1027, 8315, 535])).
% 1.43/1.67 tff(8317,plain,
% 1.43/1.67 (b(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[252, 8316])).
% 1.43/1.67 tff(8318,plain,
% 1.43/1.67 (~b(s(s(s(z))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1512, 1445, 8249, 144, 232])).
% 1.43/1.67 tff(8319,plain,
% 1.43/1.67 (~r(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1990, 299, 13, 254, 1283, 1299])).
% 1.43/1.67 tff(8320,plain,
% 1.43/1.67 (b(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1181, 8319])).
% 1.43/1.67 tff(8321,plain,
% 1.43/1.67 (~r(s(s(s(z))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2316, 8320, 13])).
% 1.43/1.67 tff(8322,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[169, 8321, 8318])).
% 1.43/1.67 tff(8323,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8324,plain,
% 1.43/1.67 (~r(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8323, 8317, 144, 13, 2492, 8312, 2490])).
% 1.43/1.67 tff(8325,plain,
% 1.43/1.67 (b(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[296, 8324])).
% 1.43/1.67 tff(8326,plain,
% 1.43/1.67 (b(s(s(z)), s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8325, 8310])).
% 1.43/1.67 tff(8327,plain,
% 1.43/1.67 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), s(elem!1))),
% 1.43/1.67 inference(transitivity,[status(thm)],[5730, 5728])).
% 1.43/1.67 tff(8328,plain,
% 1.43/1.67 (b(s(s(s(z))), s(elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[3209, 8327])).
% 1.43/1.67 tff(8329,plain,
% 1.43/1.67 (b(s(elem!1), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8317, 5626])).
% 1.43/1.67 tff(8330,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8331,plain,
% 1.43/1.67 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8332,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8331])).
% 1.43/1.67 tff(8333,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8332, 8330])).
% 1.43/1.67 tff(8334,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8335,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8334, 8333])).
% 1.43/1.67 tff(8336,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8335, 154, 144, 8329, 8328, 8326, 8308])).
% 1.43/1.67 tff(8337,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8338,plain,
% 1.43/1.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8337, 535, 13, 144, 1655])).
% 1.43/1.67 tff(8339,plain,
% 1.43/1.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[564, 8338])).
% 1.43/1.67 tff(8340,plain,
% 1.43/1.67 (b(s(s(s(s(z)))), elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2490, 5743])).
% 1.43/1.67 tff(8341,plain,
% 1.43/1.67 (b(elem!1, s(s(s(s(z)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2492, 5747])).
% 1.43/1.67 tff(8342,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8343,plain,
% 1.43/1.67 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(8344,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[8343])).
% 1.43/1.67 tff(8345,plain,
% 1.43/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.43/1.67 inference(transitivity,[status(thm)],[8344, 8342])).
% 1.43/1.67 tff(8346,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(8347,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[8346, 8345])).
% 1.43/1.67 tff(8348,plain,
% 1.43/1.67 ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8347, 154, 8341, 8340, 8339])).
% 1.43/1.67 tff(8349,plain,
% 1.43/1.67 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8348, 8301])).
% 1.43/1.67 tff(8350,plain,
% 1.43/1.67 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[343, 8349])).
% 1.43/1.67 tff(8351,plain,
% 1.43/1.67 (~r(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1957, 8350, 1655])).
% 1.43/1.67 tff(8352,plain,
% 1.43/1.67 (b(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[252, 8351])).
% 1.43/1.67 tff(8353,plain,
% 1.43/1.67 (~b(s(s(z)), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1512, 8352, 8249, 144, 8299])).
% 1.43/1.67 tff(8354,plain,
% 1.43/1.67 (r(s(s(z)), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[122, 8353])).
% 1.43/1.67 tff(8355,plain,
% 1.43/1.67 (~r(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2677, 8354, 13, 8352, 8299])).
% 1.43/1.67 tff(8356,plain,
% 1.43/1.67 (b(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[818, 8355])).
% 1.43/1.67 tff(8357,plain,
% 1.43/1.67 (~r(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1963, 8356, 13, 1655, 16, 8354, 8299])).
% 1.43/1.67 tff(8358,plain,
% 1.43/1.67 (~b(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2825, 8356, 13, 16])).
% 1.43/1.67 tff(8359,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1181, 8358, 8357])).
% 1.43/1.67 tff(8360,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8361,plain,
% 1.43/1.67 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8360, 5634, 13, 144, 5645])).
% 1.43/1.67 tff(8362,plain,
% 1.43/1.67 (b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1259, 8361])).
% 1.43/1.67 tff(8363,plain,
% 1.43/1.67 (~r(z, s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2157, 5634, 13])).
% 1.43/1.67 tff(8364,plain,
% 1.43/1.67 (b(z, s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[191, 8363])).
% 1.43/1.67 tff(8365,plain,
% 1.43/1.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8337, 5645, 13, 144, 5634])).
% 1.43/1.67 tff(8366,plain,
% 1.43/1.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[564, 8365])).
% 1.43/1.67 tff(8367,plain,
% 1.43/1.67 (~b(s(s(s(z))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2553, 8362, 5636, 144, 8366])).
% 1.43/1.67 tff(8368,plain,
% 1.43/1.67 (r(s(s(s(z))), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[169, 8367])).
% 1.43/1.67 tff(8369,plain,
% 1.43/1.67 (~b(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2316, 8368, 13])).
% 1.43/1.67 tff(8370,plain,
% 1.43/1.67 (r(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1181, 8369])).
% 1.43/1.67 tff(8371,plain,
% 1.43/1.67 (~b(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2025, 8368, 13, 8249, 8362, 5636, 8364])).
% 1.43/1.67 tff(8372,plain,
% 1.43/1.67 (r(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[296, 8371])).
% 1.43/1.67 tff(8373,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1990, 8372, 8370, 13, 8364, 8362, 5636])).
% 1.43/1.67 tff(8374,plain,(b(s(z), s(s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(8375,plain,
% 1.43/1.67 (b(s(z), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[8374, 144, 13])).
% 1.43/1.67 tff(8376,plain,
% 1.43/1.67 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8375, 5632])).
% 1.43/1.68 tff(8377,plain,
% 1.43/1.68 (b(s(elem!1), s(s(s(s(z)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8376, 5630])).
% 1.43/1.68 tff(8378,plain,
% 1.43/1.68 (b(s(s(z)), s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[231, 8310])).
% 1.43/1.68 tff(8379,plain,
% 1.43/1.68 (b(s(s(elem!1)), s(elem!1))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[231, 8255])).
% 1.43/1.68 tff(8380,plain,
% 1.43/1.68 (~r(s(s(s(elem!1))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8295, 8379, 8254, 8250, 5655, 5651])).
% 1.43/1.68 tff(8381,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4159, 8380])).
% 1.43/1.68 tff(8382,plain,
% 1.43/1.68 (b(s(s(s(z))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8298, 8381])).
% 1.43/1.68 tff(8383,plain,
% 1.43/1.68 (~b(s(z), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1437, 1283, 13, 8249, 8375, 8382, 231])).
% 1.43/1.68 tff(8384,plain,
% 1.43/1.68 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4366])).
% 1.43/1.68 tff(8385,plain,
% 1.43/1.68 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8384])).
% 1.43/1.68 tff(8386,plain,
% 1.43/1.68 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.43/1.68 inference(symmetry,[status(thm)],[460])).
% 1.43/1.68 tff(8387,plain,
% 1.43/1.68 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(z)))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8386])).
% 1.43/1.68 tff(8388,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.68 tff(8389,plain,
% 1.43/1.68 (s(z) = s(s(s(s(z))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8388, 4365])).
% 1.43/1.68 tff(8390,plain,
% 1.43/1.68 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8389])).
% 1.43/1.68 tff(8391,plain,
% 1.43/1.68 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8390])).
% 1.43/1.68 tff(8392,plain,
% 1.43/1.68 (s(s(s(z))) = z),
% 1.43/1.68 inference(transitivity,[status(thm)],[220, 8391, 91])).
% 1.43/1.68 tff(8393,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[165, 8392])).
% 1.43/1.68 tff(8394,plain,((~(s(z) = s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8395,plain,
% 1.43/1.68 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8394, 4361])).
% 1.43/1.68 tff(8396,plain,
% 1.43/1.68 (~(s(s(s(s(elem!1)))) = s(z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8395, 8387])).
% 1.43/1.68 tff(8397,plain,
% 1.43/1.68 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4366])).
% 1.43/1.68 tff(8398,plain,
% 1.43/1.68 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8397])).
% 1.43/1.68 tff(8399,plain,
% 1.43/1.68 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4366])).
% 1.43/1.68 tff(8400,plain,
% 1.43/1.68 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8399])).
% 1.43/1.68 tff(8401,plain,
% 1.43/1.68 (z = elem!1),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[4361, 4354])).
% 1.43/1.68 tff(8402,plain,
% 1.43/1.68 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4362])).
% 1.43/1.68 tff(8403,plain,
% 1.43/1.68 ((s(z) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8402])).
% 1.43/1.68 tff(8404,plain,
% 1.43/1.68 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8403])).
% 1.43/1.68 tff(8405,plain,
% 1.43/1.68 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[368, 8404])).
% 1.43/1.68 tff(8406,plain,
% 1.43/1.68 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4018, 8405])).
% 1.43/1.68 tff(8407,plain,
% 1.43/1.68 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[478])).
% 1.43/1.68 tff(8408,plain,
% 1.43/1.68 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[4292, 8407])).
% 1.43/1.68 tff(8409,plain,
% 1.43/1.68 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8408])).
% 1.43/1.68 tff(8410,plain,
% 1.43/1.68 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[363, 8409, 354])).
% 1.43/1.68 tff(8411,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4009, 8410])).
% 1.43/1.68 tff(8412,plain,((~(s(s(s(s(elem!1)))) = s(s(s(z))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8413,plain,
% 1.43/1.68 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8412, 8406, 8401])).
% 1.43/1.68 tff(8414,plain,
% 1.43/1.68 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4366])).
% 1.43/1.68 tff(8415,plain,
% 1.43/1.68 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8414])).
% 1.43/1.68 tff(8416,plain,
% 1.43/1.68 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[5459, 1283, 144, 684, 15])).
% 1.43/1.68 tff(8417,plain,
% 1.43/1.68 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8416, 8415])).
% 1.43/1.68 tff(8418,plain,
% 1.43/1.68 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[495, 8417, 8413])).
% 1.43/1.68 tff(8419,plain,
% 1.43/1.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8418, 8400])).
% 1.43/1.68 tff(8420,plain,
% 1.43/1.68 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1586, 28, 273])).
% 1.43/1.68 tff(8421,plain,
% 1.43/1.68 (~r(s(s(s(s(z)))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8420, 8419])).
% 1.43/1.68 tff(8422,plain,
% 1.43/1.68 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8421, 8398])).
% 1.43/1.68 tff(8423,plain,
% 1.43/1.68 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[440, 8422, 8396])).
% 1.43/1.68 tff(8424,plain,
% 1.43/1.68 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8423, 8385])).
% 1.43/1.68 tff(8425,plain,
% 1.43/1.68 (~b(s(s(s(s(z)))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1387, 154, 1283, 231, 684, 15])).
% 1.43/1.68 tff(8426,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8425, 8424])).
% 1.43/1.68 tff(8427,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8428,plain,
% 1.43/1.68 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8427, 5637])).
% 1.43/1.68 tff(8429,plain,
% 1.43/1.68 (~r(s(z), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8428, 1283, 8249, 144, 8375, 231])).
% 1.43/1.68 tff(8430,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[252, 8429, 8383])).
% 1.43/1.68 tff(8431,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8432,plain,
% 1.43/1.68 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8431, 231, 144, 13])).
% 1.43/1.68 tff(8433,plain,
% 1.43/1.68 (r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1259, 8432])).
% 1.43/1.68 tff(8434,plain,
% 1.43/1.68 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[5592])).
% 1.43/1.68 tff(8435,plain,
% 1.43/1.68 (b(s(elem!1), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8434])).
% 1.43/1.68 tff(8436,plain,
% 1.43/1.68 ((~b(s(elem!1), s(s(s(z))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8435])).
% 1.43/1.68 tff(8437,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8438,plain,
% 1.43/1.68 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8439,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8438])).
% 1.43/1.68 tff(8440,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8439, 8437])).
% 1.43/1.68 tff(8441,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8442,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8441, 8440])).
% 1.43/1.68 tff(8443,plain,
% 1.43/1.68 (~b(s(elem!1), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8442, 154, 144, 2195, 8378, 8308])).
% 1.43/1.68 tff(8444,plain,
% 1.43/1.68 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8443, 8436])).
% 1.43/1.68 tff(8445,plain,
% 1.43/1.68 (b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[6429, 8267])).
% 1.43/1.68 tff(8446,plain,
% 1.43/1.68 (r(s(elem!1), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8445, 8444])).
% 1.43/1.68 tff(8447,plain,
% 1.43/1.68 (~r(elem!1, s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[7736, 8446, 5655])).
% 1.43/1.68 tff(8448,plain,
% 1.43/1.68 (b(elem!1, s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8232, 8447])).
% 1.43/1.68 tff(8449,plain,
% 1.43/1.68 (b(s(s(s(z))), elem!1)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8381, 8300])).
% 1.43/1.68 tff(8450,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8451,plain,
% 1.43/1.68 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8452,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8451])).
% 1.43/1.68 tff(8453,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8452, 8450])).
% 1.43/1.68 tff(8454,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8455,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8454, 8453])).
% 1.43/1.68 tff(8456,plain,
% 1.43/1.68 (~b(s(s(s(z))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8455, 154, 144, 8449])).
% 1.43/1.68 tff(8457,plain,
% 1.43/1.68 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8456, 6207])).
% 1.43/1.68 tff(8458,plain,
% 1.43/1.68 (r(s(s(s(z))), s(s(s(z)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[5726])).
% 1.43/1.68 tff(8459,plain,
% 1.43/1.68 ((~r(s(s(s(z))), s(s(s(z))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8458])).
% 1.43/1.68 tff(8460,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8461,plain,
% 1.43/1.68 (((~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(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8462,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8461])).
% 1.43/1.68 tff(8463,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8462, 8460])).
% 1.43/1.68 tff(8464,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~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(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(z))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8465,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8464, 8463])).
% 1.43/1.68 tff(8466,plain,
% 1.43/1.68 (~r(s(s(s(z))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8465, 28, 66])).
% 1.43/1.68 tff(8467,plain,
% 1.43/1.68 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8466, 8459])).
% 1.43/1.68 tff(8468,plain,
% 1.43/1.68 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[4202, 8467, 8457])).
% 1.43/1.68 tff(8469,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[5592])).
% 1.43/1.68 tff(8470,plain,
% 1.43/1.68 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8469])).
% 1.43/1.68 tff(8471,plain,
% 1.43/1.68 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[5675, 8470])).
% 1.43/1.68 tff(8472,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2195, 8471])).
% 1.43/1.68 tff(8473,plain,
% 1.43/1.68 (r(elem!1, s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[7066, 5637])).
% 1.43/1.68 tff(8474,plain,
% 1.43/1.68 (~r(z, s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8473, 8447])).
% 1.43/1.68 tff(8475,plain,
% 1.43/1.68 (b(z, s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[3977, 8474])).
% 1.43/1.68 tff(8476,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.68 tff(8477,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8478,plain,
% 1.43/1.68 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8479,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8478])).
% 1.43/1.68 tff(8480,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8479, 8477])).
% 1.43/1.68 tff(8481,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8482,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8481, 8480])).
% 1.43/1.68 tff(8483,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8482, 154, 3852, 5702, 8476, 8222, 6866])).
% 1.43/1.68 tff(8484,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(8485,plain,
% 1.43/1.68 (~b(s(s(elem!1)), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8484, 8475, 5651, 8381, 8472])).
% 1.43/1.68 tff(8486,plain,
% 1.43/1.68 (r(s(s(elem!1)), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[6293, 8485])).
% 1.43/1.68 tff(8487,plain,
% 1.43/1.68 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[5596, 5590])).
% 1.43/1.68 tff(8488,plain,
% 1.43/1.68 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8487, 215])).
% 1.43/1.68 tff(8489,plain,
% 1.43/1.68 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8488])).
% 1.43/1.68 tff(8490,plain,
% 1.43/1.68 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8489, 4048])).
% 1.43/1.68 tff(8491,plain,
% 1.43/1.68 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8490])).
% 1.43/1.68 tff(8492,plain,
% 1.43/1.68 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[224, 8491])).
% 1.43/1.68 tff(8493,plain,
% 1.43/1.68 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[4213])).
% 1.43/1.68 tff(8494,plain,
% 1.43/1.68 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8493])).
% 1.43/1.68 tff(8495,plain,
% 1.43/1.68 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8494])).
% 1.43/1.68 tff(8496,plain,
% 1.43/1.68 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[6848])).
% 1.43/1.68 tff(8497,plain,
% 1.43/1.68 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8496, 8495])).
% 1.43/1.68 tff(8498,plain,
% 1.43/1.68 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[443, 6826])).
% 1.43/1.68 tff(8499,plain,
% 1.43/1.68 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.43/1.68 inference(monotonicity,[status(thm)],[6848])).
% 1.43/1.68 tff(8500,plain,
% 1.43/1.68 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.43/1.68 inference(symmetry,[status(thm)],[8499])).
% 1.43/1.68 tff(8501,plain,
% 1.43/1.68 (r(s(s(elem!1)), elem!1)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[6280, 8500])).
% 1.43/1.68 tff(8502,plain,
% 1.43/1.68 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[6831])).
% 1.43/1.68 tff(8503,plain,
% 1.43/1.68 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.68 inference(symmetry,[status(thm)],[8502])).
% 1.43/1.68 tff(8504,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8505,plain,
% 1.43/1.68 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8506,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8505])).
% 1.43/1.68 tff(8507,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8506, 8504])).
% 1.43/1.68 tff(8508,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(8509,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8508, 8507])).
% 1.43/1.68 tff(8510,plain,
% 1.43/1.68 (~r(s(z), s(s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[8509, 28, 6280, 13])).
% 1.43/1.68 tff(8511,plain,
% 1.43/1.68 (b(s(z), s(s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[7245, 8510])).
% 1.43/1.68 tff(8512,plain,
% 1.43/1.68 (b(s(elem!1), s(s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[8511, 8503])).
% 1.43/1.68 tff(8513,plain,
% 1.43/1.68 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[6831])).
% 1.43/1.68 tff(8514,plain,
% 1.43/1.68 ((~b(s(elem!1), s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8513])).
% 1.43/1.68 tff(8515,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8516,plain,
% 1.43/1.68 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(8517,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[8516])).
% 1.43/1.68 tff(8518,plain,
% 1.43/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[8517, 8515])).
% 1.43/1.68 tff(8519,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8520,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8519, 8518])).
% 1.43/1.69 tff(8521,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8520, 28, 6913, 7084, 7945])).
% 1.43/1.69 tff(8522,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8523,plain,
% 1.43/1.69 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8522, 6913, 7084])).
% 1.43/1.69 tff(8524,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[6975, 8523, 4051])).
% 1.43/1.69 tff(8525,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8526,plain,
% 1.43/1.69 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8527,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8526])).
% 1.43/1.69 tff(8528,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8527, 8525])).
% 1.43/1.69 tff(8529,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8530,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8529, 8528])).
% 1.43/1.69 tff(8531,plain,
% 1.43/1.69 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8530, 154, 6605, 8222, 7744])).
% 1.43/1.69 tff(8532,plain,
% 1.43/1.69 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8531, 8524])).
% 1.43/1.69 tff(8533,plain,
% 1.43/1.69 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8532, 8514])).
% 1.43/1.69 tff(8534,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[6842])).
% 1.43/1.69 tff(8535,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 1.43/1.69 inference(symmetry,[status(thm)],[8534])).
% 1.43/1.69 tff(8536,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), z)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[6913, 8535])).
% 1.43/1.69 tff(8537,plain,
% 1.43/1.69 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1016, 8536, 13])).
% 1.43/1.69 tff(8538,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[467, 8537, 8533])).
% 1.43/1.69 tff(8539,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), z)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8540,plain,
% 1.43/1.69 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8539, 4213, 13, 8512, 8222, 8498, 4051, 8501])).
% 1.43/1.69 tff(8541,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[6950, 8540, 6910])).
% 1.43/1.69 tff(8542,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8543,plain,
% 1.43/1.69 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8544,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8543])).
% 1.43/1.69 tff(8545,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8544, 8542])).
% 1.43/1.69 tff(8546,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8547,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8546, 8545])).
% 1.43/1.69 tff(8548,plain,
% 1.43/1.69 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8547, 154, 8541, 6851, 6231, 8498])).
% 1.43/1.69 tff(8549,plain,
% 1.43/1.69 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[4286, 8548, 6908])).
% 1.43/1.69 tff(8550,plain,
% 1.43/1.69 (r(z, s(s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8549, 8497])).
% 1.43/1.69 tff(8551,plain,
% 1.43/1.69 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4215])).
% 1.43/1.69 tff(8552,plain,
% 1.43/1.69 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 1.43/1.69 inference(symmetry,[status(thm)],[8551])).
% 1.43/1.69 tff(8553,plain,
% 1.43/1.69 (r(s(s(z)), z)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[6280, 8552])).
% 1.43/1.69 tff(8554,plain,
% 1.43/1.69 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4215, 8493])).
% 1.43/1.69 tff(8555,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[8554])).
% 1.43/1.69 tff(8556,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8557,plain,
% 1.43/1.69 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8558,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8557])).
% 1.43/1.69 tff(8559,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8558, 8556])).
% 1.43/1.69 tff(8560,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8561,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 1.43/1.69 tff(8562,plain,
% 1.43/1.69 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8561, 154, 8541, 6851, 8222, 8498])).
% 1.43/1.69 tff(8563,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[7668, 8562, 7657])).
% 1.43/1.69 tff(8564,plain,
% 1.43/1.69 (r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8563, 8555])).
% 1.43/1.69 tff(8565,plain,
% 1.43/1.69 (~r(z, s(s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[913, 8564, 8553])).
% 1.43/1.69 tff(8566,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8565, 8550])).
% 1.43/1.69 tff(8567,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8568,plain,
% 1.43/1.69 ((~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8567, 8492])).
% 1.43/1.69 tff(8569,plain,
% 1.43/1.69 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8568, 8486, 13, 5651, 8468, 8381, 8448])).
% 1.43/1.69 tff(8570,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[496, 8569])).
% 1.43/1.69 tff(8571,plain,
% 1.43/1.69 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8570, 5924])).
% 1.43/1.69 tff(8572,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5590, 5596])).
% 1.43/1.69 tff(8573,plain,
% 1.43/1.69 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5621])).
% 1.43/1.69 tff(8574,plain,
% 1.43/1.69 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(symmetry,[status(thm)],[8573])).
% 1.43/1.69 tff(8575,plain,
% 1.43/1.69 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8255, 8574])).
% 1.43/1.69 tff(8576,plain,
% 1.43/1.69 (b(s(s(elem!1)), s(z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[231, 8575])).
% 1.43/1.69 tff(8577,plain,
% 1.43/1.69 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5590])).
% 1.43/1.69 tff(8578,plain,
% 1.43/1.69 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[8577])).
% 1.43/1.69 tff(8579,plain,
% 1.43/1.69 (b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8375, 8578])).
% 1.43/1.69 tff(8580,plain,
% 1.43/1.69 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5621])).
% 1.43/1.69 tff(8581,plain,
% 1.43/1.69 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(symmetry,[status(thm)],[8580])).
% 1.43/1.69 tff(8582,plain,
% 1.43/1.69 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[5658, 8581])).
% 1.43/1.69 tff(8583,plain,
% 1.43/1.69 (b(s(z), s(s(elem!1)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8249, 8582])).
% 1.43/1.69 tff(8584,plain,
% 1.43/1.69 (~b(s(s(s(z))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[692, 2195, 8249, 144, 231])).
% 1.43/1.69 tff(8585,plain,
% 1.43/1.69 (r(s(s(s(z))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[818, 8584])).
% 1.43/1.69 tff(8586,plain,
% 1.43/1.69 (~r(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[853, 8585, 66])).
% 1.43/1.69 tff(8587,plain,
% 1.43/1.69 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[318, 8586])).
% 1.43/1.69 tff(8588,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8587, 8236])).
% 1.43/1.69 tff(8589,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.43/1.69 tff(8590,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.69 tff(8591,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.69 tff(8592,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8593,plain,
% 1.43/1.69 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8594,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8593])).
% 1.43/1.69 tff(8595,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8594, 8592])).
% 1.43/1.69 tff(8596,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8597,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8596, 8595])).
% 1.43/1.69 tff(8598,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8597, 154, 8591, 8590, 505, 444, 8589])).
% 1.43/1.69 tff(8599,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8600,plain,
% 1.43/1.69 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8599, 8588, 8583, 8579, 8576])).
% 1.43/1.69 tff(8601,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[6975, 8492])).
% 1.43/1.69 tff(8602,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8601, 8600])).
% 1.43/1.69 tff(8603,plain,
% 1.43/1.69 (r(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8602, 8572])).
% 1.43/1.69 tff(8604,plain,
% 1.43/1.69 (~b(s(s(z)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5683, 8485])).
% 1.43/1.69 tff(8605,plain,
% 1.43/1.69 (r(s(s(z)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[122, 8604])).
% 1.43/1.69 tff(8606,plain,
% 1.43/1.69 (~r(z, s(s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[913, 8605, 16])).
% 1.43/1.69 tff(8607,plain,
% 1.43/1.69 (b(z, s(s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[191, 8606])).
% 1.43/1.69 tff(8608,plain,
% 1.43/1.69 (b(elem!1, s(s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8607, 5747])).
% 1.43/1.69 tff(8609,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5590])).
% 1.43/1.69 tff(8610,plain,
% 1.43/1.69 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[4288])).
% 1.43/1.69 tff(8611,plain,
% 1.43/1.69 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.43/1.69 inference(symmetry,[status(thm)],[8610])).
% 1.43/1.69 tff(8612,plain,
% 1.43/1.69 (b(s(s(elem!1)), z)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[6656, 8611])).
% 1.43/1.69 tff(8613,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[5680, 8612])).
% 1.43/1.69 tff(8614,plain,((~(z = elem!1)) | b(s(s(elem!1)), z) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(8615,plain,
% 1.43/1.69 (b(s(s(elem!1)), z) | (~b(s(s(elem!1)), elem!1))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8614, 5611])).
% 1.43/1.69 tff(8616,plain,
% 1.43/1.69 (~b(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8615, 8485])).
% 1.43/1.69 tff(8617,plain,
% 1.43/1.69 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.43/1.69 inference(symmetry,[status(thm)],[4055])).
% 1.43/1.69 tff(8618,plain,
% 1.43/1.69 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5611])).
% 1.43/1.69 tff(8619,plain,
% 1.43/1.69 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8618, 4055])).
% 1.43/1.69 tff(8620,plain,
% 1.43/1.69 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.43/1.69 inference(transitivity,[status(thm)],[8619, 8617])).
% 1.43/1.69 tff(8621,plain,
% 1.43/1.69 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8620])).
% 1.43/1.69 tff(8622,plain,
% 1.43/1.69 (~(s(s(elem!1)) = elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[366, 8621])).
% 1.43/1.69 tff(8623,plain,
% 1.43/1.69 (b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[6363, 8622])).
% 1.43/1.69 tff(8624,plain,
% 1.43/1.69 (r(s(s(elem!1)), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8623, 8616])).
% 1.43/1.69 tff(8625,plain,
% 1.43/1.69 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8522, 8624, 8602])).
% 1.43/1.69 tff(8626,plain,
% 1.43/1.69 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5590])).
% 1.43/1.69 tff(8627,plain,
% 1.43/1.69 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8626, 8057])).
% 1.43/1.69 tff(8628,plain,
% 1.43/1.69 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.69 inference(symmetry,[status(thm)],[8627])).
% 1.43/1.69 tff(8629,plain,
% 1.43/1.69 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.69 inference(transitivity,[status(thm)],[8059, 8628])).
% 1.43/1.69 tff(8630,plain,
% 1.43/1.69 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8629])).
% 1.43/1.69 tff(8631,plain,
% 1.43/1.69 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[185, 8630])).
% 1.43/1.69 tff(8632,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[6950, 8631])).
% 1.43/1.69 tff(8633,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8632, 8625])).
% 1.43/1.69 tff(8634,plain,
% 1.43/1.69 (b(s(s(s(s(z)))), elem!1)),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8633, 8609])).
% 1.43/1.69 tff(8635,plain,
% 1.43/1.69 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.43/1.69 inference(commutativity,[status(thm)],[])).
% 1.43/1.69 tff(8636,plain,
% 1.43/1.69 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.43/1.69 inference(symmetry,[status(thm)],[8635])).
% 1.43/1.69 tff(8637,plain,
% 1.43/1.69 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 1.43/1.69 inference(monotonicity,[status(thm)],[5611])).
% 1.43/1.69 tff(8638,plain,
% 1.43/1.69 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8637, 8636])).
% 1.43/1.69 tff(8639,plain,
% 1.43/1.69 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8638])).
% 1.43/1.69 tff(8640,plain,
% 1.43/1.69 (~(elem!1 = s(s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[48, 8639])).
% 1.43/1.69 tff(8641,plain,
% 1.43/1.69 (b(elem!1, s(s(s(z))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8448, 6186])).
% 1.43/1.69 tff(8642,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8643,plain,
% 1.43/1.69 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8644,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[8643])).
% 1.43/1.69 tff(8645,plain,
% 1.43/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[8644, 8642])).
% 1.43/1.69 tff(8646,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8647,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[8646, 8645])).
% 1.43/1.69 tff(8648,plain,
% 1.43/1.69 (~b(elem!1, s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[8647, 154, 144, 2195, 8641, 8449])).
% 1.43/1.69 tff(8649,plain,
% 1.43/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(8650,plain,
% 1.43/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(8651,plain,
% 1.43/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[8650, 8649])).
% 1.43/1.70 tff(8652,plain,
% 1.43/1.70 (r(elem!1, s(s(z)))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8651, 60, 8648, 8640])).
% 1.43/1.70 tff(8653,plain,
% 1.43/1.70 (r(elem!1, s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[5932])).
% 1.43/1.70 tff(8654,plain,
% 1.43/1.70 ((~r(elem!1, s(s(s(s(s(s(z)))))))) <=> (~r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[8653])).
% 1.43/1.70 tff(8655,plain,
% 1.43/1.70 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8152, 5795])).
% 1.43/1.70 tff(8656,plain,
% 1.43/1.70 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8154, 8655])).
% 1.43/1.70 tff(8657,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.70 tff(8658,plain,
% 1.43/1.70 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[8657, 6185])).
% 1.43/1.70 tff(8659,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 1.43/1.70 tff(8660,plain,
% 1.43/1.70 ($false),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8659, 8658])).
% 1.43/1.70 tff(8661,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.70 tff(8662,plain,
% 1.43/1.70 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8661, 8656])).
% 1.43/1.70 tff(8663,plain,
% 1.43/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(8664,plain,
% 1.43/1.70 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(8665,plain,
% 1.43/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[8664])).
% 1.43/1.70 tff(8666,plain,
% 1.43/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.70 inference(transitivity,[status(thm)],[8665, 8663])).
% 1.43/1.70 tff(8667,plain,
% 1.43/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.43/1.70 inference(quant_inst,[status(thm)],[])).
% 1.43/1.70 tff(8668,plain,
% 1.43/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[8667, 8666])).
% 1.43/1.70 tff(8669,plain,
% 1.43/1.70 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[8668, 28, 4467, 8662])).
% 1.43/1.70 tff(8670,plain,
% 1.43/1.70 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[8669, 8654])).
% 1.53/1.70 tff(8671,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[6094, 8670])).
% 1.53/1.70 tff(8672,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8671, 5673])).
% 1.53/1.70 tff(8673,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(z)))))), s(s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[6135, 5590])).
% 1.53/1.70 tff(8674,plain,
% 1.53/1.70 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8673, 5795, 1243, 6018, 604, 6105])).
% 1.53/1.70 tff(8675,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8674, 8672])).
% 1.53/1.70 tff(8676,plain,(b(s(s(s(s(s(s(z)))))), s(s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8677,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8676, 8652, 8603, 8634, 8571, 8608])).
% 1.53/1.70 tff(8678,plain,
% 1.53/1.70 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5996, 8677, 144, 2195, 8603, 8571])).
% 1.53/1.70 tff(8679,plain,
% 1.53/1.70 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5998, 8678])).
% 1.53/1.70 tff(8680,plain,
% 1.53/1.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[6000, 8679])).
% 1.53/1.70 tff(8681,plain,
% 1.53/1.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5672])).
% 1.53/1.70 tff(8682,plain,
% 1.53/1.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[6016, 8681])).
% 1.53/1.70 tff(8683,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.53/1.70 tff(8684,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8683, 8682])).
% 1.53/1.70 tff(8685,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8686,plain,
% 1.53/1.70 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8685, 8680])).
% 1.53/1.70 tff(8687,plain,
% 1.53/1.70 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5622])).
% 1.53/1.70 tff(8688,plain,
% 1.53/1.70 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 1.53/1.70 inference(symmetry,[status(thm)],[8687])).
% 1.53/1.70 tff(8689,plain,
% 1.53/1.70 (r(s(s(s(z))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8585, 8688])).
% 1.53/1.70 tff(8690,plain,
% 1.53/1.70 (b(s(s(s(s(z)))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8587, 5625])).
% 1.53/1.70 tff(8691,plain,
% 1.53/1.70 (~r(s(s(s(s(z)))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2484, 8605, 13, 8249])).
% 1.53/1.70 tff(8692,plain,
% 1.53/1.70 (b(s(s(s(s(z)))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[206, 8691])).
% 1.53/1.70 tff(8693,plain,
% 1.53/1.70 (~b(z, s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2191, 8692, 8375, 8607, 8587])).
% 1.53/1.70 tff(8694,plain,
% 1.53/1.70 (r(z, s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1181, 8693])).
% 1.53/1.70 tff(8695,plain,
% 1.53/1.70 (r(elem!1, s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8694, 7973])).
% 1.53/1.70 tff(8696,plain,
% 1.53/1.70 (r(s(elem!1), s(s(s(s(s(s(z))))))) <=> r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5622, 5932])).
% 1.53/1.70 tff(8697,plain,
% 1.53/1.70 (r(s(z), s(s(s(s(s(s(elem!1))))))) <=> r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(symmetry,[status(thm)],[8696])).
% 1.53/1.70 tff(8698,plain,
% 1.53/1.70 (b(s(elem!1), s(s(s(s(s(s(z))))))) <=> b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[5622, 5932])).
% 1.53/1.70 tff(8699,plain,
% 1.53/1.70 ((~b(s(elem!1), s(s(s(s(s(s(z)))))))) <=> (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8698])).
% 1.53/1.70 tff(8700,assumption,(r(elem!1, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.53/1.70 tff(8701,assumption,(r(s(s(s(s(s(s(z)))))), s(elem!1))), introduced(assumption)).
% 1.53/1.70 tff(8702,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8703,plain,
% 1.53/1.70 (((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8704,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8703])).
% 1.53/1.70 tff(8705,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8704, 8702])).
% 1.53/1.70 tff(8706,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8707,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8706, 8705])).
% 1.53/1.70 tff(8708,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8707, 28, 6495, 8700, 8701])).
% 1.53/1.70 tff(8709,plain,((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8710,plain,
% 1.53/1.70 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8709, 8700, 6495])).
% 1.53/1.70 tff(8711,plain,
% 1.53/1.70 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.70 inference(symmetry,[status(thm)],[6180])).
% 1.53/1.70 tff(8712,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 1.53/1.70 tff(8713,plain,
% 1.53/1.70 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8712, 8711])).
% 1.53/1.70 tff(8714,assumption,(~r(s(s(s(s(s(s(z)))))), s(elem!1))), introduced(assumption)).
% 1.53/1.70 tff(8715,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8714, 8713])).
% 1.53/1.70 tff(8716,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | r(s(s(s(s(s(s(z)))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8717,plain,
% 1.53/1.70 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8716, 8710])).
% 1.53/1.70 tff(8718,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5866, 8717])).
% 1.53/1.70 tff(8719,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8718, 6179])).
% 1.53/1.70 tff(8720,assumption,(b(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.53/1.70 tff(8721,assumption,(b(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.53/1.70 tff(8722,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8723,plain,
% 1.53/1.70 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8724,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8723])).
% 1.53/1.70 tff(8725,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8724, 8722])).
% 1.53/1.70 tff(8726,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8727,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8726, 8725])).
% 1.53/1.70 tff(8728,plain,
% 1.53/1.70 ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8727, 154, 5964, 8721, 8720])).
% 1.53/1.70 tff(8729,plain,
% 1.53/1.70 (~b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8728, 8719])).
% 1.53/1.70 tff(8730,plain,
% 1.53/1.70 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8729, 8699])).
% 1.53/1.70 tff(8731,plain,
% 1.53/1.70 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5832, 8730])).
% 1.53/1.70 tff(8732,plain,
% 1.53/1.70 (r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8731, 8697])).
% 1.53/1.70 tff(8733,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8734,plain,
% 1.53/1.70 (((~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8735,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8734])).
% 1.53/1.70 tff(8736,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8735, 8733])).
% 1.53/1.70 tff(8737,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8738,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8737, 8736])).
% 1.53/1.70 tff(8739,plain,
% 1.53/1.70 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8738, 28, 6495, 8700])).
% 1.53/1.70 tff(8740,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8739, 8732])).
% 1.53/1.70 tff(8741,plain,((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8742,plain,
% 1.53/1.70 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8741, 8695, 8677, 8378, 8308])).
% 1.53/1.70 tff(8743,plain,
% 1.53/1.70 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8742, 8654])).
% 1.53/1.70 tff(8744,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[6094, 8743])).
% 1.53/1.70 tff(8745,assumption,(b(elem!1, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.53/1.70 tff(8746,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8745, 5673])).
% 1.53/1.70 tff(8747,assumption,(~b(elem!1, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.53/1.70 tff(8748,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8747, 8746])).
% 1.53/1.70 tff(8749,plain,((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8750,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8749, 8744])).
% 1.53/1.70 tff(8751,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 1.53/1.70 tff(8752,plain,
% 1.53/1.70 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8751, 6179])).
% 1.53/1.70 tff(8753,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.53/1.70 tff(8754,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8755,plain,
% 1.53/1.70 (((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8756,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[8755])).
% 1.53/1.70 tff(8757,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[8756, 8754])).
% 1.53/1.70 tff(8758,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(8759,plain,
% 1.53/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[8758, 8757])).
% 1.53/1.70 tff(8760,plain,
% 1.53/1.70 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8759, 154, 6105, 6103, 6151, 8753])).
% 1.53/1.70 tff(8761,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8760, 8752])).
% 1.53/1.70 tff(8762,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(8763,plain,
% 1.53/1.70 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[8762, 8608, 8750, 8686, 8690])).
% 1.53/1.70 tff(8764,plain,
% 1.53/1.70 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[5866, 8763])).
% 1.53/1.70 tff(8765,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.53/1.70 tff(8766,plain,
% 1.53/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(8767,plain,
% 1.53/1.70 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8768,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8767])).
% 1.53/1.71 tff(8769,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8768, 8766])).
% 1.53/1.71 tff(8770,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8771,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8770, 8769])).
% 1.53/1.71 tff(8772,plain,
% 1.53/1.71 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8771, 28, 5938, 8765])).
% 1.53/1.71 tff(8773,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8772, 8713])).
% 1.53/1.71 tff(8774,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8775,plain,
% 1.53/1.71 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8774, 8764, 8689])).
% 1.53/1.71 tff(8776,plain,
% 1.53/1.71 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5962, 8775])).
% 1.53/1.71 tff(8777,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8778,plain,
% 1.53/1.71 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8779,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8778])).
% 1.53/1.71 tff(8780,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8779, 8777])).
% 1.53/1.71 tff(8781,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8782,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8781, 8780])).
% 1.53/1.71 tff(8783,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8782, 154, 8641, 8634, 8750, 8776, 8686])).
% 1.53/1.71 tff(8784,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8785,plain,
% 1.53/1.71 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8784, 8433, 13, 144, 231])).
% 1.53/1.71 tff(8786,plain,
% 1.53/1.71 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[564, 8785])).
% 1.53/1.71 tff(8787,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8788,plain,
% 1.53/1.71 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8789,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8788])).
% 1.53/1.71 tff(8790,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8789, 8787])).
% 1.53/1.71 tff(8791,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8792,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8791, 8790])).
% 1.53/1.71 tff(8793,plain,
% 1.53/1.71 ((~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8792, 154, 144, 8786, 8378])).
% 1.53/1.71 tff(8794,plain,
% 1.53/1.71 (~b(s(elem!1), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8793, 8377])).
% 1.53/1.71 tff(8795,plain,
% 1.53/1.71 (~b(s(z), s(s(s(z))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8794, 5628])).
% 1.53/1.71 tff(8796,plain,
% 1.53/1.71 (r(s(z), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[252, 8795])).
% 1.53/1.71 tff(8797,plain,
% 1.53/1.71 (~b(s(s(s(z))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[764, 8786, 144, 8375, 231])).
% 1.53/1.71 tff(8798,plain,
% 1.53/1.71 (r(s(s(s(z))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[818, 8797])).
% 1.53/1.71 tff(8799,plain,
% 1.53/1.71 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8794, 8436])).
% 1.53/1.71 tff(8800,plain,
% 1.53/1.71 (r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8445, 8799])).
% 1.53/1.71 tff(8801,plain,
% 1.53/1.71 (~r(elem!1, s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[7736, 8800, 5655])).
% 1.53/1.71 tff(8802,plain,
% 1.53/1.71 (b(elem!1, s(s(s(elem!1))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8232, 8801])).
% 1.53/1.71 tff(8803,plain,
% 1.53/1.71 (~r(z, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1976, 8796, 13])).
% 1.53/1.71 tff(8804,plain,
% 1.53/1.71 (b(z, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[648, 8803])).
% 1.53/1.71 tff(8805,plain,
% 1.53/1.71 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.71 tff(8806,plain,
% 1.53/1.71 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.53/1.71 inference(symmetry,[status(thm)],[8805])).
% 1.53/1.71 tff(8807,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8235, 5624, 5620])).
% 1.53/1.71 tff(8808,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8809,plain,
% 1.53/1.71 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8810,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8809])).
% 1.53/1.71 tff(8811,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8810, 8808])).
% 1.53/1.71 tff(8812,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8813,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8812, 8811])).
% 1.53/1.71 tff(8814,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8813, 28, 345, 780, 273])).
% 1.53/1.71 tff(8815,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8816,plain,
% 1.53/1.71 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8815, 345, 273])).
% 1.53/1.71 tff(8817,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[496, 8816])).
% 1.53/1.71 tff(8818,plain,
% 1.53/1.71 (~b(z, s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[5234, 8817, 2536, 419, 566])).
% 1.53/1.71 tff(8819,plain,
% 1.53/1.71 (r(z, s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[191, 8818])).
% 1.53/1.71 tff(8820,plain,
% 1.53/1.71 (~r(z, s(s(z)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2439, 8819, 16])).
% 1.53/1.71 tff(8821,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.71 inference(symmetry,[status(thm)],[8414])).
% 1.53/1.71 tff(8822,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[443, 8821])).
% 1.53/1.71 tff(8823,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[6060, 8822])).
% 1.53/1.71 tff(8824,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8825,plain,
% 1.53/1.71 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8824, 5637])).
% 1.53/1.71 tff(8826,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8825, 8817])).
% 1.53/1.71 tff(8827,plain,
% 1.53/1.71 (~r(s(s(z)), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1232, 8826, 16, 566, 143])).
% 1.53/1.71 tff(8828,plain,
% 1.53/1.71 (b(s(s(z)), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[122, 8827])).
% 1.53/1.71 tff(8829,plain,
% 1.53/1.71 (~b(z, s(s(z)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1736, 8828, 8249, 231, 1726])).
% 1.53/1.71 tff(8830,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[64, 8829, 8820])).
% 1.53/1.71 tff(8831,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8832,plain,
% 1.53/1.71 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8831, 1726, 231, 16, 566, 143, 13, 273])).
% 1.53/1.71 tff(8833,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[441, 8832])).
% 1.53/1.71 tff(8834,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8833, 8807])).
% 1.53/1.71 tff(8835,plain,
% 1.53/1.71 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5621])).
% 1.53/1.71 tff(8836,plain,
% 1.53/1.71 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.71 tff(8837,plain,
% 1.53/1.71 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8836, 8835])).
% 1.53/1.71 tff(8838,plain,
% 1.53/1.71 (b(elem!1, s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1726, 8837])).
% 1.53/1.71 tff(8839,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8840,plain,
% 1.53/1.71 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8841,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8840])).
% 1.53/1.71 tff(8842,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8841, 8839])).
% 1.53/1.71 tff(8843,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8844,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8843, 8842])).
% 1.53/1.71 tff(8845,plain,
% 1.53/1.71 (~b(s(s(s(s(z)))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8844, 154, 8838, 8073, 566, 8834])).
% 1.53/1.71 tff(8846,plain,
% 1.53/1.71 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.53/1.71 inference(symmetry,[status(thm)],[8057])).
% 1.53/1.71 tff(8847,plain,
% 1.53/1.71 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.53/1.71 inference(transitivity,[status(thm)],[8059, 8846])).
% 1.53/1.71 tff(8848,plain,
% 1.53/1.71 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8847])).
% 1.53/1.71 tff(8849,plain,
% 1.53/1.71 (~(s(s(s(s(z)))) = elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[185, 8848])).
% 1.53/1.71 tff(8850,plain,
% 1.53/1.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8851,plain,
% 1.53/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8852,plain,
% 1.53/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8851, 8850])).
% 1.53/1.71 tff(8853,plain,
% 1.53/1.71 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8852, 60])).
% 1.53/1.71 tff(8854,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8853, 8849])).
% 1.53/1.71 tff(8855,plain,
% 1.53/1.71 (r(s(s(s(s(z)))), elem!1)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8854, 8845])).
% 1.53/1.71 tff(8856,plain,
% 1.53/1.71 (r(s(s(s(s(z)))), z)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8855, 8806])).
% 1.53/1.71 tff(8857,plain,
% 1.53/1.71 (~r(s(s(z)), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2484, 8856, 13, 8249])).
% 1.53/1.71 tff(8858,plain,
% 1.53/1.71 (b(s(s(z)), z)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[122, 8857])).
% 1.53/1.71 tff(8859,plain,
% 1.53/1.71 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.71 tff(8860,plain,
% 1.53/1.71 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 1.53/1.71 inference(symmetry,[status(thm)],[8859])).
% 1.53/1.71 tff(8861,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8862,plain,
% 1.53/1.71 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8863,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8862])).
% 1.53/1.71 tff(8864,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8863, 8861])).
% 1.53/1.71 tff(8865,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8866,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8865, 8864])).
% 1.53/1.71 tff(8867,plain,
% 1.53/1.71 (~b(elem!1, s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8866, 154, 8838, 8073, 566, 8834])).
% 1.53/1.71 tff(8868,plain,
% 1.53/1.71 (r(elem!1, s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8062, 8867])).
% 1.53/1.71 tff(8869,plain,
% 1.53/1.71 (r(z, s(s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8868, 8860])).
% 1.53/1.71 tff(8870,plain,
% 1.53/1.71 (~r(z, s(s(z)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2439, 8869, 16])).
% 1.53/1.71 tff(8871,plain,
% 1.53/1.71 (b(z, s(s(z)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[64, 8870])).
% 1.53/1.71 tff(8872,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1736, 8871, 8858, 8249, 231, 1726])).
% 1.53/1.71 tff(8873,plain,((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(8874,plain,
% 1.53/1.71 (~b(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8873, 231, 8433, 13, 8449, 8786, 8382, 8796])).
% 1.53/1.71 tff(8875,plain,
% 1.53/1.71 (r(z, s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1181, 8874])).
% 1.53/1.71 tff(8876,plain,
% 1.53/1.71 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[742, 8875, 8786, 8382, 8804])).
% 1.53/1.71 tff(8877,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[318, 8876])).
% 1.53/1.71 tff(8878,plain,
% 1.53/1.71 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8877, 8236])).
% 1.53/1.71 tff(8879,plain,
% 1.53/1.71 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8599, 8878, 8583, 8579, 8576])).
% 1.53/1.71 tff(8880,plain,
% 1.53/1.71 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8601, 8879])).
% 1.53/1.71 tff(8881,plain,
% 1.53/1.71 (r(s(s(s(z))), s(elem!1))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8798, 8688])).
% 1.53/1.71 tff(8882,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8883,plain,
% 1.53/1.71 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(8884,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[8883])).
% 1.53/1.71 tff(8885,plain,
% 1.53/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[8884, 8882])).
% 1.53/1.71 tff(8886,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(z))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(8887,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8886, 8885])).
% 1.53/1.71 tff(8888,plain,
% 1.53/1.71 (~r(s(s(s(z))), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[8887, 28, 8881])).
% 1.53/1.71 tff(8889,plain,
% 1.53/1.71 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[8888, 8459])).
% 1.53/1.71 tff(8890,plain,
% 1.53/1.71 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[4202, 8889, 8457])).
% 1.53/1.71 tff(8891,plain,
% 1.53/1.71 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.71 tff(8892,plain,
% 1.53/1.71 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 1.53/1.71 inference(symmetry,[status(thm)],[8891])).
% 1.53/1.71 tff(8893,plain,
% 1.53/1.71 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[5596])).
% 1.53/1.72 tff(8894,plain,
% 1.53/1.72 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8893, 8892])).
% 1.53/1.72 tff(8895,plain,
% 1.53/1.72 (r(z, s(s(z)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[6479, 8894])).
% 1.53/1.72 tff(8896,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8897,plain,
% 1.53/1.72 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8898,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8897])).
% 1.53/1.72 tff(8899,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8898, 8896])).
% 1.53/1.72 tff(8900,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8901,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8900, 8899])).
% 1.53/1.72 tff(8902,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8901, 28, 6479, 6913, 7945])).
% 1.53/1.72 tff(8903,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8904,plain,
% 1.53/1.72 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8903, 6479, 7945])).
% 1.53/1.72 tff(8905,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8632, 8904])).
% 1.53/1.72 tff(8906,plain,
% 1.53/1.72 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8493])).
% 1.53/1.72 tff(8907,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 1.53/1.72 inference(symmetry,[status(thm)],[8906])).
% 1.53/1.72 tff(8908,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[6848])).
% 1.53/1.72 tff(8909,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.53/1.72 inference(transitivity,[status(thm)],[8908, 8907])).
% 1.53/1.72 tff(8910,plain,
% 1.53/1.72 (b(s(s(s(s(z)))), z)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[6963, 8909])).
% 1.53/1.72 tff(8911,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.53/1.72 tff(8912,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8911, 8910])).
% 1.53/1.72 tff(8913,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(s(z)))), z) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8914,plain,
% 1.53/1.72 (b(s(s(s(s(z)))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8913, 8905, 4213])).
% 1.53/1.72 tff(8915,plain,
% 1.53/1.72 (~b(z, s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2470, 8914, 13, 566, 820, 273])).
% 1.53/1.72 tff(8916,plain,
% 1.53/1.72 (r(z, s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[191, 8915])).
% 1.53/1.72 tff(8917,plain,
% 1.53/1.72 (~r(z, s(s(z)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2439, 8916, 16])).
% 1.53/1.72 tff(8918,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8917, 8895])).
% 1.53/1.72 tff(8919,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8920,plain,
% 1.53/1.72 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8919, 8433, 13, 8786, 8798, 8796, 8890, 8880])).
% 1.53/1.72 tff(8921,plain,
% 1.53/1.72 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8619])).
% 1.53/1.72 tff(8922,plain,
% 1.53/1.72 (~(elem!1 = s(s(elem!1)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[366, 8921])).
% 1.53/1.72 tff(8923,plain,
% 1.53/1.72 (b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[6644, 8922])).
% 1.53/1.72 tff(8924,plain,
% 1.53/1.72 (b(elem!1, s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8923, 8920])).
% 1.53/1.72 tff(8925,plain,
% 1.53/1.72 (~b(s(s(elem!1)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8230, 8924, 5651, 8381, 8802])).
% 1.53/1.72 tff(8926,plain,
% 1.53/1.72 (~b(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5683, 8925])).
% 1.53/1.72 tff(8927,plain,
% 1.53/1.72 (r(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[122, 8926])).
% 1.53/1.72 tff(8928,plain,
% 1.53/1.72 (~r(s(s(s(s(z)))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2484, 8927, 13, 8249])).
% 1.53/1.72 tff(8929,plain,
% 1.53/1.72 (b(s(s(s(s(z)))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[206, 8928])).
% 1.53/1.72 tff(8930,plain,
% 1.53/1.72 (~r(z, s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[913, 8927, 8433])).
% 1.53/1.72 tff(8931,plain,
% 1.53/1.72 (b(z, s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[191, 8930])).
% 1.53/1.72 tff(8932,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2470, 8931, 8929, 13, 8786, 8798, 8796])).
% 1.53/1.72 tff(8933,plain,((~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8934,plain,
% 1.53/1.72 (~b(s(s(z)), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8933, 144, 13])).
% 1.53/1.72 tff(8935,plain,
% 1.53/1.72 (r(s(s(z)), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[296, 8934])).
% 1.53/1.72 tff(8936,plain,
% 1.53/1.72 (~b(z, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2316, 171, 13])).
% 1.53/1.72 tff(8937,plain,
% 1.53/1.72 (r(z, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1181, 8936])).
% 1.53/1.72 tff(8938,plain,
% 1.53/1.72 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1990, 3707, 13, 299, 8937, 2183])).
% 1.53/1.72 tff(8939,plain,
% 1.53/1.72 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[804, 1685, 8249, 66, 1270])).
% 1.53/1.72 tff(8940,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1259, 8939, 8938])).
% 1.53/1.72 tff(8941,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8942,plain,
% 1.53/1.72 (~r(s(s(s(z))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8941, 66, 13, 8935])).
% 1.53/1.72 tff(8943,plain,
% 1.53/1.72 (b(s(s(s(z))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[169, 8942])).
% 1.53/1.72 tff(8944,plain,
% 1.53/1.72 (b(s(s(s(elem!1))), z)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8943, 6197])).
% 1.53/1.72 tff(8945,plain,
% 1.53/1.72 (~r(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[702, 8935, 13])).
% 1.53/1.72 tff(8946,plain,
% 1.53/1.72 (b(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[122, 8945])).
% 1.53/1.72 tff(8947,plain,
% 1.53/1.72 (b(s(s(elem!1)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5683, 8946])).
% 1.53/1.72 tff(8948,plain,
% 1.53/1.72 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5622, 5592])).
% 1.53/1.72 tff(8949,plain,
% 1.53/1.72 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8948])).
% 1.53/1.72 tff(8950,plain,
% 1.53/1.72 (~b(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1512, 8943, 8249, 144, 8946])).
% 1.53/1.72 tff(8951,plain,
% 1.53/1.72 (r(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[252, 8950])).
% 1.53/1.72 tff(8952,plain,
% 1.53/1.72 (r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8951, 8949])).
% 1.53/1.72 tff(8953,plain,
% 1.53/1.72 (~r(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[7736, 8952, 5655])).
% 1.53/1.72 tff(8954,plain,
% 1.53/1.72 (b(elem!1, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8232, 8953])).
% 1.53/1.72 tff(8955,plain,
% 1.53/1.72 (~b(elem!1, s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8230, 8954, 5651, 8947, 8944])).
% 1.53/1.72 tff(8956,plain,
% 1.53/1.72 (r(elem!1, s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8923, 8955])).
% 1.53/1.72 tff(8957,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5590])).
% 1.53/1.72 tff(8958,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8957])).
% 1.53/1.72 tff(8959,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5592])).
% 1.53/1.72 tff(8960,plain,
% 1.53/1.72 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8959])).
% 1.53/1.72 tff(8961,plain,
% 1.53/1.72 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8960, 8958])).
% 1.53/1.72 tff(8962,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[66, 8961])).
% 1.53/1.72 tff(8963,plain,
% 1.53/1.72 (~r(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8473, 8953])).
% 1.53/1.72 tff(8964,plain,
% 1.53/1.72 (b(z, s(s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[3977, 8963])).
% 1.53/1.72 tff(8965,plain,
% 1.53/1.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8484, 8964, 5651, 8947, 8944])).
% 1.53/1.72 tff(8966,plain,
% 1.53/1.72 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5592])).
% 1.53/1.72 tff(8967,plain,
% 1.53/1.72 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8966])).
% 1.53/1.72 tff(8968,plain,
% 1.53/1.72 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(z)) = s(s(s(z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5596])).
% 1.53/1.72 tff(8969,plain,
% 1.53/1.72 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.53/1.72 inference(symmetry,[status(thm)],[8968])).
% 1.53/1.72 tff(8970,plain,
% 1.53/1.72 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8969, 8967, 7096])).
% 1.53/1.72 tff(8971,plain,
% 1.53/1.72 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8970])).
% 1.53/1.72 tff(8972,plain,
% 1.53/1.72 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[98, 8971])).
% 1.53/1.72 tff(8973,plain,
% 1.53/1.72 (b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[7934, 8972])).
% 1.53/1.72 tff(8974,plain,
% 1.53/1.72 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8973, 8965])).
% 1.53/1.72 tff(8975,plain,
% 1.53/1.72 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[7953, 8974, 8962])).
% 1.53/1.72 tff(8976,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8601, 8975])).
% 1.53/1.72 tff(8977,plain,
% 1.53/1.72 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.53/1.72 inference(commutativity,[status(thm)],[])).
% 1.53/1.72 tff(8978,plain,
% 1.53/1.72 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.53/1.72 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.72 tff(8979,plain,
% 1.53/1.72 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8978, 8977])).
% 1.53/1.72 tff(8980,plain,
% 1.53/1.72 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8979])).
% 1.53/1.72 tff(8981,plain,
% 1.53/1.72 (~(elem!1 = s(z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[266, 8980])).
% 1.53/1.72 tff(8982,plain,
% 1.53/1.72 ((~(s(s(s(s(elem!1)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[4255])).
% 1.53/1.72 tff(8983,plain,
% 1.53/1.72 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[4068, 8982])).
% 1.53/1.72 tff(8984,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.53/1.72 tff(8985,plain,
% 1.53/1.72 (~b(s(s(elem!1)), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8599, 444, 8590, 505, 8591])).
% 1.53/1.72 tff(8986,plain,
% 1.53/1.72 (r(s(s(elem!1)), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[7870, 8985])).
% 1.53/1.72 tff(8987,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.53/1.72 tff(8988,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8989,plain,
% 1.53/1.72 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8990,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[8989])).
% 1.53/1.72 tff(8991,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[8990, 8988])).
% 1.53/1.72 tff(8992,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8993,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8992, 8991])).
% 1.53/1.72 tff(8994,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8993, 28, 6479, 8987, 7856])).
% 1.53/1.72 tff(8995,plain,((~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(8996,plain,
% 1.53/1.72 (~r(elem!1, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8995, 8986, 6479])).
% 1.53/1.72 tff(8997,plain,
% 1.53/1.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(8998,plain,
% 1.53/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(8999,plain,
% 1.53/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[8998, 8997])).
% 1.53/1.72 tff(9000,plain,
% 1.53/1.72 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8999, 60])).
% 1.53/1.72 tff(9001,plain,
% 1.53/1.72 (b(elem!1, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9000, 8996, 8984])).
% 1.53/1.72 tff(9002,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(9003,plain,
% 1.53/1.72 (((~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))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(9004,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[9003])).
% 1.53/1.72 tff(9005,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[9004, 9002])).
% 1.53/1.72 tff(9006,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(9007,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[9006, 9005])).
% 1.53/1.72 tff(9008,plain,
% 1.53/1.72 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9007, 154, 9001, 8591, 8590, 444])).
% 1.53/1.72 tff(9009,plain,
% 1.53/1.72 ((elem!1 = s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4284, 60, 9008])).
% 1.53/1.72 tff(9010,plain,
% 1.53/1.72 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9009, 8983])).
% 1.53/1.72 tff(9011,plain,
% 1.53/1.72 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4070, 4068])).
% 1.53/1.72 tff(9012,plain,
% 1.53/1.72 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[4053, 9011])).
% 1.53/1.72 tff(9013,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.72 tff(9014,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(9015,plain,
% 1.53/1.72 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(9016,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[9015])).
% 1.53/1.72 tff(9017,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[9016, 9014])).
% 1.53/1.72 tff(9018,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(9019,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[9018, 9017])).
% 1.53/1.72 tff(9020,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9019, 154, 8591, 8590, 505, 9013, 444])).
% 1.53/1.72 tff(9021,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(9022,plain,
% 1.53/1.72 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9021, 444, 8590, 505, 8591])).
% 1.53/1.72 tff(9023,plain,
% 1.53/1.72 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[7668, 9022, 9012])).
% 1.53/1.72 tff(9024,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(9025,plain,
% 1.53/1.72 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(9026,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[9025])).
% 1.53/1.72 tff(9027,plain,
% 1.53/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[9026, 9024])).
% 1.53/1.72 tff(9028,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(9029,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[9028, 9027])).
% 1.53/1.72 tff(9030,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9029, 28, 6479, 9023, 9010])).
% 1.53/1.72 tff(9031,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(9032,plain,
% 1.53/1.72 ((~b(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9031, 8631, 8981])).
% 1.53/1.72 tff(9033,plain,
% 1.53/1.72 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[9032, 8976, 8583, 8579, 8956])).
% 1.53/1.72 tff(9034,plain,
% 1.53/1.72 (r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[441, 9033])).
% 1.53/1.72 tff(9035,plain,
% 1.53/1.72 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8815, 9034, 8951])).
% 1.53/1.72 tff(9036,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[496, 9035])).
% 1.53/1.72 tff(9037,plain,
% 1.53/1.72 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[8825, 9036])).
% 1.53/1.72 tff(9038,plain,
% 1.53/1.72 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5459, 9037, 8249, 144, 8375])).
% 1.53/1.72 tff(9039,plain,
% 1.53/1.72 (r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1259, 9038])).
% 1.53/1.72 tff(9040,plain,
% 1.53/1.72 (~r(s(s(s(z))), s(s(z)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[75, 9039, 66])).
% 1.53/1.72 tff(9041,plain,
% 1.53/1.72 (b(s(s(s(z))), s(s(z)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[104, 9040])).
% 1.53/1.72 tff(9042,plain,
% 1.53/1.72 (~r(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1976, 8951, 13])).
% 1.53/1.72 tff(9043,plain,
% 1.53/1.72 (b(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[648, 9042])).
% 1.53/1.72 tff(9044,plain,
% 1.53/1.72 (~r(z, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[5078, 9043, 8935, 8943, 8946, 8951])).
% 1.53/1.72 tff(9045,plain,
% 1.53/1.72 (b(z, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1181, 9044])).
% 1.53/1.72 tff(9046,plain,
% 1.53/1.72 (~b(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2825, 9039, 13, 9045])).
% 1.53/1.72 tff(9047,plain,
% 1.53/1.72 (r(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[818, 9046])).
% 1.53/1.72 tff(9048,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2354, 9047, 9041, 144, 8935, 9034])).
% 1.53/1.72 tff(9049,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(9050,plain,
% 1.53/1.72 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9049, 144, 13])).
% 1.53/1.73 tff(9051,plain,
% 1.53/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[564, 9050])).
% 1.53/1.73 tff(9052,plain,
% 1.53/1.73 (~b(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1512, 232, 8249, 144, 8946])).
% 1.53/1.73 tff(9053,plain,
% 1.53/1.73 (r(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[169, 9052])).
% 1.53/1.73 tff(9054,plain,
% 1.53/1.73 (~b(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2316, 9053, 13])).
% 1.53/1.73 tff(9055,plain,
% 1.53/1.73 (r(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1181, 9054])).
% 1.53/1.73 tff(9056,plain,
% 1.53/1.73 (~r(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2308, 9053, 13, 9051, 1283])).
% 1.53/1.73 tff(9057,plain,
% 1.53/1.73 (b(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[64, 9056])).
% 1.53/1.73 tff(9058,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2972, 9057, 9055, 1283, 232, 8375, 8946, 9053])).
% 1.53/1.73 tff(9059,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(9060,plain,
% 1.53/1.73 (~b(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9059, 1283, 13, 144])).
% 1.53/1.73 tff(9061,plain,
% 1.53/1.73 (r(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[252, 9060])).
% 1.53/1.73 tff(9062,plain,
% 1.53/1.73 (~r(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[281, 9061, 13])).
% 1.53/1.73 tff(9063,plain,
% 1.53/1.73 (b(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[169, 9062])).
% 1.53/1.73 tff(9064,plain,
% 1.53/1.73 (~b(s(s(s(s(z)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2553, 9063, 1283, 144, 9051])).
% 1.53/1.73 tff(9065,plain,
% 1.53/1.73 (r(s(s(s(s(z)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[206, 9064])).
% 1.53/1.73 tff(9066,plain,
% 1.53/1.73 (r(s(s(s(s(z)))), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9065, 8805])).
% 1.53/1.73 tff(9067,plain,
% 1.53/1.73 (~r(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1623, 9061, 13, 1283, 8375, 8935])).
% 1.53/1.73 tff(9068,plain,
% 1.53/1.73 (b(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1181, 9067])).
% 1.53/1.73 tff(9069,plain,
% 1.53/1.73 (~b(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2843, 9065, 13, 9068])).
% 1.53/1.73 tff(9070,plain,
% 1.53/1.73 (r(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[818, 9069])).
% 1.53/1.73 tff(9071,plain,
% 1.53/1.73 (~r(s(s(s(z))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[865, 9070, 8935])).
% 1.53/1.73 tff(9072,plain,
% 1.53/1.73 (b(s(s(s(z))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[104, 9071])).
% 1.53/1.73 tff(9073,plain,
% 1.53/1.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4526, 9072, 9051, 144, 1283])).
% 1.53/1.73 tff(9074,plain,
% 1.53/1.73 (r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[229, 9073])).
% 1.53/1.73 tff(9075,plain,
% 1.53/1.73 (~b(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2336, 9070, 8249, 8946, 9068, 9063])).
% 1.53/1.73 tff(9076,plain,
% 1.53/1.73 (r(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[64, 9075])).
% 1.53/1.73 tff(9077,plain,
% 1.53/1.73 (r(elem!1, s(s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9076, 8891])).
% 1.53/1.73 tff(9078,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9079,plain,
% 1.53/1.73 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9080,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9079])).
% 1.53/1.73 tff(9081,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[9080, 9078])).
% 1.53/1.73 tff(9082,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(9083,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9082, 9081])).
% 1.53/1.73 tff(9084,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9083, 28, 9077, 9074, 9066])).
% 1.53/1.73 tff(9085,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(9086,plain,
% 1.53/1.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9085, 144, 13])).
% 1.53/1.73 tff(9087,plain,
% 1.53/1.73 (r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1259, 9086])).
% 1.53/1.73 tff(9088,plain,
% 1.53/1.73 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[307, 9087, 8935])).
% 1.53/1.73 tff(9089,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[318, 9088])).
% 1.53/1.73 tff(9090,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9089, 5625])).
% 1.53/1.73 tff(9091,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[585, 1685, 1270, 144, 8375, 9087, 9051])).
% 1.53/1.73 tff(9092,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(9093,plain,
% 1.53/1.73 (~r(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9092, 144, 13])).
% 1.53/1.73 tff(9094,plain,
% 1.53/1.73 (b(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[169, 9093])).
% 1.53/1.73 tff(9095,plain,
% 1.53/1.73 (~b(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1512, 9094, 8249, 144, 8946])).
% 1.53/1.73 tff(9096,plain,
% 1.53/1.73 (r(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[252, 9095])).
% 1.53/1.73 tff(9097,plain,
% 1.53/1.73 (~r(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1976, 9096, 13])).
% 1.53/1.73 tff(9098,plain,
% 1.53/1.73 (b(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[648, 9097])).
% 1.53/1.73 tff(9099,plain,
% 1.53/1.73 (~r(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5078, 9098, 8935, 9094, 8946, 9096])).
% 1.53/1.73 tff(9100,plain,
% 1.53/1.73 (b(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1181, 9099])).
% 1.53/1.73 tff(9101,plain,
% 1.53/1.73 (~b(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2825, 9100, 13, 9087])).
% 1.53/1.73 tff(9102,plain,
% 1.53/1.73 (r(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[818, 9101])).
% 1.53/1.73 tff(9103,plain,
% 1.53/1.73 (~b(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2336, 9102, 8249, 8946, 9100, 9094])).
% 1.53/1.73 tff(9104,plain,
% 1.53/1.73 (r(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[64, 9103])).
% 1.53/1.73 tff(9105,plain,
% 1.53/1.73 (~r(z, s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2439, 9104, 9087])).
% 1.53/1.73 tff(9106,plain,
% 1.53/1.73 (b(z, s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[191, 9105])).
% 1.53/1.73 tff(9107,plain,
% 1.53/1.73 (b(elem!1, s(s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9106, 5747])).
% 1.53/1.73 tff(9108,plain,
% 1.53/1.73 (b(s(s(s(z))), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9094, 6196])).
% 1.53/1.73 tff(9109,plain,
% 1.53/1.73 (b(elem!1, s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9100, 8837])).
% 1.53/1.73 tff(9110,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8866, 154, 9109, 9108, 9107, 9051, 9090])).
% 1.53/1.73 tff(9111,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(9112,plain,
% 1.53/1.73 (~b(s(s(z)), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9111, 13])).
% 1.53/1.73 tff(9113,plain,
% 1.53/1.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[612, 16, 6200])).
% 1.53/1.73 tff(9114,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[343, 9113])).
% 1.53/1.73 tff(9115,plain,
% 1.53/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[132, 16, 6200])).
% 1.53/1.73 tff(9116,plain,
% 1.53/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[564, 9115])).
% 1.53/1.73 tff(9117,plain,
% 1.53/1.73 ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[6178])).
% 1.53/1.73 tff(9118,plain,
% 1.53/1.73 (r(elem!1, s(s(s(s(s(s(elem!1))))))) <=> r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[8653])).
% 1.53/1.73 tff(9119,plain,
% 1.53/1.73 (b(elem!1, s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[5673])).
% 1.53/1.73 tff(9120,plain,
% 1.53/1.73 ((~b(elem!1, s(s(s(s(s(s(z)))))))) <=> (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9119])).
% 1.53/1.73 tff(9121,plain,
% 1.53/1.73 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5590])).
% 1.53/1.73 tff(9122,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[9121])).
% 1.53/1.73 tff(9123,plain,
% 1.53/1.73 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[615, 9122])).
% 1.53/1.73 tff(9124,plain,
% 1.53/1.73 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1016, 5645, 13])).
% 1.53/1.73 tff(9125,plain,
% 1.53/1.73 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[418, 9124])).
% 1.53/1.73 tff(9126,plain,
% 1.53/1.73 (~b(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5234, 9125, 9123, 566, 8364])).
% 1.53/1.73 tff(9127,plain,
% 1.53/1.73 (r(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[648, 9126])).
% 1.53/1.73 tff(9128,plain,
% 1.53/1.73 (~r(s(s(z)), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2080, 9127, 124])).
% 1.53/1.73 tff(9129,plain,
% 1.53/1.73 (b(s(s(z)), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[122, 9128])).
% 1.53/1.73 tff(9130,plain,
% 1.53/1.73 (b(s(s(z)), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9129, 5751])).
% 1.53/1.73 tff(9131,plain,
% 1.53/1.73 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[6186])).
% 1.53/1.73 tff(9132,plain,
% 1.53/1.73 ((~b(elem!1, s(s(s(z))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9131])).
% 1.53/1.73 tff(9133,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), elem!1)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[5636, 5743])).
% 1.53/1.73 tff(9134,plain,
% 1.53/1.73 (b(elem!1, s(s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8364, 5747])).
% 1.53/1.73 tff(9135,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9136,plain,
% 1.53/1.73 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9137,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9136])).
% 1.53/1.73 tff(9138,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[9137, 9135])).
% 1.53/1.73 tff(9139,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(9140,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9139, 9138])).
% 1.53/1.73 tff(9141,plain,
% 1.53/1.73 (~b(elem!1, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9140, 154, 615, 9134, 9133, 566])).
% 1.53/1.73 tff(9142,plain,
% 1.53/1.73 (~b(elem!1, s(s(s(elem!1))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9141, 9132])).
% 1.53/1.73 tff(9143,plain,
% 1.53/1.73 (r(elem!1, s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8232, 9142])).
% 1.53/1.73 tff(9144,plain,
% 1.53/1.73 (~r(s(s(z)), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[3823, 5645, 1476])).
% 1.53/1.73 tff(9145,plain,
% 1.53/1.73 (b(s(s(z)), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[296, 9144])).
% 1.53/1.73 tff(9146,plain,
% 1.53/1.73 (b(s(s(elem!1)), s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9145, 8255])).
% 1.53/1.73 tff(9147,plain,
% 1.53/1.73 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.53/1.73 inference(transitivity,[status(thm)],[6195, 6193])).
% 1.53/1.73 tff(9148,plain,
% 1.53/1.73 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(elem!1))), z))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9147])).
% 1.53/1.73 tff(9149,plain,
% 1.53/1.73 (~b(s(s(s(z))), elem!1)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8347, 154, 615, 9134, 9133, 566])).
% 1.53/1.73 tff(9150,plain,
% 1.53/1.73 (~b(s(s(s(elem!1))), z)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9149, 9148])).
% 1.53/1.73 tff(9151,plain,
% 1.53/1.73 (r(s(s(s(elem!1))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[4159, 9150])).
% 1.53/1.73 tff(9152,plain,
% 1.53/1.73 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[8295, 9151, 8254, 8250, 5655, 9146])).
% 1.53/1.73 tff(9153,plain,
% 1.53/1.73 ((~r(elem!1, s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[6653, 8922])).
% 1.53/1.73 tff(9154,plain,
% 1.53/1.73 (b(elem!1, s(s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9153, 9152, 9143])).
% 1.53/1.73 tff(9155,plain,
% 1.53/1.73 (b(elem!1, s(s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9154, 5687])).
% 1.53/1.73 tff(9156,plain,
% 1.53/1.73 (b(s(s(z)), s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9145, 8310])).
% 1.53/1.73 tff(9157,plain,
% 1.53/1.73 (b(s(elem!1), s(s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8249, 8303])).
% 1.53/1.73 tff(9158,plain,
% 1.53/1.73 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.53/1.73 inference(symmetry,[status(thm)],[6196])).
% 1.53/1.73 tff(9159,plain,
% 1.53/1.73 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), z))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9158])).
% 1.53/1.73 tff(9160,plain,
% 1.53/1.73 (~b(s(s(s(z))), z)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9149, 9159])).
% 1.53/1.73 tff(9161,plain,
% 1.53/1.73 (r(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[169, 9160])).
% 1.53/1.73 tff(9162,plain,
% 1.53/1.73 (~r(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1268, 9161, 13])).
% 1.53/1.73 tff(9163,plain,
% 1.53/1.73 (b(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[818, 9162])).
% 1.53/1.73 tff(9164,plain,
% 1.53/1.73 (b(s(s(s(z))), s(elem!1))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9163, 8327])).
% 1.53/1.73 tff(9165,plain,
% 1.53/1.73 (~r(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1976, 9127, 13])).
% 1.53/1.73 tff(9166,plain,
% 1.53/1.73 (b(s(z), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[252, 9165])).
% 1.53/1.73 tff(9167,plain,
% 1.53/1.73 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9166, 5626])).
% 1.53/1.73 tff(9168,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9169,plain,
% 1.53/1.73 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9170,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9169])).
% 1.53/1.73 tff(9171,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[9170, 9168])).
% 1.53/1.73 tff(9172,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(9173,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9172, 9171])).
% 1.53/1.73 tff(9174,plain,
% 1.53/1.73 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(elem!1)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9173, 154, 9167, 9164, 9157])).
% 1.53/1.73 tff(9175,plain,
% 1.53/1.73 (~b(s(s(s(z))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9174, 9156])).
% 1.53/1.73 tff(9176,plain,
% 1.53/1.73 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[104, 9175])).
% 1.53/1.73 tff(9177,plain,
% 1.53/1.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5758, 154, 9155, 9130, 9134, 9133])).
% 1.53/1.73 tff(9178,plain,
% 1.53/1.73 (r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[229, 9177])).
% 1.53/1.73 tff(9179,plain,
% 1.53/1.73 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5898, 5590])).
% 1.53/1.73 tff(9180,plain,
% 1.53/1.73 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9179, 5795, 1243])).
% 1.53/1.73 tff(9181,plain,
% 1.53/1.73 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5998, 9180])).
% 1.53/1.73 tff(9182,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[6000, 9181])).
% 1.53/1.73 tff(9183,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9182, 8681])).
% 1.53/1.73 tff(9184,plain,
% 1.53/1.73 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[8656, 6185])).
% 1.53/1.73 tff(9185,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9186,plain,
% 1.53/1.73 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9187,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9186])).
% 1.53/1.73 tff(9188,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[9187, 9185])).
% 1.53/1.73 tff(9189,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(9190,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9189, 9188])).
% 1.53/1.73 tff(9191,plain,
% 1.53/1.73 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9190, 28, 67, 9184])).
% 1.53/1.73 tff(9192,plain,
% 1.53/1.73 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[5962, 9191])).
% 1.53/1.73 tff(9193,plain,
% 1.53/1.73 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5672])).
% 1.53/1.73 tff(9194,plain,
% 1.53/1.73 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[5672])).
% 1.53/1.73 tff(9195,plain,
% 1.53/1.73 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(symmetry,[status(thm)],[9194])).
% 1.53/1.73 tff(9196,plain,
% 1.53/1.73 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9195])).
% 1.53/1.73 tff(9197,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9198,plain,
% 1.53/1.73 (((~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(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9199,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[9198])).
% 1.53/1.73 tff(9200,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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)))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[9199, 9197])).
% 1.53/1.73 tff(9201,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(9202,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9201, 9200])).
% 1.53/1.73 tff(9203,plain,
% 1.53/1.73 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9202, 28, 1243, 9184])).
% 1.53/1.73 tff(9204,plain,
% 1.53/1.73 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9203, 9196])).
% 1.53/1.73 tff(9205,plain,
% 1.53/1.73 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[6124, 6109])).
% 1.53/1.73 tff(9206,plain,
% 1.53/1.73 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[9205, 9204])).
% 1.53/1.73 tff(9207,plain,
% 1.53/1.73 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[9206, 9193])).
% 1.53/1.73 tff(9208,plain,
% 1.53/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(9209,plain,
% 1.53/1.73 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9210,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9209])).
% 1.53/1.74 tff(9211,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9210, 9208])).
% 1.53/1.74 tff(9212,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(9213,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9212, 9211])).
% 1.53/1.74 tff(9214,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9213, 154, 615, 566, 9207, 9192, 9183])).
% 1.53/1.74 tff(9215,plain,(b(s(s(s(s(s(s(z)))))), s(s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(9216,plain,
% 1.53/1.74 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9215, 9178, 566, 615, 9176])).
% 1.53/1.74 tff(9217,plain,
% 1.53/1.74 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[6145, 6103, 6104, 5964, 6019])).
% 1.53/1.74 tff(9218,plain,
% 1.53/1.74 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9217, 5937])).
% 1.53/1.74 tff(9219,plain,
% 1.53/1.74 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5986, 9218])).
% 1.53/1.74 tff(9220,plain,
% 1.53/1.74 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9219, 5934])).
% 1.53/1.74 tff(9221,plain,
% 1.53/1.74 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[6159, 6103, 6018, 5964, 6019])).
% 1.53/1.74 tff(9222,plain,
% 1.53/1.74 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8685, 9221])).
% 1.53/1.74 tff(9223,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[6000, 9222])).
% 1.53/1.74 tff(9224,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5998, 9223])).
% 1.53/1.74 tff(9225,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5994, 28, 1243, 9224, 9220])).
% 1.53/1.74 tff(9226,plain,((~b(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(9227,plain,
% 1.53/1.74 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9226, 9178, 9133, 9216, 9155, 9130])).
% 1.53/1.74 tff(9228,plain,
% 1.53/1.74 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9227, 9120])).
% 1.53/1.74 tff(9229,plain,
% 1.53/1.74 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[6094, 9228])).
% 1.53/1.74 tff(9230,plain,
% 1.53/1.74 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9229, 9118])).
% 1.53/1.74 tff(9231,plain,
% 1.53/1.74 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.74 tff(9232,plain,
% 1.53/1.74 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9231, 5661])).
% 1.53/1.74 tff(9233,plain,
% 1.53/1.74 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[6187])).
% 1.53/1.74 tff(9234,plain,
% 1.53/1.74 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9131, 9233])).
% 1.53/1.74 tff(9235,plain,
% 1.53/1.74 ((~b(elem!1, s(s(s(z))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9234])).
% 1.53/1.74 tff(9236,plain,
% 1.53/1.74 (~b(z, s(s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9141, 9235])).
% 1.53/1.74 tff(9237,plain,
% 1.53/1.74 (r(z, s(s(s(elem!1))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3977, 9236])).
% 1.53/1.74 tff(9238,plain,
% 1.53/1.74 (r(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9237, 9232])).
% 1.53/1.74 tff(9239,plain,
% 1.53/1.74 (r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[8164])).
% 1.53/1.74 tff(9240,assumption,(r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.53/1.74 tff(9241,plain,
% 1.53/1.74 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9240, 9239])).
% 1.53/1.74 tff(9242,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.53/1.74 tff(9243,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9244,plain,
% 1.53/1.74 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9245,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9244])).
% 1.53/1.74 tff(9246,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9245, 9243])).
% 1.53/1.74 tff(9247,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(9248,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9247, 9246])).
% 1.53/1.74 tff(9249,plain,
% 1.53/1.74 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9248, 28, 9242, 8700])).
% 1.53/1.74 tff(9250,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9249, 9241])).
% 1.53/1.74 tff(9251,plain,((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(9252,plain,
% 1.53/1.74 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9251, 9238, 9230])).
% 1.53/1.74 tff(9253,plain,
% 1.53/1.74 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8189, 9252])).
% 1.53/1.74 tff(9254,plain,
% 1.53/1.74 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9253, 8163])).
% 1.53/1.74 tff(9255,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9256,plain,
% 1.53/1.74 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9257,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9256])).
% 1.53/1.74 tff(9258,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9257, 9255])).
% 1.53/1.74 tff(9259,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(9260,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9259, 9258])).
% 1.53/1.74 tff(9261,plain,
% 1.53/1.74 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9260, 154, 9216, 9164, 9157])).
% 1.53/1.74 tff(9262,plain,
% 1.53/1.74 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9261, 9254])).
% 1.53/1.74 tff(9263,plain,
% 1.53/1.74 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9262, 9117])).
% 1.53/1.74 tff(9264,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[5866, 9263])).
% 1.53/1.74 tff(9265,plain,
% 1.53/1.74 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9264, 8711])).
% 1.53/1.74 tff(9266,plain,
% 1.53/1.74 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5596])).
% 1.53/1.74 tff(9267,plain,
% 1.53/1.74 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.53/1.74 inference(symmetry,[status(thm)],[9266])).
% 1.53/1.74 tff(9268,plain,
% 1.53/1.74 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.53/1.74 inference(transitivity,[status(thm)],[5751, 9267])).
% 1.53/1.74 tff(9269,plain,
% 1.53/1.74 (b(s(s(elem!1)), elem!1)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9129, 9268])).
% 1.53/1.74 tff(9270,plain,
% 1.53/1.74 (~b(elem!1, s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[7881, 9154, 8250, 9269, 9146])).
% 1.53/1.74 tff(9271,plain,
% 1.53/1.74 ((s(elem!1) = z) <=> (s(elem!1) = elem!1)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.74 tff(9272,plain,
% 1.53/1.74 ((s(elem!1) = z) <=> (elem!1 = s(elem!1))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9271, 6394])).
% 1.53/1.74 tff(9273,plain,
% 1.53/1.74 ((~(s(elem!1) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9272])).
% 1.53/1.74 tff(9274,plain,
% 1.53/1.74 (~(elem!1 = s(elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[489, 9273])).
% 1.53/1.74 tff(9275,plain,
% 1.53/1.74 (b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[6508, 9274])).
% 1.53/1.74 tff(9276,plain,
% 1.53/1.74 (r(elem!1, s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9275, 9270])).
% 1.53/1.74 tff(9277,plain,
% 1.53/1.74 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8707, 28, 9276, 9230])).
% 1.53/1.74 tff(9278,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9277, 9265])).
% 1.53/1.74 tff(9279,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(9280,plain,
% 1.53/1.74 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9279, 9116, 9114, 13, 6200, 8258])).
% 1.53/1.74 tff(9281,plain,
% 1.53/1.74 (b(s(s(s(z))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[169, 5663])).
% 1.53/1.74 tff(9282,plain,
% 1.53/1.74 (b(s(s(s(z))), elem!1)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9281, 6196])).
% 1.53/1.74 tff(9283,plain,
% 1.53/1.74 (b(s(s(s(elem!1))), z)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9281, 6197])).
% 1.53/1.74 tff(9284,plain,
% 1.53/1.74 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5592, 5590])).
% 1.53/1.74 tff(9285,plain,
% 1.53/1.74 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[9284])).
% 1.53/1.74 tff(9286,plain,
% 1.53/1.74 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9116, 9285])).
% 1.53/1.74 tff(9287,plain,
% 1.53/1.74 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[4379, 5637])).
% 1.53/1.74 tff(9288,plain,
% 1.53/1.74 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9287, 9115])).
% 1.53/1.74 tff(9289,plain,
% 1.53/1.74 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[989, 9288])).
% 1.53/1.74 tff(9290,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9114, 9122])).
% 1.53/1.74 tff(9291,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5590, 5592])).
% 1.53/1.74 tff(9292,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[9291])).
% 1.53/1.74 tff(9293,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9114, 9292])).
% 1.53/1.74 tff(9294,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.74 tff(9295,assumption,(b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 1.53/1.74 tff(9296,assumption,(b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.74 tff(9297,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9298,plain,
% 1.53/1.74 (((~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(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9299,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9298])).
% 1.53/1.74 tff(9300,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9299, 9297])).
% 1.53/1.74 tff(9301,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(z))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(9302,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9301, 9300])).
% 1.53/1.74 tff(9303,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9302, 154, 9296, 443, 9295, 9294, 7744])).
% 1.53/1.74 tff(9304,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(9305,plain,
% 1.53/1.74 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9304, 9293, 9290, 9289, 9286])).
% 1.53/1.74 tff(9306,plain,
% 1.53/1.74 (~r(z, s(s(s(elem!1))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[7966, 6191, 9305, 9283])).
% 1.53/1.74 tff(9307,plain,
% 1.53/1.74 (b(z, s(s(s(elem!1))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3977, 9306])).
% 1.53/1.74 tff(9308,plain,
% 1.53/1.74 (b(elem!1, s(s(s(z))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9307, 6188])).
% 1.53/1.74 tff(9309,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9310,plain,
% 1.53/1.74 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9311,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9310])).
% 1.53/1.74 tff(9312,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9311, 9309])).
% 1.53/1.74 tff(9313,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(9314,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9313, 9312])).
% 1.53/1.74 tff(9315,plain,
% 1.53/1.74 (~b(elem!1, s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[9314, 154, 9114, 9308, 9282, 9116])).
% 1.53/1.74 tff(9316,plain,
% 1.53/1.74 (r(elem!1, s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[8062, 9315])).
% 1.53/1.74 tff(9317,plain,
% 1.53/1.74 (~r(s(s(z)), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1232, 9281, 16, 9116, 9114])).
% 1.53/1.74 tff(9318,plain,
% 1.53/1.74 (b(s(s(z)), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[122, 9317])).
% 1.53/1.74 tff(9319,plain,
% 1.53/1.74 (~r(s(s(z)), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1125, 820, 6200])).
% 1.53/1.74 tff(9320,plain,
% 1.53/1.74 (b(s(s(z)), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[296, 9319])).
% 1.53/1.74 tff(9321,plain,
% 1.53/1.74 (r(z, s(s(s(s(z)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9316, 8860])).
% 1.53/1.74 tff(9322,plain,
% 1.53/1.74 (~r(z, s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2439, 9321, 16])).
% 1.53/1.74 tff(9323,plain,
% 1.53/1.74 (b(z, s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[64, 9322])).
% 1.53/1.74 tff(9324,plain,
% 1.53/1.74 (~b(z, s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1736, 9323, 8249, 9320, 9318])).
% 1.53/1.74 tff(9325,plain,
% 1.53/1.74 (r(z, s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1181, 9324])).
% 1.53/1.74 tff(9326,plain,
% 1.53/1.74 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[3016, 9325, 820, 9281])).
% 1.53/1.74 tff(9327,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[318, 9326])).
% 1.53/1.74 tff(9328,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), s(elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9327, 5625])).
% 1.53/1.74 tff(9329,plain,
% 1.53/1.74 (b(s(s(z)), s(elem!1))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9320, 8310])).
% 1.53/1.74 tff(9330,plain,
% 1.53/1.74 (~b(s(s(s(z))), s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1190, 9323, 9320, 9281, 9318, 820])).
% 1.53/1.74 tff(9331,plain,
% 1.53/1.74 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[104, 9330])).
% 1.53/1.74 tff(9332,plain,
% 1.53/1.74 (b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9280, 8578])).
% 1.53/1.74 tff(9333,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(z))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[9320, 8575])).
% 1.53/1.74 tff(9334,plain,
% 1.53/1.74 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[5590])).
% 1.53/1.74 tff(9335,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.53/1.74 inference(symmetry,[status(thm)],[9334])).
% 1.53/1.74 tff(9336,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 1.53/1.74 inference(transitivity,[status(thm)],[8806, 9335])).
% 1.53/1.74 tff(9337,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9338,plain,
% 1.53/1.74 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(9339,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[9338])).
% 1.53/1.74 tff(9340,plain,
% 1.53/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[9339, 9337])).
% 1.53/1.74 tff(9341,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(9342,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9341, 9340])).
% 1.53/1.75 tff(9343,plain,
% 1.53/1.75 (~b(s(s(s(s(z)))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9342, 154, 9114, 9308, 9282, 9116])).
% 1.53/1.75 tff(9344,plain,
% 1.53/1.75 (r(s(s(s(s(z)))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8854, 9343])).
% 1.53/1.75 tff(9345,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9344, 9336])).
% 1.53/1.75 tff(9346,plain,
% 1.53/1.75 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[410, 9345, 13])).
% 1.53/1.75 tff(9347,plain,
% 1.53/1.75 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[441, 9346])).
% 1.53/1.75 tff(9348,plain,
% 1.53/1.75 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8599, 9347, 8583, 9333, 9332])).
% 1.53/1.75 tff(9349,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8601, 9348])).
% 1.53/1.75 tff(9350,plain,
% 1.53/1.75 (r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9349, 8572])).
% 1.53/1.75 tff(9351,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9215, 9350, 9116, 9114, 9331])).
% 1.53/1.75 tff(9352,plain,
% 1.53/1.75 (b(elem!1, s(s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9323, 5689])).
% 1.53/1.75 tff(9353,plain,
% 1.53/1.75 (b(s(s(elem!1)), s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9320, 8255])).
% 1.53/1.75 tff(9354,plain,
% 1.53/1.75 (b(s(s(elem!1)), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9318, 9268])).
% 1.53/1.75 tff(9355,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5590])).
% 1.53/1.75 tff(9356,plain,
% 1.53/1.75 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.75 inference(symmetry,[status(thm)],[9355])).
% 1.53/1.75 tff(9357,plain,
% 1.53/1.75 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9344, 9356])).
% 1.53/1.75 tff(9358,plain,
% 1.53/1.75 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8903, 9349, 9357])).
% 1.53/1.75 tff(9359,plain,
% 1.53/1.75 (b(elem!1, s(s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8923, 9358])).
% 1.53/1.75 tff(9360,plain,
% 1.53/1.75 (~b(elem!1, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[7881, 9359, 8250, 9354, 9353])).
% 1.53/1.75 tff(9361,plain,
% 1.53/1.75 (r(elem!1, s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9275, 9360])).
% 1.53/1.75 tff(9362,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5932])).
% 1.53/1.75 tff(9363,plain,
% 1.53/1.75 ((~b(s(s(s(s(s(s(z)))))), elem!1)) <=> (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9362])).
% 1.53/1.75 tff(9364,assumption,(b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.53/1.75 tff(9365,plain,
% 1.53/1.75 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9364, 8163])).
% 1.53/1.75 tff(9366,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9367,plain,
% 1.53/1.75 (((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9368,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9367])).
% 1.53/1.75 tff(9369,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[9368, 9366])).
% 1.53/1.75 tff(9370,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(9371,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9370, 9369])).
% 1.53/1.75 tff(9372,plain,
% 1.53/1.75 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9371, 154, 8073, 6019, 5964])).
% 1.53/1.75 tff(9373,plain,
% 1.53/1.75 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9372, 9365])).
% 1.53/1.75 tff(9374,plain,
% 1.53/1.75 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9373, 9363])).
% 1.53/1.75 tff(9375,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.75 inference(monotonicity,[status(thm)],[5932])).
% 1.53/1.75 tff(9376,plain,
% 1.53/1.75 ((~r(s(s(s(s(s(s(z)))))), elem!1)) <=> (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9375])).
% 1.53/1.75 tff(9377,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[9193])).
% 1.53/1.75 tff(9378,plain,
% 1.53/1.75 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9377])).
% 1.53/1.75 tff(9379,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9380,plain,
% 1.53/1.75 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9381,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9380])).
% 1.53/1.75 tff(9382,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[9381, 9379])).
% 1.53/1.75 tff(9383,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(9384,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9383, 9382])).
% 1.53/1.75 tff(9385,plain,
% 1.53/1.75 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9384, 154, 566, 8753])).
% 1.53/1.75 tff(9386,plain,
% 1.53/1.75 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9385, 9365, 8752])).
% 1.53/1.75 tff(9387,plain,
% 1.53/1.75 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9386, 9378])).
% 1.53/1.75 tff(9388,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9205, 9387])).
% 1.53/1.75 tff(9389,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9388, 9194])).
% 1.53/1.75 tff(9390,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9391,plain,
% 1.53/1.75 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9392,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9391])).
% 1.53/1.75 tff(9393,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[9392, 9390])).
% 1.53/1.75 tff(9394,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(9395,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9394, 9393])).
% 1.53/1.75 tff(9396,plain,
% 1.53/1.75 ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9395, 154, 6019, 5964, 8721])).
% 1.53/1.75 tff(9397,plain,
% 1.53/1.75 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9396, 8752])).
% 1.53/1.75 tff(9398,plain,
% 1.53/1.75 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9397, 9120])).
% 1.53/1.75 tff(9399,plain,
% 1.53/1.75 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[6094, 9398])).
% 1.53/1.75 tff(9400,plain,
% 1.53/1.75 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8125, 5590])).
% 1.53/1.75 tff(9401,plain,
% 1.53/1.75 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9400, 9399, 4111])).
% 1.53/1.75 tff(9402,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9401, 9389])).
% 1.53/1.75 tff(9403,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(9404,plain,
% 1.53/1.75 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9403, 9364, 6019, 5964, 8721, 566, 8753, 4111])).
% 1.53/1.75 tff(9405,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5866, 9404])).
% 1.53/1.75 tff(9406,plain,
% 1.53/1.75 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9405, 8711])).
% 1.53/1.75 tff(9407,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9408,plain,
% 1.53/1.75 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9409,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9408])).
% 1.53/1.75 tff(9410,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[9409, 9407])).
% 1.53/1.75 tff(9411,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(9412,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9411, 9410])).
% 1.53/1.75 tff(9413,plain,
% 1.53/1.75 ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9412, 28, 6495])).
% 1.53/1.75 tff(9414,plain,
% 1.53/1.75 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9413, 9406])).
% 1.53/1.75 tff(9415,plain,
% 1.53/1.75 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9414, 9376])).
% 1.53/1.75 tff(9416,plain,
% 1.53/1.75 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.53/1.75 inference(transitivity,[status(thm)],[6087, 6006])).
% 1.53/1.75 tff(9417,plain,
% 1.53/1.75 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9416])).
% 1.53/1.75 tff(9418,plain,
% 1.53/1.75 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[6012, 9417])).
% 1.53/1.75 tff(9419,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[6032, 9418])).
% 1.53/1.75 tff(9420,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9419, 9415, 9374])).
% 1.53/1.75 tff(9421,plain,((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(9422,plain,
% 1.53/1.75 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9421, 9361, 9282, 9352, 9351, 9329, 9116, 9328, 9316])).
% 1.53/1.75 tff(9423,plain,
% 1.53/1.75 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[8189, 9422])).
% 1.53/1.75 tff(9424,plain,
% 1.53/1.75 (r(s(s(s(z))), s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[820, 8688])).
% 1.53/1.75 tff(9425,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9426,plain,
% 1.53/1.75 (((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9427,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[9426])).
% 1.53/1.75 tff(9428,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[9427, 9425])).
% 1.53/1.75 tff(9429,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(9430,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9429, 9428])).
% 1.53/1.75 tff(9431,plain,
% 1.53/1.75 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9430, 28, 8765])).
% 1.53/1.75 tff(9432,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9431, 9241, 8701])).
% 1.53/1.75 tff(9433,plain,((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(9434,plain,
% 1.53/1.75 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9433, 9424, 9423])).
% 1.53/1.75 tff(9435,plain,
% 1.53/1.75 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9434, 6181])).
% 1.53/1.75 tff(9436,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[5866, 9435])).
% 1.53/1.75 tff(9437,plain,
% 1.53/1.75 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9436, 6179])).
% 1.53/1.75 tff(9438,plain,
% 1.53/1.75 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[9395, 154, 9352, 9351, 9329, 9437])).
% 1.53/1.75 tff(9439,plain,
% 1.53/1.75 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9438, 9120])).
% 1.53/1.75 tff(9440,plain,
% 1.53/1.75 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[6094, 9439])).
% 1.53/1.75 tff(9441,plain,
% 1.53/1.75 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[9440, 9118])).
% 1.53/1.75 tff(9442,plain,
% 1.53/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(9443,plain,
% 1.53/1.75 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9444,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9443])).
% 1.53/1.76 tff(9445,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9444, 9442])).
% 1.53/1.76 tff(9446,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9447,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9446, 9445])).
% 1.53/1.76 tff(9448,plain,
% 1.53/1.76 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9447, 154, 9351, 9328, 9157])).
% 1.53/1.76 tff(9449,plain,
% 1.53/1.76 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9448, 9437])).
% 1.53/1.76 tff(9450,plain,
% 1.53/1.76 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8685, 9449])).
% 1.53/1.76 tff(9451,plain,
% 1.53/1.76 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[6000, 9450])).
% 1.53/1.76 tff(9452,plain,
% 1.53/1.76 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5998, 9451])).
% 1.53/1.76 tff(9453,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9454,plain,
% 1.53/1.76 (((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9455,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9454])).
% 1.53/1.76 tff(9456,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9455, 9453])).
% 1.53/1.76 tff(9457,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9458,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9457, 9456])).
% 1.53/1.76 tff(9459,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9458, 28, 9344, 9452, 9441])).
% 1.53/1.76 tff(9460,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9461,plain,
% 1.53/1.76 (~r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9460, 16, 13, 6190])).
% 1.53/1.76 tff(9462,plain,
% 1.53/1.76 (b(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[818, 9461])).
% 1.53/1.76 tff(9463,plain,
% 1.53/1.76 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[752, 9462, 9116, 9114, 9280])).
% 1.53/1.76 tff(9464,plain,
% 1.53/1.76 (r(s(s(s(s(z)))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[318, 9463])).
% 1.53/1.76 tff(9465,plain,
% 1.53/1.76 (~b(z, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2825, 9462, 13, 16])).
% 1.53/1.76 tff(9466,plain,
% 1.53/1.76 (r(z, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1181, 9465])).
% 1.53/1.76 tff(9467,plain,
% 1.53/1.76 (~b(s(z), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[623, 9462, 9116, 9114, 9280])).
% 1.53/1.76 tff(9468,plain,
% 1.53/1.76 (r(s(z), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[252, 9467])).
% 1.53/1.76 tff(9469,plain,
% 1.53/1.76 (~r(s(s(s(z))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[281, 9468, 13])).
% 1.53/1.76 tff(9470,plain,
% 1.53/1.76 (b(s(s(s(z))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[169, 9469])).
% 1.53/1.76 tff(9471,plain,
% 1.53/1.76 (~r(z, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1976, 9468, 13])).
% 1.53/1.76 tff(9472,plain,
% 1.53/1.76 (b(z, s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[648, 9471])).
% 1.53/1.76 tff(9473,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[742, 9472, 9470, 9466, 9116, 9464])).
% 1.53/1.76 tff(9474,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), z)) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9475,plain,
% 1.53/1.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9474, 9112, 13])).
% 1.53/1.76 tff(9476,plain,
% 1.53/1.76 (b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1259, 9475])).
% 1.53/1.76 tff(9477,plain,
% 1.53/1.76 (r(s(s(z)), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[138, 9112])).
% 1.53/1.76 tff(9478,plain,
% 1.53/1.76 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[5632, 5630])).
% 1.53/1.76 tff(9479,plain,
% 1.53/1.76 (~r(s(s(z)), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2278, 171, 13, 8249])).
% 1.53/1.76 tff(9480,plain,
% 1.53/1.76 (b(s(s(z)), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[122, 9479])).
% 1.53/1.76 tff(9481,plain,
% 1.53/1.76 (~r(s(s(z)), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8941, 171, 13, 66])).
% 1.53/1.76 tff(9482,plain,
% 1.53/1.76 (b(s(s(z)), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[296, 9481])).
% 1.53/1.76 tff(9483,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2025, 9482, 2183, 13, 8249, 171, 9476, 3707])).
% 1.53/1.76 tff(9484,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9485,plain,
% 1.53/1.76 (~r(s(s(s(z))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9484, 66, 13])).
% 1.53/1.76 tff(9486,plain,
% 1.53/1.76 (b(s(s(s(z))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[169, 9485])).
% 1.53/1.76 tff(9487,plain,
% 1.53/1.76 (~r(z, s(s(s(s(z)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3227, 5634, 66])).
% 1.53/1.76 tff(9488,plain,
% 1.53/1.76 (b(z, s(s(s(s(z)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[191, 9487])).
% 1.53/1.76 tff(9489,plain,
% 1.53/1.76 (b(elem!1, s(s(s(s(z)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9488, 5747])).
% 1.53/1.76 tff(9490,plain,
% 1.53/1.76 (b(s(s(s(z))), elem!1)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[143, 6196])).
% 1.53/1.76 tff(9491,plain,
% 1.53/1.76 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[5592])).
% 1.53/1.76 tff(9492,plain,
% 1.53/1.76 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.53/1.76 inference(symmetry,[status(thm)],[9491])).
% 1.53/1.76 tff(9493,plain,
% 1.53/1.76 (r(s(s(z)), s(s(s(elem!1))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[124, 9492])).
% 1.53/1.76 tff(9494,plain,
% 1.53/1.76 (~b(s(s(z)), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2054, 5636, 1283, 9488, 143])).
% 1.53/1.76 tff(9495,plain,
% 1.53/1.76 (r(s(s(z)), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[122, 9494])).
% 1.53/1.76 tff(9496,plain,
% 1.53/1.76 (~r(z, s(s(s(elem!1))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[4439, 9495, 9493])).
% 1.53/1.76 tff(9497,plain,
% 1.53/1.76 (b(z, s(s(s(elem!1))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[3977, 9496])).
% 1.53/1.76 tff(9498,plain,
% 1.53/1.76 (b(elem!1, s(s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9497, 6188])).
% 1.53/1.76 tff(9499,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9500,plain,
% 1.53/1.76 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9501,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9500])).
% 1.53/1.76 tff(9502,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9501, 9499])).
% 1.53/1.76 tff(9503,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9504,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9503, 9502])).
% 1.53/1.76 tff(9505,plain,
% 1.53/1.76 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9504, 154, 9498, 9490, 9489, 9133])).
% 1.53/1.76 tff(9506,plain,
% 1.53/1.76 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[343, 9505])).
% 1.53/1.76 tff(9507,plain,
% 1.53/1.76 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8031, 9506, 124])).
% 1.53/1.76 tff(9508,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8044, 9507])).
% 1.53/1.76 tff(9509,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9508, 7975])).
% 1.53/1.76 tff(9510,plain,
% 1.53/1.76 (~r(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1930, 5634, 66])).
% 1.53/1.76 tff(9511,plain,
% 1.53/1.76 (b(s(s(s(z))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[818, 9510])).
% 1.53/1.76 tff(9512,plain,
% 1.53/1.76 (~b(z, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2861, 9495, 13, 9511])).
% 1.53/1.76 tff(9513,plain,
% 1.53/1.76 (r(z, s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1181, 9512])).
% 1.53/1.76 tff(9514,plain,
% 1.53/1.76 (r(elem!1, s(elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9513, 7973])).
% 1.53/1.76 tff(9515,plain,
% 1.53/1.76 (~r(s(s(z)), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[702, 9495, 13])).
% 1.53/1.76 tff(9516,plain,
% 1.53/1.76 (b(s(s(z)), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[296, 9515])).
% 1.53/1.76 tff(9517,plain,
% 1.53/1.76 (b(s(s(z)), s(elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9516, 8310])).
% 1.53/1.76 tff(9518,plain,
% 1.53/1.76 (b(s(s(s(z))), s(elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9511, 8327])).
% 1.53/1.76 tff(9519,plain,
% 1.53/1.76 (~r(s(z), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1027, 5645, 8315])).
% 1.53/1.76 tff(9520,plain,
% 1.53/1.76 (b(s(z), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[252, 9519])).
% 1.53/1.76 tff(9521,plain,
% 1.53/1.76 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9520, 5626])).
% 1.53/1.76 tff(9522,plain,
% 1.53/1.76 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9173, 154, 9521, 9518, 9517])).
% 1.53/1.76 tff(9523,plain,
% 1.53/1.76 (~b(s(s(s(z))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9522, 9157])).
% 1.53/1.76 tff(9524,plain,
% 1.53/1.76 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[104, 9523])).
% 1.53/1.76 tff(9525,plain,
% 1.53/1.76 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1427, 28, 124, 9506])).
% 1.53/1.76 tff(9526,plain,
% 1.53/1.76 (b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[229, 9525])).
% 1.53/1.76 tff(9527,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9528,plain,
% 1.53/1.76 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9529,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9528])).
% 1.53/1.76 tff(9530,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9529, 9527])).
% 1.53/1.76 tff(9531,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9532,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9531, 9530])).
% 1.53/1.76 tff(9533,plain,
% 1.53/1.76 (~b(elem!1, s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9532, 154, 1283, 9489, 9526, 9133])).
% 1.53/1.76 tff(9534,plain,
% 1.53/1.76 (r(elem!1, s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8651, 60, 9533, 8640])).
% 1.53/1.76 tff(9535,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.53/1.76 inference(symmetry,[status(thm)],[9362])).
% 1.53/1.76 tff(9536,assumption,(r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 1.53/1.76 tff(9537,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9538,plain,
% 1.53/1.76 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9539,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9538])).
% 1.53/1.76 tff(9540,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9539, 9537])).
% 1.53/1.76 tff(9541,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9542,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9541, 9540])).
% 1.53/1.76 tff(9543,plain,
% 1.53/1.76 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9542, 28, 6495, 4467, 9536])).
% 1.53/1.76 tff(9544,plain,
% 1.53/1.76 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9543, 9376])).
% 1.53/1.76 tff(9545,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9419, 9544])).
% 1.53/1.76 tff(9546,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9545, 9535])).
% 1.53/1.76 tff(9547,plain,
% 1.53/1.76 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8180, 28, 67, 9536])).
% 1.53/1.76 tff(9548,plain,
% 1.53/1.76 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9547, 8165])).
% 1.53/1.76 tff(9549,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8189, 9548])).
% 1.53/1.76 tff(9550,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9549, 8163])).
% 1.53/1.76 tff(9551,plain,
% 1.53/1.76 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8668, 28, 4467, 9536])).
% 1.53/1.76 tff(9552,plain,
% 1.53/1.76 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9551, 8654])).
% 1.53/1.76 tff(9553,plain,
% 1.53/1.76 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[6094, 9552])).
% 1.53/1.76 tff(9554,plain,
% 1.53/1.76 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9553, 5673])).
% 1.53/1.76 tff(9555,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9556,plain,
% 1.53/1.76 (((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9557,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[9556])).
% 1.53/1.76 tff(9558,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[9557, 9555])).
% 1.53/1.76 tff(9559,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(9560,plain,
% 1.53/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9559, 9558])).
% 1.53/1.76 tff(9561,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9560, 154, 4455, 8073, 9554, 9550, 9546])).
% 1.53/1.76 tff(9562,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(9563,plain,
% 1.53/1.76 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[9562, 9498, 9490, 9514, 9534, 9524])).
% 1.53/1.76 tff(9564,plain,
% 1.53/1.76 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8661, 9563])).
% 1.53/1.76 tff(9565,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8154, 9564])).
% 1.53/1.76 tff(9566,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8152, 9565])).
% 1.53/1.76 tff(9567,plain,
% 1.53/1.76 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8782, 154, 4455, 6018, 8072, 6151])).
% 1.53/1.76 tff(9568,plain,
% 1.53/1.76 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9567, 9120])).
% 1.53/1.76 tff(9569,plain,
% 1.53/1.76 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[6094, 9568])).
% 1.53/1.76 tff(9570,plain,
% 1.53/1.76 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9569, 9118])).
% 1.53/1.76 tff(9571,plain,
% 1.53/1.76 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8709, 9570, 6495])).
% 1.53/1.76 tff(9572,plain,
% 1.53/1.76 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[8716, 9571])).
% 1.53/1.76 tff(9573,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[5866, 9572])).
% 1.53/1.76 tff(9574,plain,
% 1.53/1.76 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[9573, 6179])).
% 1.53/1.76 tff(9575,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9576,plain,
% 1.53/1.76 (((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(9577,plain,
% 1.53/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9576])).
% 1.53/1.77 tff(9578,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9577, 9575])).
% 1.53/1.77 tff(9579,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9580,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9579, 9578])).
% 1.53/1.77 tff(9581,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9580, 154, 1603, 5964, 6151, 8721, 9574])).
% 1.53/1.77 tff(9582,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9583,plain,
% 1.53/1.77 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9582, 9526, 9566, 9517, 9514, 9498, 9133, 9509])).
% 1.53/1.77 tff(9584,plain,
% 1.53/1.77 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8685, 9583])).
% 1.53/1.77 tff(9585,plain,
% 1.53/1.77 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[6000, 9584])).
% 1.53/1.77 tff(9586,plain,
% 1.53/1.77 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5998, 9585])).
% 1.53/1.77 tff(9587,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.53/1.77 tff(9588,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9589,plain,
% 1.53/1.77 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9590,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9589])).
% 1.53/1.77 tff(9591,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9590, 9588])).
% 1.53/1.77 tff(9592,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9593,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9592, 9591])).
% 1.53/1.77 tff(9594,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9593, 28, 66, 5885, 9587])).
% 1.53/1.77 tff(9595,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9596,plain,
% 1.53/1.77 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9595, 9586, 66])).
% 1.53/1.77 tff(9597,assumption,(~r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.53/1.77 tff(9598,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9597, 9241])).
% 1.53/1.77 tff(9599,plain,(r(s(s(s(z))), s(s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9600,plain,
% 1.53/1.77 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9599, 9596])).
% 1.53/1.77 tff(9601,plain,
% 1.53/1.77 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8189, 9600])).
% 1.53/1.77 tff(9602,plain,
% 1.53/1.77 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9601, 8163])).
% 1.53/1.77 tff(9603,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9604,plain,
% 1.53/1.77 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9605,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9604])).
% 1.53/1.77 tff(9606,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9605, 9603])).
% 1.53/1.77 tff(9607,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), elem!1)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9608,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9607, 9606])).
% 1.53/1.77 tff(9609,plain,
% 1.53/1.77 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9608, 154, 9498, 9490, 9509, 9602])).
% 1.53/1.77 tff(9610,plain,
% 1.53/1.77 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9609, 9120])).
% 1.53/1.77 tff(9611,plain,
% 1.53/1.77 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[6094, 9610])).
% 1.53/1.77 tff(9612,plain,
% 1.53/1.77 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9611, 9118])).
% 1.53/1.77 tff(9613,plain,
% 1.53/1.77 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8197, 154, 9509, 9521, 9518])).
% 1.53/1.77 tff(9614,plain,
% 1.53/1.77 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9613, 9602])).
% 1.53/1.77 tff(9615,plain,
% 1.53/1.77 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9614, 9117])).
% 1.53/1.77 tff(9616,plain,
% 1.53/1.77 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5866, 9615])).
% 1.53/1.77 tff(9617,plain,
% 1.53/1.77 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8716, 9616])).
% 1.53/1.77 tff(9618,plain,
% 1.53/1.77 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8709, 9617, 9514])).
% 1.53/1.77 tff(9619,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9618, 9612])).
% 1.53/1.77 tff(9620,plain,(b(s(z), s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9621,plain,
% 1.53/1.77 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9620, 9486, 9477, 9476, 13, 66])).
% 1.53/1.77 tff(9622,plain,
% 1.53/1.77 (b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9621, 8578])).
% 1.53/1.77 tff(9623,plain,
% 1.53/1.77 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5596, 5590])).
% 1.53/1.77 tff(9624,plain,
% 1.53/1.77 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9623])).
% 1.53/1.77 tff(9625,plain,
% 1.53/1.77 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9476, 9624])).
% 1.53/1.77 tff(9626,plain,
% 1.53/1.77 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5592])).
% 1.53/1.77 tff(9627,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9626])).
% 1.53/1.77 tff(9628,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5596])).
% 1.53/1.77 tff(9629,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9628])).
% 1.53/1.77 tff(9630,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9629, 9627])).
% 1.53/1.77 tff(9631,plain,
% 1.53/1.77 (b(s(elem!1), s(s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[232, 5626])).
% 1.53/1.77 tff(9632,plain,
% 1.53/1.77 (~b(s(s(z)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1437, 9621, 13, 8249, 232, 9476, 9486])).
% 1.53/1.77 tff(9633,plain,
% 1.53/1.77 (r(s(s(z)), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[296, 9632])).
% 1.53/1.77 tff(9634,plain,
% 1.53/1.77 (~r(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[702, 9633, 13])).
% 1.53/1.77 tff(9635,plain,
% 1.53/1.77 (b(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[122, 9634])).
% 1.53/1.77 tff(9636,plain,
% 1.53/1.77 (b(s(s(z)), elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9635, 5751])).
% 1.53/1.77 tff(9637,plain,
% 1.53/1.77 (b(s(s(s(z))), elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9486, 6196])).
% 1.53/1.77 tff(9638,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9639,plain,
% 1.53/1.77 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9640,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9639])).
% 1.53/1.77 tff(9641,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9640, 9638])).
% 1.53/1.77 tff(9642,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9643,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9642, 9641])).
% 1.53/1.77 tff(9644,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9643, 154, 9637, 9636, 9631, 8308])).
% 1.53/1.77 tff(9645,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[104, 9644])).
% 1.53/1.77 tff(9646,plain,
% 1.53/1.77 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9645, 9630])).
% 1.53/1.77 tff(9647,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[7953, 9646, 8962])).
% 1.53/1.77 tff(9648,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8601, 9647])).
% 1.53/1.77 tff(9649,plain,
% 1.53/1.77 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9021, 9648, 8583, 9625, 9622])).
% 1.53/1.77 tff(9650,plain,
% 1.53/1.77 (r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[441, 9649])).
% 1.53/1.77 tff(9651,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[410, 9650, 13])).
% 1.53/1.77 tff(9652,plain,
% 1.53/1.77 ((~r(s(s(s(s(elem!1)))), elem!1)) | r(s(s(s(s(elem!1)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[7918, 5611])).
% 1.53/1.77 tff(9653,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9652, 9651])).
% 1.53/1.77 tff(9654,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8632, 9653])).
% 1.53/1.77 tff(9655,plain,
% 1.53/1.77 (b(s(s(s(s(z)))), elem!1)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9654, 8609])).
% 1.53/1.77 tff(9656,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5590, 5596])).
% 1.53/1.77 tff(9657,plain,
% 1.53/1.77 (b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9648, 9656])).
% 1.53/1.77 tff(9658,plain,
% 1.53/1.77 (r(s(s(elem!1)), s(s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9477, 5598])).
% 1.53/1.77 tff(9659,plain,
% 1.53/1.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9477, 5599])).
% 1.53/1.77 tff(9660,plain,
% 1.53/1.77 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[6311, 9659, 9658])).
% 1.53/1.77 tff(9661,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[6215, 154, 9637, 9631])).
% 1.53/1.77 tff(9662,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9661, 6207])).
% 1.53/1.77 tff(9663,plain,
% 1.53/1.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[4202, 9662, 9660])).
% 1.53/1.77 tff(9664,plain,
% 1.53/1.77 (b(s(s(s(s(z)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[8913, 9654, 9663])).
% 1.53/1.77 tff(9665,plain,
% 1.53/1.77 (~b(z, s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2054, 9664, 9476, 9635, 9486])).
% 1.53/1.77 tff(9666,plain,
% 1.53/1.77 (r(z, s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[191, 9665])).
% 1.53/1.77 tff(9667,plain,
% 1.53/1.77 (~r(z, s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2462, 9666, 13, 8249, 9635, 9664])).
% 1.53/1.77 tff(9668,plain,
% 1.53/1.77 (b(z, s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[64, 9667])).
% 1.53/1.77 tff(9669,plain,
% 1.53/1.77 (b(elem!1, s(s(z)))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9668, 5689])).
% 1.53/1.77 tff(9670,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9671,plain,
% 1.53/1.77 (((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9672,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9671])).
% 1.53/1.77 tff(9673,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9672, 9670])).
% 1.53/1.77 tff(9674,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9675,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9674, 9673])).
% 1.53/1.77 tff(9676,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9675, 154, 9476, 9669, 9636, 9657, 9655])).
% 1.53/1.77 tff(9677,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9678,plain,
% 1.53/1.77 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9677, 232, 13])).
% 1.53/1.77 tff(9679,plain,
% 1.53/1.77 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[564, 9678])).
% 1.53/1.77 tff(9680,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2306, 9679, 8249, 232, 9476])).
% 1.53/1.77 tff(9681,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[104, 9680])).
% 1.53/1.77 tff(9682,plain,
% 1.53/1.77 (~r(z, s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1346, 171, 9681])).
% 1.53/1.77 tff(9683,plain,
% 1.53/1.77 (b(z, s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[64, 9682])).
% 1.53/1.77 tff(9684,plain,
% 1.53/1.77 (~b(z, s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1307, 9683, 9480, 9476, 2183])).
% 1.53/1.77 tff(9685,plain,
% 1.53/1.77 (r(z, s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[191, 9684])).
% 1.53/1.77 tff(9686,plain,
% 1.53/1.77 (~b(s(z), s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2972, 9683, 9476, 232, 8937, 9480, 171])).
% 1.53/1.77 tff(9687,plain,
% 1.53/1.77 (r(s(z), s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1653, 9686])).
% 1.53/1.77 tff(9688,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2157, 9687, 9685, 13])).
% 1.53/1.77 tff(9689,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(9690,plain,
% 1.53/1.77 (~r(s(s(s(z))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9689, 232, 13])).
% 1.53/1.77 tff(9691,plain,
% 1.53/1.77 (b(s(s(s(z))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[169, 9690])).
% 1.53/1.77 tff(9692,plain,
% 1.53/1.77 (~r(s(s(s(z))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2677, 106, 13, 232, 9691])).
% 1.53/1.77 tff(9693,plain,
% 1.53/1.77 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.77 tff(9694,plain,
% 1.53/1.77 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9693])).
% 1.53/1.77 tff(9695,plain,
% 1.53/1.77 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[6187, 6186, 9694])).
% 1.53/1.77 tff(9696,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9697,plain,
% 1.53/1.77 (((~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))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(9698,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[9697])).
% 1.53/1.77 tff(9699,plain,
% 1.53/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[9698, 9696])).
% 1.53/1.77 tff(9700,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(9701,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9700, 9699])).
% 1.53/1.77 tff(9702,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[9701, 154, 9679, 9631])).
% 1.53/1.77 tff(9703,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9702, 6207])).
% 1.53/1.77 tff(9704,plain,
% 1.53/1.77 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9112, 6189])).
% 1.53/1.77 tff(9705,plain,
% 1.53/1.77 (b(s(s(s(elem!1))), z)),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9691, 6197])).
% 1.53/1.77 tff(9706,plain,
% 1.53/1.77 (~r(z, s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[7966, 9705, 9704, 9703])).
% 1.53/1.77 tff(9707,plain,
% 1.53/1.77 (b(z, s(s(s(elem!1))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3977, 9706])).
% 1.53/1.77 tff(9708,plain,
% 1.53/1.77 (b(z, s(s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9707, 9695])).
% 1.53/1.77 tff(9709,plain,
% 1.53/1.77 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[742, 14, 9679, 9691, 9708])).
% 1.53/1.77 tff(9710,plain,
% 1.53/1.77 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[318, 9709])).
% 1.53/1.77 tff(9711,plain,
% 1.53/1.77 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9679, 9285])).
% 1.53/1.77 tff(9712,plain,
% 1.53/1.77 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[5590])).
% 1.53/1.77 tff(9713,plain,
% 1.53/1.77 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(symmetry,[status(thm)],[9712])).
% 1.53/1.77 tff(9714,plain,
% 1.53/1.77 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[9476, 9713])).
% 1.53/1.77 tff(9715,plain,
% 1.53/1.77 (~b(s(z), s(s(s(s(z)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1389, 2268, 8249, 506, 9476])).
% 1.53/1.77 tff(9716,plain,
% 1.53/1.77 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[5643, 9715])).
% 1.53/1.77 tff(9717,plain,
% 1.53/1.77 (r(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[467, 9716])).
% 1.53/1.77 tff(9718,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1016, 9717, 13])).
% 1.53/1.77 tff(9719,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[418, 9718])).
% 1.53/1.78 tff(9720,plain,
% 1.53/1.78 (~r(z, s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[543, 9717, 14])).
% 1.53/1.78 tff(9721,plain,
% 1.53/1.78 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[548, 9720])).
% 1.53/1.78 tff(9722,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.78 tff(9723,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9724,plain,
% 1.53/1.78 (((~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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9725,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9724])).
% 1.53/1.78 tff(9726,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9725, 9723])).
% 1.53/1.78 tff(9727,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9728,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9727, 9726])).
% 1.53/1.78 tff(9729,plain,
% 1.53/1.78 ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9728, 154, 3852, 3811, 9722])).
% 1.53/1.78 tff(9730,plain,
% 1.53/1.78 (~b(z, s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9729, 9294])).
% 1.53/1.78 tff(9731,plain,
% 1.53/1.78 (r(z, s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3977, 9730])).
% 1.53/1.78 tff(9732,plain,
% 1.53/1.78 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4439, 9731, 106])).
% 1.53/1.78 tff(9733,assumption,(b(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.78 tff(9734,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9735,plain,
% 1.53/1.78 (((~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(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9736,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9735])).
% 1.53/1.78 tff(9737,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9736, 9734])).
% 1.53/1.78 tff(9738,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9739,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9738, 9737])).
% 1.53/1.78 tff(9740,plain,
% 1.53/1.78 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9739, 154, 3852, 3811, 9733])).
% 1.53/1.78 tff(9741,plain,
% 1.53/1.78 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9740, 9294])).
% 1.53/1.78 tff(9742,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3922, 60, 3906, 9741, 9732])).
% 1.53/1.78 tff(9743,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9744,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9743, 9721, 9719, 9714, 9294, 106, 3852])).
% 1.53/1.78 tff(9745,plain,((~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9746,plain,
% 1.53/1.78 (~r(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9745, 14, 9705, 9711, 13, 9710])).
% 1.53/1.78 tff(9747,plain,
% 1.53/1.78 (b(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[122, 9746])).
% 1.53/1.78 tff(9748,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2054, 2492, 2490, 9476, 143, 142])).
% 1.53/1.78 tff(9749,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9750,plain,
% 1.53/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9749, 9747, 9691, 13])).
% 1.53/1.78 tff(9751,plain,
% 1.53/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1653, 9750])).
% 1.53/1.78 tff(9752,plain,
% 1.53/1.78 (b(s(elem!1), s(s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9751, 9478])).
% 1.53/1.78 tff(9753,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), s(elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9710, 5625])).
% 1.53/1.78 tff(9754,plain,
% 1.53/1.78 (~b(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1437, 9751, 13, 8249, 232, 9476, 9691])).
% 1.53/1.78 tff(9755,plain,
% 1.53/1.78 (r(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[296, 9754])).
% 1.53/1.78 tff(9756,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1125, 9755, 9477])).
% 1.53/1.78 tff(9757,plain,
% 1.53/1.78 (b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[818, 9756])).
% 1.53/1.78 tff(9758,plain,
% 1.53/1.78 (b(s(s(s(z))), s(elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9757, 8327])).
% 1.53/1.78 tff(9759,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9760,plain,
% 1.53/1.78 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9761,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9760])).
% 1.53/1.78 tff(9762,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9761, 9759])).
% 1.53/1.78 tff(9763,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9764,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9763, 9762])).
% 1.53/1.78 tff(9765,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9764, 154, 9679, 9631, 9758, 9753, 9752])).
% 1.53/1.78 tff(9766,plain,((~r(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9767,plain,
% 1.53/1.78 (~r(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9766, 232, 13])).
% 1.53/1.78 tff(9768,plain,
% 1.53/1.78 (b(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1181, 9767])).
% 1.53/1.78 tff(9769,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2861, 106, 13, 9768])).
% 1.53/1.78 tff(9770,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[818, 9769, 9692])).
% 1.53/1.78 tff(9771,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9772,plain,
% 1.53/1.78 (~r(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9771, 232, 13])).
% 1.53/1.78 tff(9773,plain,
% 1.53/1.78 (b(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[122, 9772])).
% 1.53/1.78 tff(9774,plain,
% 1.53/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9749, 9773, 9691, 13])).
% 1.53/1.78 tff(9775,plain,
% 1.53/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1653, 9774])).
% 1.53/1.78 tff(9776,plain,
% 1.53/1.78 (b(s(elem!1), s(s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9775, 9478])).
% 1.53/1.78 tff(9777,plain,
% 1.53/1.78 (~b(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1437, 9775, 13, 8249, 232, 9476, 9691])).
% 1.53/1.78 tff(9778,plain,
% 1.53/1.78 (r(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[296, 9777])).
% 1.53/1.78 tff(9779,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1125, 9778, 9477])).
% 1.53/1.78 tff(9780,plain,
% 1.53/1.78 (b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[818, 9779])).
% 1.53/1.78 tff(9781,plain,
% 1.53/1.78 (~r(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2843, 9780, 13, 9768])).
% 1.53/1.78 tff(9782,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[206, 9781])).
% 1.53/1.78 tff(9783,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9782, 5743])).
% 1.53/1.78 tff(9784,plain,
% 1.53/1.78 (b(s(s(z)), elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9773, 5751])).
% 1.53/1.78 tff(9785,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9786,plain,
% 1.53/1.78 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9787,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9786])).
% 1.53/1.78 tff(9788,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9787, 9785])).
% 1.53/1.78 tff(9789,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9790,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9789, 9788])).
% 1.53/1.78 tff(9791,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9790, 154, 9476, 9784, 9783, 8308, 9776])).
% 1.53/1.78 tff(9792,plain,((~b(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9793,plain,
% 1.53/1.78 (~b(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9792, 13])).
% 1.53/1.78 tff(9794,plain,
% 1.53/1.78 (r(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[252, 9793])).
% 1.53/1.78 tff(9795,plain,
% 1.53/1.78 (~r(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[657, 9794, 9477])).
% 1.53/1.78 tff(9796,plain,
% 1.53/1.78 (b(s(s(z)), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[296, 9795])).
% 1.53/1.78 tff(9797,plain,
% 1.53/1.78 (~r(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1391, 9796, 13, 8249, 9476])).
% 1.53/1.78 tff(9798,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[206, 9797])).
% 1.53/1.78 tff(9799,plain,
% 1.53/1.78 (~r(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[281, 9794, 13])).
% 1.53/1.78 tff(9800,plain,
% 1.53/1.78 (b(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[169, 9799])).
% 1.53/1.78 tff(9801,plain,
% 1.53/1.78 (~r(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2066, 1655, 9794, 9800, 9798])).
% 1.53/1.78 tff(9802,plain,
% 1.53/1.78 (b(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1181, 9801])).
% 1.53/1.78 tff(9803,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2496, 1655, 13, 9794])).
% 1.53/1.78 tff(9804,plain,
% 1.53/1.78 (b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[818, 9803])).
% 1.53/1.78 tff(9805,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2861, 9804, 9802, 13, 106])).
% 1.53/1.78 tff(9806,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9807,plain,
% 1.53/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9806, 106, 13])).
% 1.53/1.78 tff(9808,plain,
% 1.53/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1653, 9807])).
% 1.53/1.78 tff(9809,plain,
% 1.53/1.78 (~r(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1588, 9808, 13, 8249, 9476, 9796, 9794])).
% 1.53/1.78 tff(9810,plain,
% 1.53/1.78 (b(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1181, 9809])).
% 1.53/1.78 tff(9811,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2520, 9810, 13, 9476, 9794, 9796, 9798])).
% 1.53/1.78 tff(9812,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2861, 9810, 13, 106])).
% 1.53/1.78 tff(9813,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[818, 9812, 9811])).
% 1.53/1.78 tff(9814,plain,((~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9815,plain,
% 1.53/1.78 (~r(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9814, 13])).
% 1.53/1.78 tff(9816,plain,
% 1.53/1.78 (b(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[122, 9815])).
% 1.53/1.78 tff(9817,plain,
% 1.53/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9749, 9816, 9800, 13])).
% 1.53/1.78 tff(9818,plain,
% 1.53/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1653, 9817])).
% 1.53/1.78 tff(9819,plain,
% 1.53/1.78 (~r(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1588, 9818, 13, 8249, 9476, 9796, 9794])).
% 1.53/1.78 tff(9820,plain,
% 1.53/1.78 (b(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1181, 9819])).
% 1.53/1.78 tff(9821,plain,
% 1.53/1.78 (~b(z, s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2054, 9816, 9476, 9800, 9798])).
% 1.53/1.78 tff(9822,plain,
% 1.53/1.78 (r(z, s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[191, 9821])).
% 1.53/1.78 tff(9823,plain,
% 1.53/1.78 (~r(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2462, 9822, 13, 8249, 9816, 9798])).
% 1.53/1.78 tff(9824,plain,
% 1.53/1.78 (b(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[64, 9823])).
% 1.53/1.78 tff(9825,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1736, 9824, 9820, 8249, 9796, 9816])).
% 1.53/1.78 tff(9826,plain,(~r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(9827,plain,
% 1.53/1.78 (b(s(z), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[271, 9826])).
% 1.53/1.78 tff(9828,plain,
% 1.53/1.78 (~r(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3172, 17, 9827])).
% 1.53/1.78 tff(9829,plain,
% 1.53/1.78 (b(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1181, 9828])).
% 1.53/1.78 tff(9830,plain,
% 1.53/1.78 (~r(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3199, 16, 9827, 17])).
% 1.53/1.78 tff(9831,plain,
% 1.53/1.78 (b(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[122, 9830])).
% 1.53/1.78 tff(9832,plain,
% 1.53/1.78 (~r(s(s(z)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4591, 9831, 9827, 17, 16])).
% 1.53/1.78 tff(9833,plain,
% 1.53/1.78 (b(s(s(z)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[138, 9832])).
% 1.53/1.78 tff(9834,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4780, 9831, 9827, 17, 2258])).
% 1.53/1.78 tff(9835,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[564, 9834])).
% 1.53/1.78 tff(9836,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9837,plain,
% 1.53/1.78 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9838,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9837])).
% 1.53/1.78 tff(9839,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[9838, 9836])).
% 1.53/1.78 tff(9840,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(9841,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 1.53/1.78 tff(9842,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[9841, 154, 9833, 4572])).
% 1.53/1.78 tff(9843,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9842, 6207])).
% 1.53/1.78 tff(9844,plain,
% 1.53/1.78 (r(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[169, 3862])).
% 1.53/1.78 tff(9845,plain,
% 1.53/1.78 (~b(s(s(s(elem!1))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8298, 3862])).
% 1.53/1.78 tff(9846,plain,
% 1.53/1.78 (r(s(s(s(elem!1))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4159, 9845])).
% 1.53/1.78 tff(9847,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4194, 9846, 9844])).
% 1.53/1.78 tff(9848,plain,
% 1.53/1.78 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4202, 9847, 9843])).
% 1.53/1.78 tff(9849,plain,
% 1.53/1.78 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.78 tff(9850,plain,
% 1.53/1.78 (r(s(s(s(z))), elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9844, 9849])).
% 1.53/1.78 tff(9851,plain,
% 1.53/1.78 (b(s(z), s(s(s(s(s(s(elem!1))))))) <=> b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.78 inference(symmetry,[status(thm)],[8698])).
% 1.53/1.78 tff(9852,plain,
% 1.53/1.78 ((~r(s(elem!1), s(s(s(s(s(s(z)))))))) <=> (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[8696])).
% 1.53/1.78 tff(9853,plain,
% 1.53/1.78 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[5726])).
% 1.53/1.78 tff(9854,plain,
% 1.53/1.78 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.53/1.78 inference(symmetry,[status(thm)],[9853])).
% 1.53/1.78 tff(9855,plain,
% 1.53/1.78 (r(s(elem!1), s(s(s(elem!1))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[273, 8949])).
% 1.53/1.78 tff(9856,plain,
% 1.53/1.78 (r(s(elem!1), s(s(s(z))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9855, 9854])).
% 1.53/1.78 tff(9857,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4780, 142, 9827, 17, 15])).
% 1.53/1.78 tff(9858,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[564, 9857])).
% 1.53/1.78 tff(9859,plain,
% 1.53/1.78 (~b(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[4629, 273, 9827, 17, 15, 142, 9858, 141])).
% 1.53/1.78 tff(9860,plain,
% 1.53/1.78 (r(s(s(s(s(z)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[206, 9859])).
% 1.53/1.78 tff(9861,plain,
% 1.53/1.78 (r(s(s(s(s(z)))), elem!1)),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[9860, 8805])).
% 1.53/1.78 tff(9862,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8913, 9859, 4213])).
% 1.53/1.78 tff(9863,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[8632, 9862])).
% 1.53/1.78 tff(9864,plain,
% 1.53/1.78 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.78 inference(symmetry,[status(thm)],[8572])).
% 1.53/1.78 tff(9865,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.53/1.78 tff(9866,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9867,plain,
% 1.53/1.78 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(9868,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[9867])).
% 1.53/1.78 tff(9869,plain,
% 1.53/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9868, 9866])).
% 1.53/1.79 tff(9870,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9871,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9870, 9869])).
% 1.53/1.79 tff(9872,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9871, 28, 9865, 9861])).
% 1.53/1.79 tff(9873,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[343, 9872])).
% 1.53/1.79 tff(9874,plain,
% 1.53/1.79 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4639, 154, 144, 9873, 141, 9858])).
% 1.53/1.79 tff(9875,plain,
% 1.53/1.79 (r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[229, 9874])).
% 1.53/1.79 tff(9876,plain,
% 1.53/1.79 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9875, 9864])).
% 1.53/1.79 tff(9877,plain,
% 1.53/1.79 (~r(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8903, 9876, 9863])).
% 1.53/1.79 tff(9878,plain,
% 1.53/1.79 (b(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8923, 9877])).
% 1.53/1.79 tff(9879,plain,
% 1.53/1.79 (b(elem!1, s(s(z)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9878, 5687])).
% 1.53/1.79 tff(9880,plain,
% 1.53/1.79 (b(s(elem!1), s(s(s(s(z)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[15, 9478])).
% 1.53/1.79 tff(9881,assumption,(r(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.53/1.79 tff(9882,plain,
% 1.53/1.79 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5813, 28, 8662, 9881])).
% 1.53/1.79 tff(9883,plain,
% 1.53/1.79 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9882, 9852])).
% 1.53/1.79 tff(9884,plain,
% 1.53/1.79 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5832, 9883])).
% 1.53/1.79 tff(9885,plain,
% 1.53/1.79 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9884, 9851])).
% 1.53/1.79 tff(9886,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.53/1.79 tff(9887,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9888,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9889,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9888, 9887])).
% 1.53/1.79 tff(9890,plain,
% 1.53/1.79 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9889, 28, 8662, 9881, 9886])).
% 1.53/1.79 tff(9891,plain,
% 1.53/1.79 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8716, 9890])).
% 1.53/1.79 tff(9892,plain,
% 1.53/1.79 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5866, 9891])).
% 1.53/1.79 tff(9893,plain,
% 1.53/1.79 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9892, 6179])).
% 1.53/1.79 tff(9894,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.53/1.79 tff(9895,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8685, 9182])).
% 1.53/1.79 tff(9896,plain,
% 1.53/1.79 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9202, 28, 1243, 8662])).
% 1.53/1.79 tff(9897,plain,
% 1.53/1.79 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9896, 9196])).
% 1.53/1.79 tff(9898,plain,
% 1.53/1.79 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9205, 9897])).
% 1.53/1.79 tff(9899,plain,
% 1.53/1.79 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9898, 9193])).
% 1.53/1.79 tff(9900,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9901,plain,
% 1.53/1.79 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9902,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9901])).
% 1.53/1.79 tff(9903,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9902, 9900])).
% 1.53/1.79 tff(9904,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9905,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9904, 9903])).
% 1.53/1.79 tff(9906,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9905, 154, 9899, 9895, 9894, 9893, 9885])).
% 1.53/1.79 tff(9907,plain,(b(s(s(s(s(s(s(z)))))), s(s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9908,plain,
% 1.53/1.79 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9907, 9875, 9880, 6184, 9856])).
% 1.53/1.79 tff(9909,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.53/1.79 tff(9910,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9458, 28, 9909, 5885, 8700])).
% 1.53/1.79 tff(9911,plain,((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9912,plain,
% 1.53/1.79 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9911, 5885, 9909])).
% 1.53/1.79 tff(9913,plain,
% 1.53/1.79 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9912, 8654])).
% 1.53/1.79 tff(9914,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6094, 9913])).
% 1.53/1.79 tff(9915,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8749, 9914])).
% 1.53/1.79 tff(9916,plain,
% 1.53/1.79 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6145, 9915, 6104, 5964, 6019])).
% 1.53/1.79 tff(9917,plain,
% 1.53/1.79 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9916, 5937])).
% 1.53/1.79 tff(9918,plain,
% 1.53/1.79 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5986, 9917])).
% 1.53/1.79 tff(9919,plain,
% 1.53/1.79 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9918, 5934])).
% 1.53/1.79 tff(9920,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5994, 28, 1243, 5885, 9919])).
% 1.53/1.79 tff(9921,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9922,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9921, 9875, 8049, 9908, 9879, 9861])).
% 1.53/1.79 tff(9923,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5998, 9922])).
% 1.53/1.79 tff(9924,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6000, 9923])).
% 1.53/1.79 tff(9925,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8685, 9924])).
% 1.53/1.79 tff(9926,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9927,plain,
% 1.53/1.79 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9928,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9927])).
% 1.53/1.79 tff(9929,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9928, 9926])).
% 1.53/1.79 tff(9930,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9931,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9930, 9929])).
% 1.53/1.79 tff(9932,plain,
% 1.53/1.79 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9931, 154, 9873, 141, 9908, 9925])).
% 1.53/1.79 tff(9933,plain,
% 1.53/1.79 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5962, 9932])).
% 1.53/1.79 tff(9934,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9935,plain,
% 1.53/1.79 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9936,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9935])).
% 1.53/1.79 tff(9937,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9936, 9934])).
% 1.53/1.79 tff(9938,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9939,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9938, 9937])).
% 1.53/1.79 tff(9940,plain,
% 1.53/1.79 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9939, 28, 9933, 9856])).
% 1.53/1.79 tff(9941,plain,
% 1.53/1.79 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9940, 9852])).
% 1.53/1.79 tff(9942,plain,
% 1.53/1.79 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5832, 9941])).
% 1.53/1.79 tff(9943,plain,
% 1.53/1.79 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9942, 9851])).
% 1.53/1.79 tff(9944,plain,
% 1.53/1.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[141, 8471])).
% 1.53/1.79 tff(9945,plain,
% 1.53/1.79 (b(s(s(elem!1)), elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[142, 9268])).
% 1.53/1.79 tff(9946,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9947,plain,
% 1.53/1.79 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9948,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9947])).
% 1.53/1.79 tff(9949,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9948, 9946])).
% 1.53/1.79 tff(9950,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9951,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9950, 9949])).
% 1.53/1.79 tff(9952,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9951, 154, 6655, 6656, 6231, 8222, 6866])).
% 1.53/1.79 tff(9953,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9954,plain,
% 1.53/1.79 (~b(elem!1, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9953, 9878, 5651, 9945, 9944])).
% 1.53/1.79 tff(9955,plain,
% 1.53/1.79 (r(elem!1, s(s(s(elem!1))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8232, 9954])).
% 1.53/1.79 tff(9956,plain,
% 1.53/1.79 (r(z, s(s(s(z))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9955, 5662])).
% 1.53/1.79 tff(9957,plain,
% 1.53/1.79 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6084, 9933, 9956])).
% 1.53/1.79 tff(9958,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[6094, 9957])).
% 1.53/1.79 tff(9959,plain,
% 1.53/1.79 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[8749, 9958])).
% 1.53/1.79 tff(9960,plain,
% 1.53/1.79 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5621])).
% 1.53/1.79 tff(9961,plain,
% 1.53/1.79 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[5611])).
% 1.53/1.79 tff(9962,plain,
% 1.53/1.79 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 1.53/1.79 inference(transitivity,[status(thm)],[9961, 9960])).
% 1.53/1.79 tff(9963,plain,
% 1.53/1.79 (b(s(elem!1), elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9827, 9962])).
% 1.53/1.79 tff(9964,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9965,plain,
% 1.53/1.79 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(9966,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[9965])).
% 1.53/1.79 tff(9967,plain,
% 1.53/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[9966, 9964])).
% 1.53/1.79 tff(9968,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(9969,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[9968, 9967])).
% 1.53/1.79 tff(9970,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9969, 154, 9963, 9879, 9908, 9959, 9943])).
% 1.53/1.79 tff(9971,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9972,plain,
% 1.53/1.79 (~r(s(z), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9971, 9850, 17, 9833, 4572, 9848, 2258, 9831])).
% 1.53/1.79 tff(9973,plain,
% 1.53/1.79 (b(s(z), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[252, 9972])).
% 1.53/1.79 tff(9974,plain,
% 1.53/1.79 (~b(s(s(s(z))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[585, 9973, 9833, 2258, 16, 9835])).
% 1.53/1.79 tff(9975,plain,
% 1.53/1.79 (~r(s(s(s(z))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[4609, 9973, 2258, 16, 9844, 9829, 9827, 9835, 9833])).
% 1.53/1.79 tff(9976,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[818, 9975, 9974])).
% 1.53/1.79 tff(9977,plain,(b(s(s(s(z))), z) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(9978,plain,
% 1.53/1.79 (b(s(s(s(z))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[9977, 16, 17])).
% 1.53/1.79 tff(9979,plain,
% 1.53/1.79 (~b(z, s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[162, 9978, 4572, 9833, 9831])).
% 1.53/1.79 tff(9980,plain,
% 1.53/1.79 (r(z, s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[64, 9979])).
% 1.53/1.79 tff(9981,plain,
% 1.53/1.79 (~r(s(s(z)), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[5425, 9980, 9827, 16, 9829, 2258])).
% 1.53/1.80 tff(9982,plain,
% 1.53/1.80 (b(s(s(z)), s(z))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[296, 9981])).
% 1.53/1.80 tff(9983,plain,
% 1.53/1.80 (b(s(s(z)), s(elem!1))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[9982, 8310])).
% 1.53/1.80 tff(9984,plain,
% 1.53/1.80 (b(s(s(z)), elem!1)),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[9831, 5751])).
% 1.53/1.80 tff(9985,plain,
% 1.53/1.80 (b(s(s(s(z))), elem!1)),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[9978, 6196])).
% 1.53/1.80 tff(9986,plain,
% 1.53/1.80 (b(elem!1, s(elem!1))),
% 1.53/1.80 inference(modus_ponens,[status(thm)],[9829, 8837])).
% 1.53/1.80 tff(9987,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(9988,plain,
% 1.53/1.80 (((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(9989,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[9988])).
% 1.53/1.80 tff(9990,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[9989, 9987])).
% 1.63/1.80 tff(9991,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(9992,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[9991, 9990])).
% 1.63/1.80 tff(9993,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9992, 154, 9986, 4572, 9985, 9984, 9983])).
% 1.63/1.80 tff(9994,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(9995,plain,
% 1.63/1.80 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9994, 17])).
% 1.63/1.80 tff(9996,plain,
% 1.63/1.80 (b(s(s(z)), s(s(s(s(z)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1259, 9995])).
% 1.63/1.80 tff(9997,plain,
% 1.63/1.80 (r(s(s(z)), elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[106, 5616])).
% 1.63/1.80 tff(9998,plain,
% 1.63/1.80 (r(s(s(s(z))), elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[171, 9849])).
% 1.63/1.80 tff(9999,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10000,plain,
% 1.63/1.80 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10001,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10000])).
% 1.63/1.80 tff(10002,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[10001, 9999])).
% 1.63/1.80 tff(10003,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(10004,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10003, 10002])).
% 1.63/1.80 tff(10005,plain,
% 1.63/1.80 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10004, 28, 9998, 9997])).
% 1.63/1.80 tff(10006,plain,
% 1.63/1.80 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[138, 10005])).
% 1.63/1.80 tff(10007,plain,
% 1.63/1.80 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[4526, 10006, 1283, 1603, 1282])).
% 1.63/1.80 tff(10008,plain,
% 1.63/1.80 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[564, 10007])).
% 1.63/1.80 tff(10009,plain,
% 1.63/1.80 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10008, 8314])).
% 1.63/1.80 tff(10010,plain,
% 1.63/1.80 (~r(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1027, 10009, 535])).
% 1.63/1.80 tff(10011,plain,
% 1.63/1.80 (b(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[252, 10010])).
% 1.63/1.80 tff(10012,plain,
% 1.63/1.80 (b(s(elem!1), s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10011, 5626])).
% 1.63/1.80 tff(10013,plain,
% 1.63/1.80 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3601, 154, 10006, 1283, 1282, 1603])).
% 1.63/1.80 tff(10014,plain,
% 1.63/1.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[343, 10013])).
% 1.63/1.80 tff(10015,plain,
% 1.63/1.80 (~r(s(s(s(s(z)))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[201, 10008, 171])).
% 1.63/1.80 tff(10016,plain,
% 1.63/1.80 (b(s(s(s(s(z)))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[206, 10015])).
% 1.63/1.80 tff(10017,plain,
% 1.63/1.80 (b(s(s(s(s(z)))), elem!1)),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10016, 5743])).
% 1.63/1.80 tff(10018,plain,
% 1.63/1.80 (~r(z, s(s(s(s(z)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[180, 10008, 171])).
% 1.63/1.80 tff(10019,plain,
% 1.63/1.80 (b(z, s(s(s(s(z)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[191, 10018])).
% 1.63/1.80 tff(10020,plain,
% 1.63/1.80 (b(elem!1, s(s(s(s(z)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10019, 5747])).
% 1.63/1.80 tff(10021,plain,
% 1.63/1.80 (~b(elem!1, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[9532, 154, 1283, 10020, 1603, 10017])).
% 1.63/1.80 tff(10022,plain,
% 1.63/1.80 (r(elem!1, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8651, 60, 10021, 8640])).
% 1.63/1.80 tff(10023,plain,
% 1.63/1.80 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5618])).
% 1.63/1.80 tff(10024,plain,
% 1.63/1.80 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.63/1.80 inference(symmetry,[status(thm)],[10023])).
% 1.63/1.80 tff(10025,plain,
% 1.63/1.80 (r(s(elem!1), s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[7821, 5611])).
% 1.63/1.80 tff(10026,plain,
% 1.63/1.80 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10025, 535])).
% 1.63/1.80 tff(10027,plain,
% 1.63/1.80 (r(s(elem!1), s(s(s(s(z)))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10026, 10024])).
% 1.63/1.80 tff(10028,plain,
% 1.63/1.80 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.63/1.80 inference(symmetry,[status(thm)],[5689])).
% 1.63/1.80 tff(10029,plain,
% 1.63/1.80 ((~b(elem!1, s(s(z)))) <=> (~b(z, s(s(z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10028])).
% 1.63/1.80 tff(10030,plain,
% 1.63/1.80 (~b(z, s(s(z)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10021, 10029])).
% 1.63/1.80 tff(10031,plain,
% 1.63/1.80 (r(z, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[64, 10030])).
% 1.63/1.80 tff(10032,plain,
% 1.63/1.80 (~r(s(s(s(z))), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1930, 10008, 1655])).
% 1.63/1.80 tff(10033,plain,
% 1.63/1.80 (b(s(s(s(z))), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[818, 10032])).
% 1.63/1.80 tff(10034,plain,
% 1.63/1.80 (~b(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3660, 10011, 9827, 1726, 10033])).
% 1.63/1.80 tff(10035,plain,
% 1.63/1.80 (r(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[648, 10034])).
% 1.63/1.80 tff(10036,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.63/1.80 tff(10037,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10038,plain,
% 1.63/1.80 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10039,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10038])).
% 1.63/1.80 tff(10040,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[10039, 10037])).
% 1.63/1.80 tff(10041,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(10042,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10041, 10040])).
% 1.63/1.80 tff(10043,plain,
% 1.63/1.80 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10042, 28, 9536, 9881, 10036])).
% 1.63/1.80 tff(10044,plain,
% 1.63/1.80 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8716, 10043])).
% 1.63/1.80 tff(10045,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5866, 10044])).
% 1.63/1.80 tff(10046,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10045, 6179])).
% 1.63/1.80 tff(10047,plain,
% 1.63/1.80 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8749, 9553])).
% 1.63/1.80 tff(10048,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10049,plain,
% 1.63/1.80 (((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10050,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10049])).
% 1.63/1.80 tff(10051,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[10050, 10048])).
% 1.63/1.80 tff(10052,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(10053,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10052, 10051])).
% 1.63/1.80 tff(10054,plain,
% 1.63/1.80 ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10053, 154, 6511, 6018, 6151])).
% 1.63/1.80 tff(10055,plain,
% 1.63/1.80 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10054, 10047])).
% 1.63/1.80 tff(10056,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10055, 10046])).
% 1.63/1.80 tff(10057,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(10058,plain,
% 1.63/1.80 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10057, 6151, 6018, 6511, 9881, 10036, 4467])).
% 1.63/1.80 tff(10059,plain,
% 1.63/1.80 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8661, 10058])).
% 1.63/1.80 tff(10060,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(z)))))), s(s(z))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5763, 5606])).
% 1.63/1.80 tff(10061,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.80 inference(symmetry,[status(thm)],[10060])).
% 1.63/1.80 tff(10062,assumption,(~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), introduced(assumption)).
% 1.63/1.80 tff(10063,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5805, 5978, 10062])).
% 1.63/1.80 tff(10064,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10063, 10061])).
% 1.63/1.80 tff(10065,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))), introduced(assumption)).
% 1.63/1.80 tff(10066,plain,
% 1.63/1.80 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5980, 5978])).
% 1.63/1.80 tff(10067,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.63/1.80 tff(10068,plain,
% 1.63/1.80 (b(s(s(z)), s(s(s(s(s(s(z))))))) <=> b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5606, 5763])).
% 1.63/1.80 tff(10069,plain,
% 1.63/1.80 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10068])).
% 1.63/1.80 tff(10070,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5763])).
% 1.63/1.80 tff(10071,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.80 inference(symmetry,[status(thm)],[10070])).
% 1.63/1.80 tff(10072,plain,
% 1.63/1.80 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[5763])).
% 1.63/1.80 tff(10073,plain,
% 1.63/1.80 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10072])).
% 1.63/1.80 tff(10074,plain,
% 1.63/1.80 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6083, 6073, 628, 5601])).
% 1.63/1.80 tff(10075,plain,
% 1.63/1.80 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10074, 10073])).
% 1.63/1.80 tff(10076,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8043, 10075, 10065])).
% 1.63/1.80 tff(10077,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10076, 10071])).
% 1.63/1.80 tff(10078,plain,
% 1.63/1.80 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5970, 154, 144, 141])).
% 1.63/1.80 tff(10079,plain,
% 1.63/1.80 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10078, 10077, 5964])).
% 1.63/1.80 tff(10080,plain,
% 1.63/1.80 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10079, 10069])).
% 1.63/1.80 tff(10081,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[5985, 10080, 10067])).
% 1.63/1.80 tff(10082,plain,
% 1.63/1.80 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10081, 6098])).
% 1.63/1.80 tff(10083,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10084,plain,
% 1.63/1.80 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10085,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10084])).
% 1.63/1.80 tff(10086,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[10085, 10083])).
% 1.63/1.80 tff(10087,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(10088,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[10087, 10086])).
% 1.63/1.80 tff(10089,plain,
% 1.63/1.80 ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10088, 28, 18])).
% 1.63/1.80 tff(10090,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10089, 10082, 6074])).
% 1.63/1.80 tff(10091,plain,((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(10092,plain,
% 1.63/1.80 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10091, 10066, 5601, 10065, 6073, 144, 141, 18, 628])).
% 1.63/1.80 tff(10093,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10092, 10064])).
% 1.63/1.80 tff(10094,plain,((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(10095,plain,
% 1.63/1.80 ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10094, 5974, 8039, 5590])).
% 1.63/1.80 tff(10096,plain,
% 1.63/1.80 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[10095, 10059, 144, 141, 628, 18])).
% 1.63/1.80 tff(10097,plain,
% 1.63/1.80 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[6094, 10096])).
% 1.63/1.80 tff(10098,plain,
% 1.63/1.80 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8749, 10097])).
% 1.63/1.80 tff(10099,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8154, 10059])).
% 1.63/1.80 tff(10100,plain,
% 1.63/1.80 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[8152, 10099])).
% 1.63/1.80 tff(10101,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10102,plain,
% 1.63/1.80 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(10103,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[10102])).
% 1.63/1.80 tff(10104,plain,
% 1.63/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[10103, 10101])).
% 1.63/1.81 tff(10105,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(10106,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10105, 10104])).
% 1.63/1.81 tff(10107,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10106, 154, 6105, 1603, 10100, 10098, 6151])).
% 1.63/1.81 tff(10108,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(10109,plain,
% 1.63/1.81 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10108, 10020, 1603, 10006, 1282, 10035, 10031, 10017, 8838, 9881, 10027, 10022])).
% 1.63/1.81 tff(10110,plain,
% 1.63/1.81 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8685, 10109])).
% 1.63/1.81 tff(10111,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6000, 10110])).
% 1.63/1.81 tff(10112,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5998, 10111])).
% 1.63/1.81 tff(10113,plain,
% 1.63/1.81 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5946, 10112, 10014])).
% 1.63/1.81 tff(10114,plain,
% 1.63/1.81 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5962, 10113])).
% 1.63/1.81 tff(10115,plain,
% 1.63/1.81 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[6073, 9118])).
% 1.63/1.81 tff(10116,plain,
% 1.63/1.81 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10095, 6073, 144, 141, 628, 18])).
% 1.63/1.81 tff(10117,plain,
% 1.63/1.81 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8661, 10116])).
% 1.63/1.81 tff(10118,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8668, 28, 4467, 10117, 10115])).
% 1.63/1.81 tff(10119,plain,((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(10120,plain,
% 1.63/1.81 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10119, 10022, 10006, 1282, 10035, 10031])).
% 1.63/1.81 tff(10121,plain,
% 1.63/1.81 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6094, 10120])).
% 1.63/1.81 tff(10122,plain,
% 1.63/1.81 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8749, 10121])).
% 1.63/1.81 tff(10123,plain,
% 1.63/1.81 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5813, 28, 9536, 9881])).
% 1.63/1.81 tff(10124,plain,
% 1.63/1.81 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10123, 9852])).
% 1.63/1.81 tff(10125,plain,
% 1.63/1.81 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5832, 10124])).
% 1.63/1.81 tff(10126,plain,
% 1.63/1.81 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10125, 9851])).
% 1.63/1.81 tff(10127,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10128,plain,
% 1.63/1.81 (((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10129,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[10128])).
% 1.63/1.81 tff(10130,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[10129, 10127])).
% 1.63/1.81 tff(10131,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(10132,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10131, 10130])).
% 1.63/1.81 tff(10133,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10132, 154, 6511, 9963, 6103, 10046, 10126])).
% 1.63/1.81 tff(10134,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(10135,plain,
% 1.63/1.81 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10134, 10122, 8838, 9881, 10027])).
% 1.63/1.81 tff(10136,plain,
% 1.63/1.81 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8661, 10135])).
% 1.63/1.81 tff(10137,plain,
% 1.63/1.81 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8154, 10136])).
% 1.63/1.81 tff(10138,plain,
% 1.63/1.81 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8152, 10137])).
% 1.63/1.81 tff(10139,plain,
% 1.63/1.81 (~b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6051, 154, 1282, 10138, 10114, 10012])).
% 1.63/1.81 tff(10140,plain,
% 1.63/1.81 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10139, 8699])).
% 1.63/1.81 tff(10141,plain,
% 1.63/1.81 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5832, 10140])).
% 1.63/1.81 tff(10142,plain,
% 1.63/1.81 (r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10141, 8697])).
% 1.63/1.81 tff(10143,plain,
% 1.63/1.81 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5970, 154, 10006, 1282, 10138, 10114])).
% 1.63/1.81 tff(10144,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10143, 5937])).
% 1.63/1.81 tff(10145,plain,
% 1.63/1.81 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5986, 10144])).
% 1.63/1.81 tff(10146,plain,
% 1.63/1.81 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10145, 5934])).
% 1.63/1.81 tff(10147,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10148,plain,
% 1.63/1.81 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10149,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[10148])).
% 1.63/1.81 tff(10150,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[10149, 10147])).
% 1.63/1.81 tff(10151,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(z)))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(10152,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10151, 10150])).
% 1.63/1.81 tff(10153,plain,
% 1.63/1.81 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10152, 28, 9881, 10146])).
% 1.63/1.81 tff(10154,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10153, 10142])).
% 1.63/1.81 tff(10155,plain,((~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(10156,plain,
% 1.63/1.81 (~r(s(s(z)), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10155, 171, 2879, 9829, 535, 9996, 6184, 1655])).
% 1.63/1.81 tff(10157,plain,
% 1.63/1.81 (b(s(s(z)), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[122, 10156])).
% 1.63/1.81 tff(10158,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[4721, 1298, 1296, 1283, 1603, 142])).
% 1.63/1.81 tff(10159,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(10160,plain,
% 1.63/1.81 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10159, 10157, 2879, 9996, 171])).
% 1.63/1.81 tff(10161,plain,
% 1.63/1.81 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[564, 10160])).
% 1.63/1.81 tff(10162,plain,
% 1.63/1.81 (~b(z, s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3660, 1, 9827, 1726, 232])).
% 1.63/1.81 tff(10163,plain,
% 1.63/1.81 (r(z, s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[648, 10162])).
% 1.63/1.81 tff(10164,plain,
% 1.63/1.81 (b(s(s(s(z))), s(elem!1))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1, 8327])).
% 1.63/1.81 tff(10165,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10166,plain,
% 1.63/1.81 (((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10167,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[10166])).
% 1.63/1.81 tff(10168,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[10167, 10165])).
% 1.63/1.81 tff(10169,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), elem!1)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(10170,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10169, 10168])).
% 1.63/1.81 tff(10171,plain,
% 1.63/1.81 (~b(elem!1, s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10170, 154, 8838, 9963, 9631, 10164])).
% 1.63/1.81 tff(10172,plain,
% 1.63/1.81 (~b(z, s(s(s(elem!1))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10171, 9235])).
% 1.63/1.81 tff(10173,plain,
% 1.63/1.81 (r(z, s(s(s(elem!1))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3977, 10172])).
% 1.63/1.81 tff(10174,plain,
% 1.63/1.81 (r(elem!1, s(s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10173, 9232])).
% 1.63/1.81 tff(10175,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10176,plain,
% 1.63/1.81 (((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10177,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[10176])).
% 1.63/1.81 tff(10178,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[10177, 10175])).
% 1.63/1.81 tff(10179,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(10180,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10179, 10178])).
% 1.63/1.81 tff(10181,plain,
% 1.63/1.81 (~r(elem!1, s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10180, 28, 124, 10174])).
% 1.63/1.81 tff(10182,plain,
% 1.63/1.81 (b(elem!1, s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8651, 60, 10181, 8640])).
% 1.63/1.81 tff(10183,plain,
% 1.63/1.81 (~b(s(s(s(s(z)))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9675, 154, 1283, 10182, 8049, 1603])).
% 1.63/1.81 tff(10184,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8854, 10183])).
% 1.63/1.81 tff(10185,plain,
% 1.63/1.81 ((~r(elem!1, s(s(z)))) <=> (~r(z, s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[8892])).
% 1.63/1.81 tff(10186,plain,
% 1.63/1.81 (~r(z, s(s(z)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10181, 10185])).
% 1.63/1.81 tff(10187,plain,
% 1.63/1.81 (b(z, s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[64, 10186])).
% 1.63/1.81 tff(10188,plain,
% 1.63/1.81 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1309, 10187, 1283, 171, 142])).
% 1.63/1.81 tff(10189,plain,
% 1.63/1.81 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[564, 10188])).
% 1.63/1.81 tff(10190,plain,
% 1.63/1.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1471, 10187, 142, 10163, 1283])).
% 1.63/1.81 tff(10191,plain,
% 1.63/1.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[343, 10190])).
% 1.63/1.81 tff(10192,plain,
% 1.63/1.81 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9251, 10115, 9242])).
% 1.63/1.81 tff(10193,plain,
% 1.63/1.81 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8189, 10192])).
% 1.63/1.81 tff(10194,assumption,(~b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.63/1.81 tff(10195,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10194, 9365])).
% 1.63/1.81 tff(10196,plain,(b(s(s(s(z))), s(s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(10197,plain,
% 1.63/1.81 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10196, 10193])).
% 1.63/1.81 tff(10198,plain,
% 1.63/1.81 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[9911, 10115, 9909])).
% 1.63/1.81 tff(10199,plain,
% 1.63/1.81 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5998, 10198])).
% 1.63/1.81 tff(10200,plain,
% 1.63/1.81 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6000, 10199])).
% 1.63/1.81 tff(10201,plain,
% 1.63/1.81 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8685, 10200])).
% 1.63/1.81 tff(10202,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.63/1.81 tff(10203,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10204,plain,
% 1.63/1.81 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10205,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[10204])).
% 1.63/1.81 tff(10206,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[10205, 10203])).
% 1.63/1.81 tff(10207,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(10208,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10207, 10206])).
% 1.63/1.81 tff(10209,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10208, 154, 1603, 566, 5964, 6151, 10202])).
% 1.63/1.81 tff(10210,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(10211,plain,
% 1.63/1.81 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10210, 10201, 566, 1603, 10197])).
% 1.63/1.81 tff(10212,plain,
% 1.63/1.81 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8152, 10211])).
% 1.63/1.81 tff(10213,plain,
% 1.63/1.81 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8154, 10212])).
% 1.63/1.81 tff(10214,plain,
% 1.63/1.81 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8661, 10213])).
% 1.63/1.81 tff(10215,plain,
% 1.63/1.81 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[10042, 28, 10214, 9881, 10036])).
% 1.63/1.81 tff(10216,plain,
% 1.63/1.81 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[8716, 10215])).
% 1.63/1.81 tff(10217,plain,
% 1.63/1.81 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5866, 10216])).
% 1.63/1.81 tff(10218,plain,
% 1.63/1.81 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[10217, 6179])).
% 1.63/1.81 tff(10219,plain,
% 1.63/1.81 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[6084, 6073, 628])).
% 1.63/1.81 tff(10220,plain,
% 1.63/1.81 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[5962, 10219])).
% 1.63/1.81 tff(10221,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10222,plain,
% 1.63/1.81 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(10223,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[10222])).
% 1.63/1.81 tff(10224,plain,
% 1.63/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[10223, 10221])).
% 1.63/1.82 tff(10225,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(10226,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10225, 10224])).
% 1.63/1.82 tff(10227,plain,
% 1.63/1.82 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10226, 154, 615, 10220, 10201, 7982])).
% 1.63/1.82 tff(10228,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10227, 10218])).
% 1.63/1.82 tff(10229,plain,((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10230,plain,
% 1.63/1.82 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10229, 10191, 10164, 9881, 10036, 10189, 1603, 10184, 10174, 10163])).
% 1.63/1.82 tff(10231,plain,
% 1.63/1.82 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[6094, 10230])).
% 1.63/1.82 tff(10232,plain,
% 1.63/1.82 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8749, 10231])).
% 1.63/1.82 tff(10233,plain,
% 1.63/1.82 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10134, 10232, 10036, 9881, 8838])).
% 1.63/1.82 tff(10234,plain,
% 1.63/1.82 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8661, 10233])).
% 1.63/1.82 tff(10235,plain,
% 1.63/1.82 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8154, 10234])).
% 1.63/1.82 tff(10236,plain,
% 1.63/1.82 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8152, 10235])).
% 1.63/1.82 tff(10237,plain,
% 1.63/1.82 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8086, 10236, 1283, 10182, 10232])).
% 1.63/1.82 tff(10238,plain,
% 1.63/1.82 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10237, 9378])).
% 1.63/1.82 tff(10239,plain,
% 1.63/1.82 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9205, 10238])).
% 1.63/1.82 tff(10240,plain,
% 1.63/1.82 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10239, 9194])).
% 1.63/1.82 tff(10241,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10242,plain,
% 1.63/1.82 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10243,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[10242])).
% 1.63/1.82 tff(10244,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[10243, 10241])).
% 1.63/1.82 tff(10245,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z)))))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(10246,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(z))))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10245, 10244])).
% 1.63/1.82 tff(10247,plain,
% 1.63/1.82 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10246, 28, 10240, 10036])).
% 1.63/1.82 tff(10248,plain,
% 1.63/1.82 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10247, 9852])).
% 1.63/1.82 tff(10249,plain,
% 1.63/1.82 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[5832, 10248])).
% 1.63/1.82 tff(10250,plain,
% 1.63/1.82 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10249, 9851])).
% 1.63/1.82 tff(10251,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[9969, 154, 9963, 10182, 10236, 10232, 10250])).
% 1.63/1.82 tff(10252,plain,((~b(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10253,plain,
% 1.63/1.82 (~b(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10252, 124, 9996, 6184, 1603, 142, 171, 10027, 9829, 3658])).
% 1.63/1.82 tff(10254,plain,
% 1.63/1.82 (r(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[818, 10253])).
% 1.63/1.82 tff(10255,plain,
% 1.63/1.82 ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4372, 5637])).
% 1.63/1.82 tff(10256,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10255, 10254, 535])).
% 1.63/1.82 tff(10257,plain,
% 1.63/1.82 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[564, 10256])).
% 1.63/1.82 tff(10258,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1556, 10254, 17])).
% 1.63/1.82 tff(10259,plain,
% 1.63/1.82 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[104, 10258])).
% 1.63/1.82 tff(10260,plain,
% 1.63/1.82 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3235, 154, 9996, 10259, 1603, 10257])).
% 1.63/1.82 tff(10261,plain,
% 1.63/1.82 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[343, 10260])).
% 1.63/1.82 tff(10262,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1411, 10261, 10254])).
% 1.63/1.82 tff(10263,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[318, 10262])).
% 1.63/1.82 tff(10264,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10263, 5625])).
% 1.63/1.82 tff(10265,plain,
% 1.63/1.82 (~r(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1125, 10254, 124])).
% 1.63/1.82 tff(10266,plain,
% 1.63/1.82 (b(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[296, 10265])).
% 1.63/1.82 tff(10267,plain,
% 1.63/1.82 (b(s(s(z)), s(elem!1))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10266, 8310])).
% 1.63/1.82 tff(10268,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10269,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(10270,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10269, 10268])).
% 1.63/1.82 tff(10271,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10270, 154, 9963, 8049, 1603, 10267, 10264])).
% 1.63/1.82 tff(10272,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10273,plain,
% 1.63/1.82 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10272, 10157, 17, 535, 2879, 171])).
% 1.63/1.82 tff(10274,plain,
% 1.63/1.82 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[138, 10273])).
% 1.63/1.82 tff(10275,plain,
% 1.63/1.82 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4526, 10161, 9996, 2879, 10274])).
% 1.63/1.82 tff(10276,plain,
% 1.63/1.82 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[104, 10275])).
% 1.63/1.82 tff(10277,plain,
% 1.63/1.82 (~r(z, s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1346, 10276, 171])).
% 1.63/1.82 tff(10278,plain,
% 1.63/1.82 (b(z, s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[64, 10277])).
% 1.63/1.82 tff(10279,plain,
% 1.63/1.82 (~r(s(z), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[597, 10276, 17])).
% 1.63/1.82 tff(10280,plain,
% 1.63/1.82 (b(s(z), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[252, 10279])).
% 1.63/1.82 tff(10281,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1556, 10276, 17])).
% 1.63/1.82 tff(10282,plain,
% 1.63/1.82 (b(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[818, 10281])).
% 1.63/1.82 tff(10283,plain,
% 1.63/1.82 (~b(z, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3660, 10282, 9827, 9829, 10280])).
% 1.63/1.82 tff(10284,plain,
% 1.63/1.82 (r(z, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[648, 10283])).
% 1.63/1.82 tff(10285,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1471, 10284, 10157, 10278, 9996])).
% 1.63/1.82 tff(10286,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[343, 10285])).
% 1.63/1.82 tff(10287,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2654, 154, 10274, 10286, 9996, 2879, 10161])).
% 1.63/1.82 tff(10288,plain,((~r(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10289,plain,
% 1.63/1.82 (~r(s(s(s(z))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10288, 5645, 17, 5634])).
% 1.63/1.82 tff(10290,plain,
% 1.63/1.82 (b(s(s(s(z))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[169, 10289])).
% 1.63/1.82 tff(10291,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4729, 66, 9827, 9829, 1655])).
% 1.63/1.82 tff(10292,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[206, 10291])).
% 1.63/1.82 tff(10293,plain,
% 1.63/1.82 (~b(s(z), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3184, 3209, 9827, 9829, 143])).
% 1.63/1.82 tff(10294,plain,
% 1.63/1.82 (r(s(z), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[252, 10293])).
% 1.63/1.82 tff(10295,plain,
% 1.63/1.82 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3656, 10294, 17])).
% 1.63/1.82 tff(10296,plain,
% 1.63/1.82 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[138, 10295])).
% 1.63/1.82 tff(10297,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1957, 10294, 1655])).
% 1.63/1.82 tff(10298,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[343, 10297])).
% 1.63/1.82 tff(10299,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3731, 10298, 10296, 9996, 143, 10292])).
% 1.63/1.82 tff(10300,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10301,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10300, 10290, 5634, 17])).
% 1.63/1.82 tff(10302,plain,
% 1.63/1.82 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[564, 10301])).
% 1.63/1.82 tff(10303,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2000, 5634, 17])).
% 1.63/1.82 tff(10304,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[229, 10303])).
% 1.63/1.82 tff(10305,plain,
% 1.63/1.82 ((~b(elem!1, s(s(s(z))))) <=> (~b(z, s(s(s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[9694])).
% 1.63/1.82 tff(10306,plain,
% 1.63/1.82 (b(elem!1, s(z))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9829, 8836])).
% 1.63/1.82 tff(10307,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3186, 106, 17, 9827])).
% 1.63/1.82 tff(10308,plain,
% 1.63/1.82 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[104, 10307])).
% 1.63/1.82 tff(10309,plain,
% 1.63/1.82 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4526, 10308, 9996, 1603, 566])).
% 1.63/1.82 tff(10310,plain,
% 1.63/1.82 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[138, 10309])).
% 1.63/1.82 tff(10311,plain,
% 1.63/1.82 (~r(s(z), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3656, 10310, 17])).
% 1.63/1.82 tff(10312,plain,
% 1.63/1.82 (b(s(z), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[252, 10311])).
% 1.63/1.82 tff(10313,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10314,plain,
% 1.63/1.82 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10315,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[10314])).
% 1.63/1.82 tff(10316,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[10315, 10313])).
% 1.63/1.82 tff(10317,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~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))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(10318,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10317, 10316])).
% 1.63/1.82 tff(10319,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10318, 154, 4456, 2604, 232, 143, 4455])).
% 1.63/1.82 tff(10320,plain,((~b(s(s(s(z))), z)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10321,plain,
% 1.63/1.82 (~b(elem!1, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10320, 10312, 9827, 10306, 143])).
% 1.63/1.82 tff(10322,plain,
% 1.63/1.82 (~b(z, s(s(s(z))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10321, 10305])).
% 1.63/1.82 tff(10323,plain,
% 1.63/1.82 (~r(z, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2080, 10310, 106])).
% 1.63/1.82 tff(10324,plain,
% 1.63/1.82 (b(z, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[648, 10323])).
% 1.63/1.82 tff(10325,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10324, 10322])).
% 1.63/1.82 tff(10326,plain,((~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10327,plain,
% 1.63/1.82 (~r(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10326, 10290, 17, 10304, 10302])).
% 1.63/1.82 tff(10328,plain,
% 1.63/1.82 (b(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[122, 10327])).
% 1.63/1.82 tff(10329,plain,
% 1.63/1.82 (~b(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4762, 10328, 9827, 17, 10290])).
% 1.63/1.82 tff(10330,plain,
% 1.63/1.82 (r(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[818, 10329])).
% 1.63/1.82 tff(10331,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1556, 10330, 17])).
% 1.63/1.82 tff(10332,plain,
% 1.63/1.82 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[104, 10331])).
% 1.63/1.82 tff(10333,plain,
% 1.63/1.82 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3235, 154, 9996, 10304, 10302])).
% 1.63/1.82 tff(10334,plain,
% 1.63/1.82 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10333, 10332])).
% 1.63/1.82 tff(10335,plain,
% 1.63/1.82 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[343, 10334])).
% 1.63/1.82 tff(10336,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1411, 10335, 10330])).
% 1.63/1.82 tff(10337,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[318, 10336])).
% 1.63/1.82 tff(10338,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10337, 5625])).
% 1.63/1.82 tff(10339,plain,
% 1.63/1.82 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4526, 10332, 9996, 10304, 10302])).
% 1.63/1.82 tff(10340,plain,
% 1.63/1.82 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[138, 10339])).
% 1.63/1.82 tff(10341,plain,
% 1.63/1.82 (~r(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1125, 10340, 10330])).
% 1.63/1.82 tff(10342,plain,
% 1.63/1.82 (b(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[296, 10341])).
% 1.63/1.82 tff(10343,plain,
% 1.63/1.82 (b(s(s(z)), s(elem!1))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10342, 8310])).
% 1.63/1.82 tff(10344,plain,
% 1.63/1.82 (b(s(s(z)), elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10328, 5751])).
% 1.63/1.82 tff(10345,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10270, 154, 9963, 10344, 10304, 10343, 10338])).
% 1.63/1.82 tff(10346,plain,(b(s(z), s(s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10347,plain,
% 1.63/1.82 (b(s(z), s(s(s(s(z)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10346, 17])).
% 1.63/1.82 tff(10348,plain,
% 1.63/1.82 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5618])).
% 1.63/1.82 tff(10349,plain,
% 1.63/1.82 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.82 inference(symmetry,[status(thm)],[10348])).
% 1.63/1.82 tff(10350,plain,
% 1.63/1.82 (b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10347, 8578])).
% 1.63/1.82 tff(10351,plain,
% 1.63/1.82 (b(s(z), elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[9827, 9961])).
% 1.63/1.82 tff(10352,plain,
% 1.63/1.82 (~b(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[4780, 66, 9827, 17, 10347])).
% 1.63/1.82 tff(10353,plain,
% 1.63/1.82 (r(s(s(z)), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[122, 10352])).
% 1.63/1.82 tff(10354,plain,
% 1.63/1.82 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3703, 10353, 9827, 17, 10347])).
% 1.63/1.82 tff(10355,plain,
% 1.63/1.82 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[138, 10354])).
% 1.63/1.82 tff(10356,plain,
% 1.63/1.82 (~r(s(s(s(z))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3711, 66, 9827, 9829, 10347])).
% 1.63/1.82 tff(10357,plain,
% 1.63/1.82 (b(s(s(s(z))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[169, 10356])).
% 1.63/1.82 tff(10358,plain,
% 1.63/1.82 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3186, 10353, 17, 9827])).
% 1.63/1.82 tff(10359,plain,
% 1.63/1.82 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[104, 10358])).
% 1.63/1.82 tff(10360,plain,
% 1.63/1.82 (~b(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3741, 10359, 9827, 10347, 10353, 9996, 10357, 10355, 9829])).
% 1.63/1.82 tff(10361,plain,
% 1.63/1.82 (r(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[818, 10360])).
% 1.63/1.82 tff(10362,plain,
% 1.63/1.82 (~r(z, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3802, 10361, 66])).
% 1.63/1.82 tff(10363,plain,
% 1.63/1.82 (b(z, s(s(s(z))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[648, 10362])).
% 1.63/1.82 tff(10364,plain,
% 1.63/1.82 (~b(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3681, 10363, 9827, 17, 10347, 66, 10353, 10361])).
% 1.63/1.82 tff(10365,plain,
% 1.63/1.82 (r(s(s(z)), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[296, 10364])).
% 1.63/1.82 tff(10366,plain,
% 1.63/1.82 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[2354, 10365, 10355, 10359, 10361])).
% 1.63/1.82 tff(10367,plain,
% 1.63/1.82 (b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[441, 10366])).
% 1.63/1.82 tff(10368,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.63/1.82 tff(10369,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10370,plain,
% 1.63/1.82 (((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10371,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[10370])).
% 1.63/1.82 tff(10372,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[10371, 10369])).
% 1.63/1.82 tff(10373,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(10374,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10373, 10372])).
% 1.63/1.82 tff(10375,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10374, 154, 6963, 4456, 10368, 505, 444])).
% 1.63/1.82 tff(10376,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(10377,plain,
% 1.63/1.82 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[10376, 10367, 10351, 10306, 10350])).
% 1.63/1.82 tff(10378,plain,
% 1.63/1.82 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[8632, 10377])).
% 1.63/1.82 tff(10379,plain,
% 1.63/1.82 (r(s(s(s(s(z)))), elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10378, 9355])).
% 1.63/1.82 tff(10380,plain,
% 1.63/1.82 (r(s(s(s(z))), s(elem!1))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10361, 8688])).
% 1.63/1.82 tff(10381,plain,
% 1.63/1.82 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.82 inference(transitivity,[status(thm)],[6196, 6195])).
% 1.63/1.82 tff(10382,plain,
% 1.63/1.82 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10357, 10381])).
% 1.63/1.82 tff(10383,plain,
% 1.63/1.82 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[5590])).
% 1.63/1.82 tff(10384,plain,
% 1.63/1.82 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(symmetry,[status(thm)],[10383])).
% 1.63/1.82 tff(10385,plain,
% 1.63/1.82 (b(s(elem!1), s(s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10347, 9478])).
% 1.63/1.82 tff(10386,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[853, 10361, 66])).
% 1.63/1.82 tff(10387,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[318, 10386])).
% 1.63/1.82 tff(10388,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[10387, 5625])).
% 1.63/1.82 tff(10389,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10390,plain,
% 1.63/1.82 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(10391,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[10390])).
% 1.63/1.82 tff(10392,plain,
% 1.63/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10391, 10389])).
% 1.63/1.83 tff(10393,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(10394,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10393, 10392])).
% 1.63/1.83 tff(10395,plain,
% 1.63/1.83 (~b(elem!1, s(s(s(s(z)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10394, 154, 9986, 9963, 10388, 10385])).
% 1.63/1.83 tff(10396,plain,
% 1.63/1.83 (r(elem!1, s(s(s(s(z)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8062, 10395])).
% 1.63/1.83 tff(10397,plain,
% 1.63/1.83 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10396, 10384])).
% 1.63/1.83 tff(10398,plain,
% 1.63/1.83 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[7792, 5611])).
% 1.63/1.83 tff(10399,plain,
% 1.63/1.83 (~r(elem!1, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10398, 10397, 8315])).
% 1.63/1.83 tff(10400,plain,
% 1.63/1.83 (b(elem!1, s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8232, 10399])).
% 1.63/1.83 tff(10401,plain,
% 1.63/1.83 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[7462, 10400, 9963, 9986, 10382])).
% 1.63/1.83 tff(10402,plain,
% 1.63/1.83 (r(s(elem!1), s(s(s(elem!1))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8445, 10401])).
% 1.63/1.83 tff(10403,plain,
% 1.63/1.83 (r(s(elem!1), s(s(s(z))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10402, 9854])).
% 1.63/1.83 tff(10404,plain,
% 1.63/1.83 (r(s(s(z)), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10353, 5616])).
% 1.63/1.83 tff(10405,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10406,plain,
% 1.63/1.83 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10407,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[10406])).
% 1.63/1.83 tff(10408,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10407, 10405])).
% 1.63/1.83 tff(10409,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(10410,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10409, 10408])).
% 1.63/1.83 tff(10411,plain,
% 1.63/1.83 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10410, 28, 10404, 10379])).
% 1.63/1.83 tff(10412,plain,
% 1.63/1.83 (b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[229, 10411])).
% 1.63/1.83 tff(10413,plain,
% 1.63/1.83 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3601, 154, 10355, 9996, 10359, 10412])).
% 1.63/1.83 tff(10414,plain,
% 1.63/1.83 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[343, 10413])).
% 1.63/1.83 tff(10415,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8774, 5938, 8765])).
% 1.63/1.83 tff(10416,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5866, 10415])).
% 1.63/1.83 tff(10417,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10416, 6179])).
% 1.63/1.83 tff(10418,plain,
% 1.63/1.83 (~r(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9939, 28, 5938, 9886])).
% 1.63/1.83 tff(10419,plain,
% 1.63/1.83 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10418, 9852])).
% 1.63/1.83 tff(10420,plain,
% 1.63/1.83 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5832, 10419])).
% 1.63/1.83 tff(10421,plain,
% 1.63/1.83 (b(s(elem!1), s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10420, 9851])).
% 1.63/1.83 tff(10422,plain,
% 1.63/1.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5946, 5938, 604])).
% 1.63/1.83 tff(10423,plain,
% 1.63/1.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5998, 10422])).
% 1.63/1.83 tff(10424,plain,
% 1.63/1.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6000, 10423])).
% 1.63/1.83 tff(10425,plain,
% 1.63/1.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8685, 10424])).
% 1.63/1.83 tff(10426,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10427,plain,
% 1.63/1.83 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10428,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[10427])).
% 1.63/1.83 tff(10429,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10428, 10426])).
% 1.63/1.83 tff(10430,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(10431,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10430, 10429])).
% 1.63/1.83 tff(10432,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10431, 28, 604, 5938])).
% 1.63/1.83 tff(10433,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10432, 9196])).
% 1.63/1.83 tff(10434,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9205, 10433])).
% 1.63/1.83 tff(10435,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10434, 9193])).
% 1.63/1.83 tff(10436,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9905, 154, 10435, 10425, 9894, 10421, 10417])).
% 1.63/1.83 tff(10437,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(10438,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10437, 10414, 10385, 10403, 10380])).
% 1.63/1.83 tff(10439,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5962, 10438])).
% 1.63/1.83 tff(10440,plain,
% 1.63/1.83 (b(s(s(s(z))), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10357, 6196])).
% 1.63/1.83 tff(10441,plain,
% 1.63/1.83 (b(elem!1, s(s(s(z))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10400, 6186])).
% 1.63/1.83 tff(10442,plain,
% 1.63/1.83 (~b(elem!1, s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8647, 154, 10355, 10359, 10441, 10440])).
% 1.63/1.83 tff(10443,plain,
% 1.63/1.83 (r(elem!1, s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8651, 60, 10442, 8640])).
% 1.63/1.83 tff(10444,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10445,plain,
% 1.63/1.83 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10446,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[10445])).
% 1.63/1.83 tff(10447,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10446, 10444])).
% 1.63/1.83 tff(10448,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(10449,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10448, 10447])).
% 1.63/1.83 tff(10450,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10449, 28, 4467, 9536])).
% 1.63/1.83 tff(10451,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10450, 9376])).
% 1.63/1.83 tff(10452,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9419, 10451])).
% 1.63/1.83 tff(10453,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10452, 9535])).
% 1.63/1.83 tff(10454,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10455,plain,
% 1.63/1.83 (((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10456,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[10455])).
% 1.63/1.83 tff(10457,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10456, 10454])).
% 1.63/1.83 tff(10458,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(elem!1))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(10459,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10458, 10457])).
% 1.63/1.83 tff(10460,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10459, 154, 6511, 9963, 10047, 10453, 10126])).
% 1.63/1.83 tff(10461,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(10462,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10461, 10443, 9986, 6184])).
% 1.63/1.83 tff(10463,plain,
% 1.63/1.83 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8661, 10462])).
% 1.63/1.83 tff(10464,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8154, 10463])).
% 1.63/1.83 tff(10465,plain,
% 1.63/1.83 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8152, 10464])).
% 1.63/1.83 tff(10466,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10467,plain,
% 1.63/1.83 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10468,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[10467])).
% 1.63/1.83 tff(10469,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10468, 10466])).
% 1.63/1.83 tff(10470,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(10471,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10470, 10469])).
% 1.63/1.83 tff(10472,plain,
% 1.63/1.83 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10471, 154, 10359, 10441, 10465])).
% 1.63/1.83 tff(10473,plain,
% 1.63/1.83 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10472, 10439])).
% 1.63/1.83 tff(10474,plain,
% 1.63/1.83 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8749, 10473])).
% 1.63/1.83 tff(10475,plain,
% 1.63/1.83 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6094, 10474])).
% 1.63/1.83 tff(10476,plain,
% 1.63/1.83 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10475, 9118])).
% 1.63/1.83 tff(10477,plain,
% 1.63/1.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[9911, 10476, 10379])).
% 1.63/1.83 tff(10478,plain,
% 1.63/1.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[5998, 10477])).
% 1.63/1.83 tff(10479,plain,
% 1.63/1.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[6000, 10478])).
% 1.63/1.83 tff(10480,plain,
% 1.63/1.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[8685, 10479])).
% 1.63/1.83 tff(10481,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10482,plain,
% 1.63/1.83 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10483,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[10482])).
% 1.63/1.83 tff(10484,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10483, 10481])).
% 1.63/1.83 tff(10485,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(10486,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10485, 10484])).
% 1.63/1.83 tff(10487,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10486, 154, 10355, 10412, 10465, 10439, 10480])).
% 1.63/1.83 tff(10488,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(10489,plain,
% 1.63/1.83 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[10488, 17])).
% 1.63/1.83 tff(10490,plain,
% 1.63/1.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[564, 10489])).
% 1.63/1.83 tff(10491,plain,
% 1.63/1.83 (~r(s(s(z)), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3703, 124, 9827, 17, 10347])).
% 1.63/1.83 tff(10492,plain,
% 1.63/1.83 (b(s(s(z)), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[122, 10491])).
% 1.63/1.83 tff(10493,plain,
% 1.63/1.83 (~b(s(s(s(z))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[4833, 10492, 9827, 17, 9996, 10347])).
% 1.63/1.83 tff(10494,plain,
% 1.63/1.83 (r(s(s(s(z))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[818, 10493])).
% 1.63/1.83 tff(10495,plain,
% 1.63/1.83 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1556, 10494, 17])).
% 1.63/1.83 tff(10496,plain,
% 1.63/1.83 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[104, 10495])).
% 1.63/1.83 tff(10497,plain,
% 1.63/1.83 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3691, 10496, 10347, 10490, 3658])).
% 1.63/1.83 tff(10498,plain,
% 1.63/1.83 (r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[229, 10497])).
% 1.63/1.83 tff(10499,plain,
% 1.63/1.83 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10498, 9864])).
% 1.63/1.83 tff(10500,plain,
% 1.63/1.83 (b(s(s(elem!1)), elem!1)),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10492, 9268])).
% 1.63/1.83 tff(10501,plain,
% 1.63/1.83 (~r(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[1125, 10494, 124])).
% 1.63/1.83 tff(10502,plain,
% 1.63/1.83 (b(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[296, 10501])).
% 1.63/1.83 tff(10503,plain,
% 1.63/1.83 (b(s(s(elem!1)), s(elem!1))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[10502, 8255])).
% 1.63/1.83 tff(10504,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10505,plain,
% 1.63/1.83 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(10506,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[10505])).
% 1.63/1.83 tff(10507,plain,
% 1.63/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[10506, 10504])).
% 1.63/1.83 tff(10508,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10509,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10508, 10507])).
% 1.63/1.84 tff(10510,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10509, 154, 6511, 6868, 6655, 6656, 7873])).
% 1.63/1.84 tff(10511,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10512,plain,
% 1.63/1.84 (~b(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10511, 10503, 9963, 9986, 10500])).
% 1.63/1.84 tff(10513,plain,
% 1.63/1.84 (r(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8923, 10512])).
% 1.63/1.84 tff(10514,plain,
% 1.63/1.84 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8903, 10513, 10499])).
% 1.63/1.84 tff(10515,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8632, 10514])).
% 1.63/1.84 tff(10516,plain,
% 1.63/1.84 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10376, 10515, 10351, 10306, 10350])).
% 1.63/1.84 tff(10517,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[441, 10516])).
% 1.63/1.84 tff(10518,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.84 inference(symmetry,[status(thm)],[7756])).
% 1.63/1.84 tff(10519,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[345, 10518])).
% 1.63/1.84 tff(10520,assumption,(~r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.63/1.84 tff(10521,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10520, 10519])).
% 1.63/1.84 tff(10522,plain,((~r(s(s(s(s(elem!1)))), s(z))) | r(s(s(s(s(elem!1)))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10523,plain,
% 1.63/1.84 ((~r(s(s(s(s(elem!1)))), s(z))) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10522, 5611])).
% 1.63/1.84 tff(10524,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10523, 10517])).
% 1.63/1.84 tff(10525,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10524, 10349])).
% 1.63/1.84 tff(10526,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10527,plain,
% 1.63/1.84 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10528,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(z))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10527])).
% 1.63/1.84 tff(10529,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10528, 10526])).
% 1.63/1.84 tff(10530,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10531,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(s(z))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10530, 10529])).
% 1.63/1.84 tff(10532,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10531, 28, 10498, 6184])).
% 1.63/1.84 tff(10533,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10532, 10525])).
% 1.63/1.84 tff(10534,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10535,plain,
% 1.63/1.84 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10534, 17])).
% 1.63/1.84 tff(10536,plain,
% 1.63/1.84 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[138, 10535])).
% 1.63/1.84 tff(10537,plain,
% 1.63/1.84 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5687, 10028])).
% 1.63/1.84 tff(10538,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1243, 9864])).
% 1.63/1.84 tff(10539,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5590])).
% 1.63/1.84 tff(10540,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(symmetry,[status(thm)],[10539])).
% 1.63/1.84 tff(10541,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5590, 5622])).
% 1.63/1.84 tff(10542,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10348, 10541, 10540])).
% 1.63/1.84 tff(10543,plain,
% 1.63/1.84 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10542])).
% 1.63/1.84 tff(10544,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10531, 28, 1243, 6184])).
% 1.63/1.84 tff(10545,plain,
% 1.63/1.84 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10544, 10543])).
% 1.63/1.84 tff(10546,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[441, 10545])).
% 1.63/1.84 tff(10547,plain,
% 1.63/1.84 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10376, 10546, 10351, 10306, 10350])).
% 1.63/1.84 tff(10548,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8632, 10547])).
% 1.63/1.84 tff(10549,plain,
% 1.63/1.84 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8903, 10548, 10538])).
% 1.63/1.84 tff(10550,plain,
% 1.63/1.84 (b(elem!1, s(s(elem!1)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8923, 10549])).
% 1.63/1.84 tff(10551,plain,
% 1.63/1.84 (b(z, s(s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10550, 10537])).
% 1.63/1.84 tff(10552,plain,
% 1.63/1.84 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.63/1.84 inference(symmetry,[status(thm)],[5751])).
% 1.63/1.84 tff(10553,plain,
% 1.63/1.84 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5611])).
% 1.63/1.84 tff(10554,plain,
% 1.63/1.84 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.63/1.84 inference(transitivity,[status(thm)],[10553, 9266, 10552])).
% 1.63/1.84 tff(10555,plain,
% 1.63/1.84 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8522, 10548, 10538])).
% 1.63/1.84 tff(10556,plain,
% 1.63/1.84 (b(s(s(elem!1)), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8623, 10555])).
% 1.63/1.84 tff(10557,plain,
% 1.63/1.84 (b(s(s(elem!1)), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[8615, 10556])).
% 1.63/1.84 tff(10558,plain,
% 1.63/1.84 (b(s(s(z)), z)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10557, 10554])).
% 1.63/1.84 tff(10559,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4833, 10558, 9827, 17, 9996, 10347])).
% 1.63/1.84 tff(10560,plain,
% 1.63/1.84 (r(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[818, 10559])).
% 1.63/1.84 tff(10561,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 1.63/1.84 inference(symmetry,[status(thm)],[8255])).
% 1.63/1.84 tff(10562,plain,
% 1.63/1.84 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(z)), s(z)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10561])).
% 1.63/1.84 tff(10563,plain,
% 1.63/1.84 (~b(s(s(elem!1)), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10511, 10550, 9963, 9986, 10556])).
% 1.63/1.84 tff(10564,plain,
% 1.63/1.84 (~b(s(s(z)), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10563, 10562])).
% 1.63/1.84 tff(10565,plain,
% 1.63/1.84 (r(s(s(z)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[296, 10564])).
% 1.63/1.84 tff(10566,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[865, 10565, 10560])).
% 1.63/1.84 tff(10567,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[104, 10566])).
% 1.63/1.84 tff(10568,plain,
% 1.63/1.84 (~b(s(s(s(z))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[162, 10567, 10558, 10551, 10536])).
% 1.63/1.84 tff(10569,plain,
% 1.63/1.84 (~r(s(s(s(z))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4548, 10567, 9827, 9829, 9996, 10347, 10536, 10560])).
% 1.63/1.84 tff(10570,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[169, 10569, 10568])).
% 1.63/1.84 tff(10571,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10572,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10571, 17])).
% 1.63/1.84 tff(10573,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[229, 10572])).
% 1.63/1.84 tff(10574,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4526, 10573, 9996, 10490, 10536])).
% 1.63/1.84 tff(10575,plain,
% 1.63/1.84 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[104, 10574])).
% 1.63/1.84 tff(10576,plain,
% 1.63/1.84 (~r(s(s(z)), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3186, 10575, 17, 9827])).
% 1.63/1.84 tff(10577,plain,
% 1.63/1.84 (b(s(s(z)), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[122, 10576])).
% 1.63/1.84 tff(10578,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1556, 10575, 17])).
% 1.63/1.84 tff(10579,plain,
% 1.63/1.84 (b(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[818, 10578])).
% 1.63/1.84 tff(10580,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4833, 10579, 10577, 9827, 17, 9996, 10347])).
% 1.63/1.84 tff(10581,plain,(~r(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10582,plain,
% 1.63/1.84 (b(s(z), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[680, 10581])).
% 1.63/1.84 tff(10583,plain,
% 1.63/1.84 (~r(z, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5189, 10582, 9827])).
% 1.63/1.84 tff(10584,plain,
% 1.63/1.84 (b(z, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1181, 10583])).
% 1.63/1.84 tff(10585,plain,
% 1.63/1.84 ((~b(s(s(z)), z)) | (~b(z, s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3557, 9827, 10582, 10584])).
% 1.63/1.84 tff(10586,plain,
% 1.63/1.84 (~b(z, s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10585, 142])).
% 1.63/1.84 tff(10587,plain,
% 1.63/1.84 (r(z, s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[64, 10586])).
% 1.63/1.84 tff(10588,plain,
% 1.63/1.84 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3847, 10584])).
% 1.63/1.84 tff(10589,plain,
% 1.63/1.84 (~r(s(s(z)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10588, 106, 16])).
% 1.63/1.84 tff(10590,plain,
% 1.63/1.84 (b(s(s(z)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[296, 10589])).
% 1.63/1.84 tff(10591,plain,
% 1.63/1.84 ((~r(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3196, 9827, 10584])).
% 1.63/1.84 tff(10592,plain,
% 1.63/1.84 (~b(s(z), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10591, 106, 16])).
% 1.63/1.84 tff(10593,plain,
% 1.63/1.84 (r(s(z), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1653, 10592])).
% 1.63/1.84 tff(10594,plain,
% 1.63/1.84 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[4953, 10582])).
% 1.63/1.84 tff(10595,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10594, 10593, 16])).
% 1.63/1.84 tff(10596,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[564, 10595])).
% 1.63/1.84 tff(10597,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5590])).
% 1.63/1.84 tff(10598,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.63/1.84 inference(symmetry,[status(thm)],[10597])).
% 1.63/1.84 tff(10599,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), z)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1299, 10598])).
% 1.63/1.84 tff(10600,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5619, 5623, 8236])).
% 1.63/1.84 tff(10601,plain,
% 1.63/1.84 ((~b(s(s(s(s(z)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10600])).
% 1.63/1.84 tff(10602,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[1299, 5743])).
% 1.63/1.84 tff(10603,plain,
% 1.63/1.84 (b(elem!1, s(s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[254, 5747])).
% 1.63/1.84 tff(10604,plain,
% 1.63/1.84 (b(elem!1, s(elem!1))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10584, 8837])).
% 1.63/1.84 tff(10605,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10606,plain,
% 1.63/1.84 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10607,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10606])).
% 1.63/1.84 tff(10608,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10607, 10605])).
% 1.63/1.84 tff(10609,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10610,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10609, 10608])).
% 1.63/1.84 tff(10611,plain,
% 1.63/1.84 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10610, 154, 10604, 9963, 10603, 10602])).
% 1.63/1.84 tff(10612,plain,
% 1.63/1.84 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10611, 10601])).
% 1.63/1.84 tff(10613,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[441, 10612])).
% 1.63/1.84 tff(10614,plain,
% 1.63/1.84 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[942, 820, 10613])).
% 1.63/1.84 tff(10615,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[496, 10614])).
% 1.63/1.84 tff(10616,plain,
% 1.63/1.84 (~b(z, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5234, 10615, 566, 10599, 254])).
% 1.63/1.84 tff(10617,plain,
% 1.63/1.84 (r(z, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[648, 10616])).
% 1.63/1.84 tff(10618,plain,
% 1.63/1.84 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2080, 10617, 106])).
% 1.63/1.84 tff(10619,plain,
% 1.63/1.84 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[138, 10618])).
% 1.63/1.84 tff(10620,plain,
% 1.63/1.84 ((~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2612, 9827, 10582, 10584])).
% 1.63/1.84 tff(10621,plain,
% 1.63/1.84 (~b(z, s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10620, 231])).
% 1.63/1.84 tff(10622,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5619, 5623])).
% 1.63/1.84 tff(10623,plain,
% 1.63/1.84 ((~b(s(s(s(s(z)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10622])).
% 1.63/1.84 tff(10624,plain,
% 1.63/1.84 (~b(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10611, 10623])).
% 1.63/1.84 tff(10625,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[318, 10624])).
% 1.63/1.84 tff(10626,plain,
% 1.63/1.84 ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2616, 9827])).
% 1.63/1.84 tff(10627,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10626, 10617, 820, 231])).
% 1.63/1.84 tff(10628,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[104, 10627])).
% 1.63/1.84 tff(10629,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.63/1.84 tff(10630,plain,
% 1.63/1.84 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5780, 5606])).
% 1.63/1.84 tff(10631,plain,
% 1.63/1.84 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10630])).
% 1.63/1.84 tff(10632,plain,
% 1.63/1.84 (r(z, s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[64, 10629])).
% 1.63/1.84 tff(10633,plain,
% 1.63/1.84 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.84 inference(symmetry,[status(thm)],[6107])).
% 1.63/1.84 tff(10634,plain,
% 1.63/1.84 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10633])).
% 1.63/1.84 tff(10635,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.63/1.84 tff(10636,plain,
% 1.63/1.84 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5780, 10635])).
% 1.63/1.84 tff(10637,plain,
% 1.63/1.84 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10636])).
% 1.63/1.84 tff(10638,plain,
% 1.63/1.84 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[5761, 5785, 10637, 11])).
% 1.63/1.84 tff(10639,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5882, 10638])).
% 1.63/1.84 tff(10640,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(10641,plain,
% 1.63/1.84 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10640, 5601])).
% 1.63/1.84 tff(10642,plain,
% 1.63/1.84 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10641, 10634])).
% 1.63/1.84 tff(10643,plain,
% 1.63/1.84 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5900])).
% 1.63/1.84 tff(10644,plain,
% 1.63/1.84 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5896, 28, 1243])).
% 1.63/1.84 tff(10645,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10644, 9536])).
% 1.63/1.84 tff(10646,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10645, 10643])).
% 1.63/1.84 tff(10647,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[5911, 10646, 10642])).
% 1.63/1.84 tff(10648,plain,
% 1.63/1.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10647, 5870])).
% 1.63/1.84 tff(10649,plain,
% 1.63/1.84 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5763, 6070])).
% 1.63/1.84 tff(10650,plain,
% 1.63/1.84 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), z)),
% 1.63/1.84 inference(symmetry,[status(thm)],[10649])).
% 1.63/1.84 tff(10651,plain,
% 1.63/1.84 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 1.63/1.84 inference(commutativity,[status(thm)],[])).
% 1.63/1.84 tff(10652,plain,
% 1.63/1.84 (elem!1 = z),
% 1.63/1.84 inference(transitivity,[status(thm)],[4024, 6068, 91])).
% 1.63/1.84 tff(10653,plain,
% 1.63/1.84 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (z = s(s(s(s(s(s(z)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10652, 5762])).
% 1.63/1.84 tff(10654,plain,
% 1.63/1.84 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 1.63/1.84 inference(transitivity,[status(thm)],[10653, 10651])).
% 1.63/1.84 tff(10655,plain,
% 1.63/1.84 ((s(s(s(s(s(s(z)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.84 inference(symmetry,[status(thm)],[10654])).
% 1.63/1.84 tff(10656,plain,
% 1.63/1.84 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.63/1.84 inference(transitivity,[status(thm)],[10655, 6006])).
% 1.63/1.84 tff(10657,plain,
% 1.63/1.84 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10656])).
% 1.63/1.84 tff(10658,plain,
% 1.63/1.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10659,plain,
% 1.63/1.84 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10658, 46])).
% 1.63/1.84 tff(10660,plain,
% 1.63/1.84 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10659, 10657])).
% 1.63/1.84 tff(10661,plain,
% 1.63/1.84 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.84 inference(monotonicity,[status(thm)],[5763, 6070])).
% 1.63/1.84 tff(10662,plain,
% 1.63/1.84 ((~r(s(s(s(s(s(s(z)))))), z)) <=> (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10661])).
% 1.63/1.84 tff(10663,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10664,plain,
% 1.63/1.84 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10665,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10664])).
% 1.63/1.84 tff(10666,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10665, 10663])).
% 1.63/1.84 tff(10667,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10668,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10667, 10666])).
% 1.63/1.84 tff(10669,plain,
% 1.63/1.84 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10668, 28, 628, 18])).
% 1.63/1.84 tff(10670,plain,
% 1.63/1.84 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[10669, 9536])).
% 1.63/1.84 tff(10671,plain,
% 1.63/1.84 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10670, 10662])).
% 1.63/1.84 tff(10672,plain,
% 1.63/1.84 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[6032, 10671, 10660])).
% 1.63/1.84 tff(10673,plain,
% 1.63/1.84 (b(s(s(s(s(s(s(z)))))), z)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10672, 10650])).
% 1.63/1.84 tff(10674,plain,
% 1.63/1.84 (b(z, s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6070, 5763])).
% 1.63/1.84 tff(10675,plain,
% 1.63/1.84 (b(elem!1, s(s(s(s(s(s(elem!1))))))) <=> b(z, s(s(s(s(s(s(z)))))))),
% 1.63/1.84 inference(symmetry,[status(thm)],[10674])).
% 1.63/1.84 tff(10676,plain,
% 1.63/1.84 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10655])).
% 1.63/1.84 tff(10677,plain,
% 1.63/1.84 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[10659, 10676])).
% 1.63/1.84 tff(10678,plain,
% 1.63/1.84 ((~r(z, s(s(s(s(s(s(z)))))))) <=> (~r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[6071])).
% 1.63/1.84 tff(10679,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10680,plain,
% 1.63/1.84 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(10681,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[10680])).
% 1.63/1.84 tff(10682,plain,
% 1.63/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[10681, 10679])).
% 1.63/1.84 tff(10683,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(10684,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10683, 10682])).
% 1.63/1.85 tff(10685,plain,
% 1.63/1.85 ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10684, 28, 18])).
% 1.63/1.85 tff(10686,plain,
% 1.63/1.85 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10685, 9536])).
% 1.63/1.85 tff(10687,plain,
% 1.63/1.85 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10686, 10678])).
% 1.63/1.85 tff(10688,plain,
% 1.63/1.85 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6093, 10687, 10677])).
% 1.63/1.85 tff(10689,plain,
% 1.63/1.85 (b(z, s(s(s(s(s(s(z)))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10688, 10675])).
% 1.63/1.85 tff(10690,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10691,plain,
% 1.63/1.85 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10692,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10691])).
% 1.63/1.85 tff(10693,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10692, 10690])).
% 1.63/1.85 tff(10694,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10695,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10694, 10693])).
% 1.63/1.85 tff(10696,plain,
% 1.63/1.85 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10695, 154, 1299, 254])).
% 1.63/1.85 tff(10697,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10696, 10689, 10673, 10648])).
% 1.63/1.85 tff(10698,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10699,plain,
% 1.63/1.85 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10698, 5601, 254, 1299, 628, 10632, 1243])).
% 1.63/1.85 tff(10700,plain,
% 1.63/1.85 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10699, 10631])).
% 1.63/1.85 tff(10701,plain,
% 1.63/1.85 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5763])).
% 1.63/1.85 tff(10702,plain,
% 1.63/1.85 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10701])).
% 1.63/1.85 tff(10703,plain,
% 1.63/1.85 (s(z) = s(s(s(s(s(s(z))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5817, 5762])).
% 1.63/1.85 tff(10704,plain,
% 1.63/1.85 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10703])).
% 1.63/1.85 tff(10705,plain,
% 1.63/1.85 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10704])).
% 1.63/1.85 tff(10706,plain,
% 1.63/1.85 (s(s(s(s(s(z))))) = z),
% 1.63/1.85 inference(transitivity,[status(thm)],[5785, 10705, 91])).
% 1.63/1.85 tff(10707,plain,
% 1.63/1.85 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10708,plain,
% 1.63/1.85 (~(s(s(s(s(s(z))))) = z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10707, 46])).
% 1.63/1.85 tff(10709,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10708, 10706])).
% 1.63/1.85 tff(10710,plain,((~(s(z) = s(s(s(s(s(s(elem!1)))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10711,plain,
% 1.63/1.85 (~(s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10710, 5601])).
% 1.63/1.85 tff(10712,plain,
% 1.63/1.85 (~(s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10711, 5860])).
% 1.63/1.85 tff(10713,plain,
% 1.63/1.85 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[5763])).
% 1.63/1.85 tff(10714,plain,
% 1.63/1.85 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10713])).
% 1.63/1.85 tff(10715,plain,
% 1.63/1.85 (b(z, s(s(s(s(s(s(z)))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[8745, 10675])).
% 1.63/1.85 tff(10716,plain,
% 1.63/1.85 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5778, 363, 5604, 86])).
% 1.63/1.85 tff(10717,plain,
% 1.63/1.85 (b(elem!1, s(s(s(s(s(s(elem!1))))))) <=> b(z, s(s(z)))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10652, 10716])).
% 1.63/1.85 tff(10718,plain,
% 1.63/1.85 (b(z, s(s(z))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10717])).
% 1.63/1.85 tff(10719,plain,
% 1.63/1.85 ((~b(z, s(s(z)))) <=> (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10718])).
% 1.63/1.85 tff(10720,plain,
% 1.63/1.85 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10629, 10719])).
% 1.63/1.85 tff(10721,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[8745, 10720])).
% 1.63/1.85 tff(10722,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | b(z, s(s(z))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10723,plain,
% 1.63/1.85 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10722, 8745, 10629, 5601])).
% 1.63/1.85 tff(10724,plain,
% 1.63/1.85 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5805, 10723, 10062])).
% 1.63/1.85 tff(10725,plain,
% 1.63/1.85 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10724, 10061])).
% 1.63/1.85 tff(10726,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10727,plain,
% 1.63/1.85 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10728,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10727])).
% 1.63/1.85 tff(10729,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10728, 10726])).
% 1.63/1.85 tff(10730,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10731,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10730, 10729])).
% 1.63/1.85 tff(10732,plain,
% 1.63/1.85 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10731, 154, 1726, 684, 10725])).
% 1.63/1.85 tff(10733,plain,
% 1.63/1.85 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10732, 10715])).
% 1.63/1.85 tff(10734,plain,
% 1.63/1.85 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10733, 10714])).
% 1.63/1.85 tff(10735,plain,
% 1.63/1.85 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5865, 10734, 10712])).
% 1.63/1.85 tff(10736,plain,
% 1.63/1.85 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10735, 10702])).
% 1.63/1.85 tff(10737,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10738,plain,
% 1.63/1.85 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10739,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10738])).
% 1.63/1.85 tff(10740,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10739, 10737])).
% 1.63/1.85 tff(10741,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10742,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10741, 10740])).
% 1.63/1.85 tff(10743,plain,
% 1.63/1.85 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10742, 28, 298])).
% 1.63/1.85 tff(10744,plain,
% 1.63/1.85 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10743, 10736])).
% 1.63/1.85 tff(10745,plain,
% 1.63/1.85 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10744, 10643])).
% 1.63/1.85 tff(10746,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5911, 10745, 10642])).
% 1.63/1.85 tff(10747,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10746, 5870])).
% 1.63/1.85 tff(10748,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10749,plain,
% 1.63/1.85 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10750,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10749])).
% 1.63/1.85 tff(10751,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10750, 10748])).
% 1.63/1.85 tff(10752,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10753,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10752, 10751])).
% 1.63/1.85 tff(10754,plain,
% 1.63/1.85 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10753, 28, 820])).
% 1.63/1.85 tff(10755,plain,
% 1.63/1.85 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10754, 10736])).
% 1.63/1.85 tff(10756,plain,
% 1.63/1.85 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10755, 10073])).
% 1.63/1.85 tff(10757,plain,
% 1.63/1.85 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[8043, 10756, 10065])).
% 1.63/1.85 tff(10758,plain,
% 1.63/1.85 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10757, 10071])).
% 1.63/1.85 tff(10759,plain,
% 1.63/1.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1409, 28, 820, 298])).
% 1.63/1.85 tff(10760,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[343, 10759])).
% 1.63/1.85 tff(10761,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10762,plain,
% 1.63/1.85 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(10763,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10762])).
% 1.63/1.85 tff(10764,plain,
% 1.63/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[10763, 10761])).
% 1.63/1.85 tff(10765,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(10766,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[10765, 10764])).
% 1.63/1.85 tff(10767,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10766, 154, 10760, 254, 10715, 10758, 10747])).
% 1.63/1.85 tff(10768,plain,((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10769,plain,
% 1.63/1.85 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10768, 10065, 5601, 254, 820, 298, 1726, 684, 10062, 10629])).
% 1.63/1.85 tff(10770,plain,
% 1.63/1.85 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10094, 10065, 5601, 5794, 144, 141, 10632, 628, 10062])).
% 1.63/1.85 tff(10771,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[6093, 10770, 10769, 10677])).
% 1.63/1.85 tff(10772,plain,((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10773,plain,
% 1.63/1.85 (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10772, 5601, 144, 141, 628, 10700, 254, 820, 298, 1726, 684, 10629])).
% 1.63/1.85 tff(10774,plain,
% 1.63/1.85 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[5780, 10773])).
% 1.63/1.85 tff(10775,plain,
% 1.63/1.85 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10774])).
% 1.63/1.85 tff(10776,plain,
% 1.63/1.85 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[10775])).
% 1.63/1.85 tff(10777,plain,
% 1.63/1.85 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[87, 10776, 5784])).
% 1.63/1.85 tff(10778,plain,
% 1.63/1.85 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[10777])).
% 1.63/1.85 tff(10779,plain,
% 1.63/1.85 (s(z) = s(s(s(s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[289, 10778, 5789])).
% 1.63/1.85 tff(10780,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1361, 10779])).
% 1.63/1.85 tff(10781,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | b(z, s(s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10782,plain,
% 1.63/1.85 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | b(z, s(s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10781, 5590])).
% 1.63/1.85 tff(10783,plain,
% 1.63/1.85 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | b(z, s(s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10782, 10584, 10582])).
% 1.63/1.85 tff(10784,plain,
% 1.63/1.85 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10783, 10628, 254, 10625, 10617, 820, 10621, 1299, 10619])).
% 1.63/1.85 tff(10785,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[229, 10784])).
% 1.63/1.85 tff(10786,plain,
% 1.63/1.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1411, 820, 10625])).
% 1.63/1.85 tff(10787,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[343, 10786])).
% 1.63/1.85 tff(10788,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[4639, 154, 10619, 10787, 10628, 10785, 566])).
% 1.63/1.85 tff(10789,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10790,plain,
% 1.63/1.85 (~r(s(s(s(z))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10789, 10596, 1222, 1224, 10590, 106])).
% 1.63/1.85 tff(10791,plain,
% 1.63/1.85 (b(s(s(s(z))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[818, 10790])).
% 1.63/1.85 tff(10792,plain,
% 1.63/1.85 ((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5334, 9827, 10582])).
% 1.63/1.85 tff(10793,plain,
% 1.63/1.85 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10792, 10791, 16, 10593])).
% 1.63/1.85 tff(10794,plain,
% 1.63/1.85 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[138, 10793])).
% 1.63/1.85 tff(10795,plain,
% 1.63/1.85 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[692, 10582])).
% 1.63/1.85 tff(10796,plain,
% 1.63/1.85 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10795, 10794, 10590, 10791])).
% 1.63/1.85 tff(10797,plain,
% 1.63/1.85 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[104, 10796])).
% 1.63/1.85 tff(10798,plain,
% 1.63/1.85 (~b(z, s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1705, 10797, 16, 106])).
% 1.63/1.85 tff(10799,plain,
% 1.63/1.85 (~b(z, s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10620, 10590])).
% 1.63/1.85 tff(10800,plain,
% 1.63/1.85 (r(z, s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[64, 10799])).
% 1.63/1.85 tff(10801,plain,
% 1.63/1.85 (~r(z, s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3150, 10797, 10800])).
% 1.63/1.85 tff(10802,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[648, 10801, 10798])).
% 1.63/1.85 tff(10803,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10804,plain,
% 1.63/1.85 (~r(s(s(z)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10803, 16])).
% 1.63/1.85 tff(10805,plain,
% 1.63/1.85 (b(s(s(z)), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[122, 10804])).
% 1.63/1.85 tff(10806,plain,
% 1.63/1.85 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3436, 9827, 10582, 10584])).
% 1.63/1.85 tff(10807,plain,
% 1.63/1.85 (~b(s(s(z)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10806, 10805])).
% 1.63/1.85 tff(10808,plain,
% 1.63/1.85 (r(s(s(z)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[296, 10807])).
% 1.63/1.85 tff(10809,plain,
% 1.63/1.85 ((~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5465, 9827, 10582])).
% 1.63/1.85 tff(10810,plain,
% 1.63/1.85 (~b(s(z), s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10809, 10805])).
% 1.63/1.85 tff(10811,plain,
% 1.63/1.85 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5643, 10810])).
% 1.63/1.85 tff(10812,plain,
% 1.63/1.85 (r(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[467, 10811])).
% 1.63/1.85 tff(10813,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3823, 10812, 10808, 8258])).
% 1.63/1.85 tff(10814,plain,(~r(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(10815,plain,
% 1.63/1.85 (b(s(s(z)), s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1259, 10814])).
% 1.63/1.85 tff(10816,plain,
% 1.63/1.85 (~b(s(z), s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10809, 142])).
% 1.63/1.85 tff(10817,plain,
% 1.63/1.85 (r(s(z), s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1653, 10816])).
% 1.63/1.85 tff(10818,plain,
% 1.63/1.85 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5364, 9827, 10582])).
% 1.63/1.85 tff(10819,plain,
% 1.63/1.85 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10818, 10817, 1])).
% 1.63/1.85 tff(10820,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[564, 10819])).
% 1.63/1.85 tff(10821,plain,
% 1.63/1.85 (~b(s(s(z)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[10806, 142])).
% 1.63/1.85 tff(10822,plain,
% 1.63/1.85 (r(s(s(z)), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[296, 10821])).
% 1.63/1.85 tff(10823,plain,
% 1.63/1.85 ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[5387, 9827, 10582])).
% 1.63/1.86 tff(10824,plain,
% 1.63/1.86 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10823, 142, 1])).
% 1.63/1.86 tff(10825,plain,
% 1.63/1.86 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[138, 10824])).
% 1.63/1.86 tff(10826,plain,
% 1.63/1.86 (~r(s(z), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[657, 10825, 10822])).
% 1.63/1.86 tff(10827,plain,
% 1.63/1.86 (b(s(z), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[252, 10826])).
% 1.63/1.86 tff(10828,plain,
% 1.63/1.86 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[2306, 10582])).
% 1.63/1.86 tff(10829,plain,
% 1.63/1.86 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10828, 10827, 10820, 10815])).
% 1.63/1.86 tff(10830,plain,
% 1.63/1.86 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[104, 10829])).
% 1.63/1.86 tff(10831,plain,
% 1.63/1.86 ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3660, 9827, 10584])).
% 1.63/1.86 tff(10832,plain,
% 1.63/1.86 (~b(z, s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10831, 10827, 1])).
% 1.63/1.86 tff(10833,plain,
% 1.63/1.86 (r(z, s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[648, 10832])).
% 1.63/1.86 tff(10834,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3150, 10833, 10830, 10587])).
% 1.63/1.86 tff(10835,plain,((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10836,plain,
% 1.63/1.86 (~b(s(s(z)), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10835, 1])).
% 1.63/1.86 tff(10837,plain,
% 1.63/1.86 (r(s(s(z)), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[122, 10836])).
% 1.63/1.86 tff(10838,plain,
% 1.63/1.86 (r(s(s(elem!1)), z)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10837, 5617])).
% 1.63/1.86 tff(10839,plain,
% 1.63/1.86 (~r(z, s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[2080, 124, 10837])).
% 1.63/1.86 tff(10840,plain,
% 1.63/1.86 (b(z, s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[648, 10839])).
% 1.63/1.86 tff(10841,plain,
% 1.63/1.86 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3217, 9827, 10584])).
% 1.63/1.86 tff(10842,plain,
% 1.63/1.86 (~b(s(s(s(z))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10841, 10840, 1])).
% 1.63/1.86 tff(10843,plain,
% 1.63/1.86 (~b(s(s(s(elem!1))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8298, 10842])).
% 1.63/1.86 tff(10844,plain,
% 1.63/1.86 (r(s(s(s(elem!1))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4159, 10843])).
% 1.63/1.86 tff(10845,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10846,plain,
% 1.63/1.86 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10847,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10846])).
% 1.63/1.86 tff(10848,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10847, 10845])).
% 1.63/1.86 tff(10849,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10850,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10849, 10848])).
% 1.63/1.86 tff(10851,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10850, 28, 4161, 6280, 6279])).
% 1.63/1.86 tff(10852,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,[]))).
% 1.63/1.86 tff(10853,plain,
% 1.63/1.86 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10852, 10844, 10838])).
% 1.63/1.86 tff(10854,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10853, 5600])).
% 1.63/1.86 tff(10855,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10856,plain,
% 1.63/1.86 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10855, 1])).
% 1.63/1.86 tff(10857,plain,
% 1.63/1.86 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[138, 10856])).
% 1.63/1.86 tff(10858,plain,
% 1.63/1.86 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5575, 9827, 10582])).
% 1.63/1.86 tff(10859,plain,
% 1.63/1.86 (~b(s(z), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10858, 10857, 1])).
% 1.63/1.86 tff(10860,plain,
% 1.63/1.86 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5405, 9827, 10582])).
% 1.63/1.86 tff(10861,plain,
% 1.63/1.86 (~r(s(z), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10860, 10857, 10815, 1])).
% 1.63/1.86 tff(10862,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1653, 10861, 10859])).
% 1.63/1.86 tff(10863,plain,(~b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10864,plain,
% 1.63/1.86 (r(s(s(s(z))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[818, 10863])).
% 1.63/1.86 tff(10865,plain,
% 1.63/1.86 ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5201, 10582])).
% 1.63/1.86 tff(10866,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10865, 10822, 10817, 10864])).
% 1.63/1.86 tff(10867,plain,(~b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10868,plain,
% 1.63/1.86 (r(s(s(z)), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[122, 10867])).
% 1.63/1.86 tff(10869,plain,
% 1.63/1.86 (~r(s(s(z)), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10865, 1655, 10864])).
% 1.63/1.86 tff(10870,plain,
% 1.63/1.86 (b(s(s(z)), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[296, 10869])).
% 1.63/1.86 tff(10871,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[2656, 10870, 10864, 10868, 144])).
% 1.63/1.86 tff(10872,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1930, 1655, 10864])).
% 1.63/1.86 tff(10873,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[564, 10872])).
% 1.63/1.86 tff(10874,plain,
% 1.63/1.86 ((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5197, 10582])).
% 1.63/1.86 tff(10875,plain,
% 1.63/1.86 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10874, 10873, 10815, 144, 1655])).
% 1.63/1.86 tff(10876,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[104, 10875, 10871])).
% 1.63/1.86 tff(10877,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10878,plain,
% 1.63/1.86 (~r(s(z), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10877, 144])).
% 1.63/1.86 tff(10879,plain,
% 1.63/1.86 (b(s(z), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1653, 10878])).
% 1.63/1.86 tff(10880,plain,
% 1.63/1.86 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5527, 9827, 10582])).
% 1.63/1.86 tff(10881,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10880, 10879])).
% 1.63/1.86 tff(10882,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[318, 10881])).
% 1.63/1.86 tff(10883,plain,
% 1.63/1.86 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5459, 10582])).
% 1.63/1.86 tff(10884,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10883, 10879, 10815, 144])).
% 1.63/1.86 tff(10885,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[343, 10884])).
% 1.63/1.86 tff(10886,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1411, 10885, 10882, 10864])).
% 1.63/1.86 tff(10887,plain,(~b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10888,plain,
% 1.63/1.86 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[138, 10887])).
% 1.63/1.86 tff(10889,plain,
% 1.63/1.86 (b(s(elem!1), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8307, 10582])).
% 1.63/1.86 tff(10890,plain,
% 1.63/1.86 (~r(s(s(z)), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1125, 10888, 10864])).
% 1.63/1.86 tff(10891,plain,
% 1.63/1.86 (b(s(s(z)), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[296, 10890])).
% 1.63/1.86 tff(10892,plain,
% 1.63/1.86 (b(s(s(z)), s(elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10891, 8310])).
% 1.63/1.86 tff(10893,plain,
% 1.63/1.86 (r(s(s(elem!1)), z)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10868, 5617])).
% 1.63/1.86 tff(10894,plain,
% 1.63/1.86 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10888, 5599])).
% 1.63/1.86 tff(10895,plain,
% 1.63/1.86 (~r(s(s(s(elem!1))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10852, 10894, 10893])).
% 1.63/1.86 tff(10896,plain,
% 1.63/1.86 (b(s(s(s(elem!1))), z)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4159, 10895])).
% 1.63/1.86 tff(10897,plain,
% 1.63/1.86 (b(s(s(s(z))), elem!1)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10896, 8300])).
% 1.63/1.86 tff(10898,plain,
% 1.63/1.86 (~r(z, s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6288, 10894, 10893])).
% 1.63/1.86 tff(10899,plain,
% 1.63/1.86 (b(z, s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3977, 10898])).
% 1.63/1.86 tff(10900,plain,
% 1.63/1.86 (b(elem!1, s(s(s(z))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10899, 6188])).
% 1.63/1.86 tff(10901,plain,
% 1.63/1.86 ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1135, 10582])).
% 1.63/1.86 tff(10902,plain,
% 1.63/1.86 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10901, 10888, 10864])).
% 1.63/1.86 tff(10903,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[496, 10902])).
% 1.63/1.86 tff(10904,plain,
% 1.63/1.86 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8825, 10903])).
% 1.63/1.86 tff(10905,plain,
% 1.63/1.86 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[9342, 154, 10904, 10900, 10897])).
% 1.63/1.86 tff(10906,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10905, 566])).
% 1.63/1.86 tff(10907,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), elem!1)),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8854, 10906])).
% 1.63/1.86 tff(10908,plain,
% 1.63/1.86 (r(s(s(z)), elem!1)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10868, 5616])).
% 1.63/1.86 tff(10909,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10910,plain,
% 1.63/1.86 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10911,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10910])).
% 1.63/1.86 tff(10912,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10911, 10909])).
% 1.63/1.86 tff(10913,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10914,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10913, 10912])).
% 1.63/1.86 tff(10915,plain,
% 1.63/1.86 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10914, 28, 10888, 10908, 10907])).
% 1.63/1.86 tff(10916,plain,
% 1.63/1.86 (b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[229, 10915])).
% 1.63/1.86 tff(10917,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10918,plain,
% 1.63/1.86 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10919,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10918])).
% 1.63/1.86 tff(10920,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10919, 10917])).
% 1.63/1.86 tff(10921,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10922,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10921, 10920])).
% 1.63/1.86 tff(10923,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10922, 154, 10815, 10916, 10892, 10889])).
% 1.63/1.86 tff(10924,plain,
% 1.63/1.86 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10923, 10601])).
% 1.63/1.86 tff(10925,plain,
% 1.63/1.86 (r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[441, 10924])).
% 1.63/1.86 tff(10926,plain,
% 1.63/1.86 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10523, 10925])).
% 1.63/1.86 tff(10927,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10926, 10349])).
% 1.63/1.86 tff(10928,plain,
% 1.63/1.86 (r(s(s(s(z))), s(elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10864, 8688])).
% 1.63/1.86 tff(10929,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[9433, 8701, 10928])).
% 1.63/1.86 tff(10930,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8189, 10929])).
% 1.63/1.86 tff(10931,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10196, 10930])).
% 1.63/1.86 tff(10932,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10210, 10931, 566, 5964, 10916])).
% 1.63/1.86 tff(10933,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8685, 10932])).
% 1.63/1.86 tff(10934,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6000, 10933])).
% 1.63/1.86 tff(10935,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5998, 10934])).
% 1.63/1.86 tff(10936,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10937,plain,
% 1.63/1.86 (((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10938,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10937])).
% 1.63/1.86 tff(10939,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10938, 10936])).
% 1.63/1.86 tff(10940,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10941,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10940, 10939])).
% 1.63/1.86 tff(10942,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10941, 28, 10935, 8701, 10927])).
% 1.63/1.86 tff(10943,plain,((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10944,plain,
% 1.63/1.86 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10943, 5964, 566])).
% 1.63/1.86 tff(10945,plain,
% 1.63/1.86 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8716, 10944])).
% 1.63/1.86 tff(10946,plain,
% 1.63/1.86 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5866, 10945])).
% 1.63/1.86 tff(10947,plain,
% 1.63/1.86 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10946, 6179])).
% 1.63/1.86 tff(10948,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10949,plain,
% 1.63/1.86 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10950,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[10949])).
% 1.63/1.86 tff(10951,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[10950, 10948])).
% 1.63/1.86 tff(10952,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(10953,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10952, 10951])).
% 1.63/1.86 tff(10954,plain,
% 1.63/1.86 ((~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10953, 154, 10604, 5964, 10889])).
% 1.63/1.86 tff(10955,plain,
% 1.63/1.86 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10954, 10947])).
% 1.63/1.86 tff(10956,plain,
% 1.63/1.86 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8749, 10955])).
% 1.63/1.86 tff(10957,plain,
% 1.63/1.86 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6094, 10956])).
% 1.63/1.86 tff(10958,plain,
% 1.63/1.86 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[10957, 9118])).
% 1.63/1.86 tff(10959,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[9580, 154, 10916, 5964, 10892, 10947])).
% 1.63/1.86 tff(10960,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8685, 10959])).
% 1.63/1.86 tff(10961,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[6000, 10960])).
% 1.63/1.86 tff(10962,plain,
% 1.63/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[5998, 10961])).
% 1.63/1.86 tff(10963,plain,
% 1.63/1.86 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[9911, 10962, 10907])).
% 1.63/1.86 tff(10964,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10963, 10958])).
% 1.63/1.86 tff(10965,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(10966,plain,
% 1.63/1.86 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10965, 566])).
% 1.63/1.86 tff(10967,plain,
% 1.63/1.86 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8152, 10966])).
% 1.63/1.86 tff(10968,plain,
% 1.63/1.86 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8154, 10967])).
% 1.63/1.86 tff(10969,plain,
% 1.63/1.86 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8661, 10968])).
% 1.63/1.86 tff(10970,plain,
% 1.63/1.86 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3235, 154, 10904, 10815, 10916, 566])).
% 1.63/1.86 tff(10971,plain,
% 1.63/1.86 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[104, 10970])).
% 1.63/1.86 tff(10972,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8180, 28, 10971, 10969])).
% 1.63/1.86 tff(10973,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[9599, 10972])).
% 1.63/1.86 tff(10974,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[8189, 10973])).
% 1.63/1.86 tff(10975,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[10196, 10974])).
% 1.63/1.86 tff(10976,plain,
% 1.63/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(10977,plain,
% 1.63/1.86 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(10978,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[10977])).
% 1.63/1.87 tff(10979,plain,
% 1.63/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[10978, 10976])).
% 1.63/1.87 tff(10980,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(10981,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10980, 10979])).
% 1.63/1.87 tff(10982,plain,
% 1.63/1.87 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10981, 28, 10971, 10969, 10928])).
% 1.63/1.87 tff(10983,plain,
% 1.63/1.87 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[5962, 10982])).
% 1.63/1.87 tff(10984,plain,
% 1.63/1.87 (~b(z, s(s(z)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10620, 10891])).
% 1.63/1.87 tff(10985,plain,
% 1.63/1.87 (r(z, s(s(z)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[64, 10984])).
% 1.63/1.87 tff(10986,plain,
% 1.63/1.87 (r(elem!1, s(s(z)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10985, 8891])).
% 1.63/1.87 tff(10987,plain,
% 1.63/1.87 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[8668, 28, 10986, 10969])).
% 1.63/1.87 tff(10988,plain,
% 1.63/1.87 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[10987, 8654])).
% 1.63/1.87 tff(10989,plain,
% 1.63/1.87 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[6094, 10988])).
% 1.63/1.87 tff(10990,plain,
% 1.63/1.87 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[8749, 10989])).
% 1.63/1.87 tff(10991,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[9608, 154, 10900, 10897, 10990, 10983, 10975])).
% 1.63/1.87 tff(10992,plain,(~b(s(s(s(z))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(10993,plain,
% 1.63/1.87 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[564, 10992])).
% 1.63/1.87 tff(10994,plain,
% 1.63/1.87 (~r(s(s(z)), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1125, 820, 124])).
% 1.63/1.87 tff(10995,plain,
% 1.63/1.87 (b(s(s(z)), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[296, 10994])).
% 1.63/1.87 tff(10996,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1389, 10995, 3755, 684, 1283, 15])).
% 1.63/1.87 tff(10997,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(10998,plain,
% 1.63/1.87 ((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10997, 10582])).
% 1.63/1.87 tff(10999,plain,
% 1.63/1.87 (~b(s(z), s(s(s(s(z)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[10998, 10993, 10864, 10815, 10888])).
% 1.63/1.87 tff(11000,plain,
% 1.63/1.87 (~r(s(z), s(s(s(s(z)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1930, 10993, 10864])).
% 1.63/1.87 tff(11001,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1653, 11000, 10999])).
% 1.63/1.87 % SZS output end Proof
% 1.63/1.87 % E exiting
%------------------------------------------------------------------------------