%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA137-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:48 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.49s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA137-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n014.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 23:06:23 EDT 2026
% 0.14/0.32 % CPUTime :
% 1.23/1.49 % SZS status Unsatisfiable
% 1.23/1.49 % SZS output start Proof
% 1.23/1.49 tff(b_type, type, (
% 1.23/1.49 b: ( $i * $i ) > $o)).
% 1.23/1.49 tff(s_type, type, (
% 1.23/1.49 s: $i > $i)).
% 1.23/1.49 tff(elem_1_type, type, (
% 1.23/1.49 elem_1: $i)).
% 1.23/1.49 tff(z_type, type, (
% 1.23/1.49 z: $i)).
% 1.23/1.49 tff(r_type, type, (
% 1.23/1.49 r: ( $i * $i ) > $o)).
% 1.23/1.49 tff(inj_0_type, type, (
% 1.23/1.49 inj_0: $i > $i)).
% 1.23/1.49 tff(1,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.23/1.49 tff(2,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.23/1.49 tff(3,assumption,(~b(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.23/1.49 tff(4,plain,
% 1.23/1.49 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(5,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(6,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(7,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.23/1.49 tff(8,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.23/1.49 tff(9,plain,(
% 1.23/1.49 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.23/1.49 inference(skolemize,[status(sab)],[8])).
% 1.23/1.49 tff(10,plain,
% 1.23/1.49 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.23/1.49 tff(11,plain,
% 1.23/1.49 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[10, 4])).
% 1.23/1.49 tff(12,plain,
% 1.23/1.49 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(13,plain,
% 1.23/1.49 (inj_0(s(z)) = z),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[12, 11])).
% 1.23/1.49 tff(14,plain,
% 1.23/1.49 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(15,plain,
% 1.23/1.49 (inj_0(s(s(z))) = s(z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[14, 11])).
% 1.23/1.49 tff(16,assumption,(s(s(s(s(elem!1)))) = s(s(z))), introduced(assumption)).
% 1.23/1.49 tff(17,plain,
% 1.23/1.49 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[16])).
% 1.23/1.49 tff(18,plain,
% 1.23/1.49 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(19,plain,
% 1.23/1.49 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[18, 11])).
% 1.23/1.49 tff(20,plain,
% 1.23/1.49 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[19])).
% 1.23/1.49 tff(21,plain,
% 1.23/1.49 (s(s(s(elem!1))) = s(z)),
% 1.23/1.49 inference(transitivity,[status(thm)],[20, 17, 15])).
% 1.23/1.49 tff(22,plain,
% 1.23/1.49 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[21])).
% 1.23/1.49 tff(23,plain,
% 1.23/1.49 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(24,plain,
% 1.23/1.49 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[23, 11])).
% 1.23/1.49 tff(25,plain,
% 1.23/1.49 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[24])).
% 1.23/1.49 tff(26,plain,
% 1.23/1.49 (s(s(elem!1)) = z),
% 1.23/1.49 inference(transitivity,[status(thm)],[25, 22, 13])).
% 1.23/1.49 tff(27,plain,
% 1.23/1.49 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.23/1.49 inference(bind,[status(th)],[])).
% 1.23/1.49 tff(28,plain,
% 1.23/1.49 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.23/1.49 inference(quant_intro,[status(thm)],[27])).
% 1.23/1.49 tff(29,plain,
% 1.23/1.49 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(30,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.23/1.49 tff(31,plain,
% 1.23/1.49 (![X: $i] : (~(s(X) = z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.23/1.49 tff(32,plain,(
% 1.23/1.49 ![X: $i] : (~(s(X) = z))),
% 1.23/1.49 inference(skolemize,[status(sab)],[31])).
% 1.23/1.49 tff(33,plain,
% 1.23/1.49 (![X: $i] : (~(s(X) = z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.23/1.49 tff(34,plain,
% 1.23/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(35,plain,
% 1.23/1.49 (~(s(s(elem!1)) = z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[34, 33])).
% 1.23/1.49 tff(36,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[35, 26])).
% 1.23/1.49 tff(37,plain,(~(s(s(s(s(elem!1)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(38,plain,
% 1.23/1.49 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.23/1.49 inference(bind,[status(th)],[])).
% 1.23/1.49 tff(39,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.49 inference(quant_intro,[status(thm)],[38])).
% 1.23/1.49 tff(40,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(41,plain,
% 1.23/1.49 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.23/1.49 inference(bind,[status(th)],[])).
% 1.23/1.49 tff(42,plain,
% 1.23/1.49 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.49 inference(quant_intro,[status(thm)],[41])).
% 1.23/1.49 tff(43,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.23/1.49 tff(44,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.23/1.49 tff(45,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.23/1.49 tff(46,plain,(
% 1.23/1.49 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.49 inference(skolemize,[status(sab)],[45])).
% 1.23/1.49 tff(47,plain,
% 1.23/1.49 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.23/1.49 tff(48,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(49,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(50,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.23/1.49 tff(51,plain,
% 1.23/1.49 ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[50, 47])).
% 1.23/1.49 tff(52,plain,
% 1.23/1.49 (b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[51, 37])).
% 1.23/1.49 tff(53,plain,
% 1.23/1.49 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[52, 3])).
% 1.23/1.49 tff(54,assumption,(r(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.23/1.49 tff(55,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.23/1.49 tff(56,plain,
% 1.23/1.49 (^[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))))),
% 1.23/1.49 inference(bind,[status(th)],[])).
% 1.23/1.49 tff(57,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))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.23/1.49 inference(quant_intro,[status(thm)],[56])).
% 1.23/1.49 tff(58,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))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(59,plain,
% 1.23/1.49 (^[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)))))),
% 1.23/1.49 inference(bind,[status(th)],[])).
% 1.23/1.49 tff(60,plain,
% 1.23/1.49 (![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)))),
% 1.23/1.49 inference(quant_intro,[status(thm)],[59])).
% 1.23/1.49 tff(61,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.23/1.49 tff(62,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)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.23/1.49 tff(63,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)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.23/1.49 tff(64,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)))),
% 1.23/1.49 inference(skolemize,[status(sab)],[63])).
% 1.23/1.49 tff(65,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)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[64, 57])).
% 1.23/1.49 tff(66,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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(67,plain,
% 1.23/1.49 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(68,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(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[67])).
% 1.23/1.49 tff(69,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(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[68, 66])).
% 1.23/1.49 tff(70,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(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(71,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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.23/1.49 tff(72,plain,
% 1.23/1.49 (~r(z, s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[71, 65, 54, 55])).
% 1.23/1.49 tff(73,plain,
% 1.23/1.49 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.23/1.49 inference(commutativity,[status(thm)],[])).
% 1.23/1.49 tff(74,plain,
% 1.23/1.49 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(symmetry,[status(thm)],[73])).
% 1.23/1.49 tff(75,plain,
% 1.23/1.49 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[74])).
% 1.23/1.49 tff(76,plain,
% 1.23/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(77,plain,
% 1.23/1.49 (~(s(s(s(s(elem!1)))) = z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[76, 33])).
% 1.23/1.49 tff(78,plain,
% 1.23/1.49 (~(z = s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[77, 75])).
% 1.23/1.49 tff(79,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(80,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(81,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.23/1.49 tff(82,plain,
% 1.23/1.49 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[81, 47])).
% 1.23/1.49 tff(83,plain,
% 1.23/1.49 (b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[82, 78])).
% 1.23/1.49 tff(84,plain,
% 1.23/1.49 (b(z, s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[83, 72])).
% 1.23/1.49 tff(85,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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(86,plain,
% 1.23/1.49 (((~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(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(87,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(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(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[86])).
% 1.23/1.49 tff(88,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(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(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[87, 85])).
% 1.23/1.49 tff(89,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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(90,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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.23/1.49 tff(91,plain,
% 1.23/1.49 (~r(s(s(s(s(elem!1)))), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[90, 65, 54, 55])).
% 1.23/1.49 tff(92,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(93,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(94,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.23/1.49 tff(95,plain,
% 1.23/1.49 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[94, 47, 77])).
% 1.23/1.49 tff(96,plain,
% 1.23/1.49 (b(s(s(s(s(elem!1)))), z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[95, 91])).
% 1.23/1.49 tff(97,assumption,(r(z, s(z))), introduced(assumption)).
% 1.23/1.49 tff(98,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(z))) | (~r(s(s(z)), 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(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(99,plain,
% 1.23/1.49 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(100,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(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), 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(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[99])).
% 1.23/1.49 tff(101,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(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), 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(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[100, 98])).
% 1.23/1.49 tff(102,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(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(103,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.23/1.49 tff(104,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[103, 65, 97, 55, 2])).
% 1.23/1.49 tff(105,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(106,plain,
% 1.23/1.49 (~r(z, s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[105, 2, 55])).
% 1.23/1.49 tff(107,plain,
% 1.23/1.49 ((z = s(z)) <=> (s(z) = z)),
% 1.23/1.49 inference(commutativity,[status(thm)],[])).
% 1.23/1.49 tff(108,plain,
% 1.23/1.49 ((s(z) = z) <=> (z = s(z))),
% 1.23/1.49 inference(symmetry,[status(thm)],[107])).
% 1.23/1.49 tff(109,plain,
% 1.23/1.49 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[108])).
% 1.23/1.49 tff(110,plain,
% 1.23/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(111,plain,
% 1.23/1.49 (~(s(z) = z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[110, 33])).
% 1.23/1.49 tff(112,plain,
% 1.23/1.49 (~(z = s(z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[111, 109])).
% 1.23/1.49 tff(113,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(114,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(115,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.23/1.49 tff(116,plain,
% 1.23/1.49 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[115, 47])).
% 1.23/1.49 tff(117,plain,
% 1.23/1.49 (b(z, s(z)) | r(z, s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[116, 112])).
% 1.23/1.49 tff(118,plain,
% 1.23/1.49 (b(z, s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[117, 106])).
% 1.23/1.49 tff(119,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.49 tff(120,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.23/1.49 tff(121,assumption,(b(z, s(z))), introduced(assumption)).
% 1.23/1.49 tff(122,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.23/1.49 tff(123,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.23/1.49 tff(124,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(elem!1)))), s(z))) | (~r(s(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(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(125,plain,
% 1.23/1.49 (((~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(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(126,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(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)))))))) <=> ((~![X0: $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(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[125])).
% 1.23/1.49 tff(127,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(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)))))))) <=> ((~![X0: $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(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.23/1.49 inference(transitivity,[status(thm)],[126, 124])).
% 1.23/1.49 tff(128,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(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)))))))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(129,plain,
% 1.23/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.23/1.49 tff(130,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[129, 65, 123, 119, 2])).
% 1.23/1.49 tff(131,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(132,plain,
% 1.23/1.49 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[131, 119, 2])).
% 1.23/1.49 tff(133,plain,
% 1.23/1.49 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(commutativity,[status(thm)],[])).
% 1.23/1.49 tff(134,plain,
% 1.23/1.49 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.23/1.49 inference(symmetry,[status(thm)],[133])).
% 1.23/1.49 tff(135,plain,
% 1.23/1.49 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(z)))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[134])).
% 1.23/1.49 tff(136,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.23/1.49 tff(137,plain,
% 1.23/1.49 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.23/1.49 inference(monotonicity,[status(thm)],[136])).
% 1.23/1.49 tff(138,plain,
% 1.23/1.49 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.23/1.49 inference(symmetry,[status(thm)],[137])).
% 1.23/1.49 tff(139,plain,
% 1.23/1.49 (s(s(s(elem!1))) = z),
% 1.23/1.49 inference(transitivity,[status(thm)],[20, 138, 13])).
% 1.23/1.49 tff(140,plain,
% 1.23/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(141,plain,
% 1.23/1.49 (~(s(s(s(elem!1))) = z)),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[140, 33])).
% 1.23/1.49 tff(142,plain,
% 1.23/1.49 ($false),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[141, 139])).
% 1.23/1.49 tff(143,plain,(~(s(z) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.23/1.49 tff(144,plain,
% 1.23/1.49 (~(s(s(s(s(elem!1)))) = s(z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[143, 135])).
% 1.23/1.49 tff(145,plain,
% 1.23/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(146,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.23/1.49 inference(quant_inst,[status(thm)],[])).
% 1.23/1.49 tff(147,plain,
% 1.23/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.49 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.23/1.49 tff(148,plain,
% 1.23/1.49 ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[147, 47])).
% 1.23/1.49 tff(149,plain,
% 1.23/1.49 (b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[148, 144])).
% 1.23/1.49 tff(150,plain,
% 1.23/1.49 (b(s(s(s(s(elem!1)))), s(z))),
% 1.23/1.49 inference(unit_resolution,[status(thm)],[149, 132])).
% 1.23/1.49 tff(151,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.23/1.49 tff(152,assumption,(b(s(z), z)), introduced(assumption)).
% 1.23/1.49 tff(153,plain,
% 1.23/1.49 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.23/1.49 inference(bind,[status(th)],[])).
% 1.23/1.49 tff(154,plain,
% 1.23/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.49 inference(quant_intro,[status(thm)],[153])).
% 1.23/1.49 tff(155,plain,
% 1.23/1.49 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.49 inference(rewrite,[status(thm)],[])).
% 1.23/1.49 tff(156,plain,
% 1.23/1.49 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X2, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> (((~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.23/1.50 inference(bind,[status(th)],[])).
% 1.23/1.50 tff(157,plain,
% 1.23/1.50 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.50 inference(quant_intro,[status(thm)],[156])).
% 1.23/1.50 tff(158,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.23/1.50 tff(159,plain,
% 1.23/1.50 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.23/1.50 tff(160,plain,
% 1.23/1.50 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[159, 155])).
% 1.23/1.50 tff(161,plain,(
% 1.23/1.50 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.50 inference(skolemize,[status(sab)],[160])).
% 1.23/1.50 tff(162,plain,
% 1.23/1.50 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.23/1.50 inference(modus_ponens,[status(thm)],[161, 154])).
% 1.23/1.50 tff(163,plain,
% 1.23/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(164,plain,
% 1.23/1.50 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.23/1.50 inference(rewrite,[status(thm)],[])).
% 1.23/1.50 tff(165,plain,
% 1.23/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.23/1.50 inference(monotonicity,[status(thm)],[164])).
% 1.23/1.50 tff(166,plain,
% 1.23/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[165, 163])).
% 1.34/1.50 tff(167,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(168,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.34/1.50 tff(169,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[168, 162, 152, 121, 151, 122, 120])).
% 1.34/1.50 tff(170,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(171,plain,
% 1.34/1.50 (~b(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[170, 150, 122, 121, 120])).
% 1.34/1.50 tff(172,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(173,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(174,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.34/1.50 tff(175,plain,
% 1.34/1.50 (b(s(z), z) | r(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[174, 47, 111])).
% 1.34/1.50 tff(176,plain,
% 1.34/1.50 (r(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[175, 171])).
% 1.34/1.50 tff(177,assumption,(b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.50 tff(178,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(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(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(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(elem!1)))), z)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(179,plain,
% 1.34/1.50 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(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(elem!1)))), z)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(180,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(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(elem!1)))), z))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[179])).
% 1.34/1.50 tff(181,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(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(elem!1)))), z)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[180, 178])).
% 1.34/1.50 tff(182,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(183,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.34/1.50 tff(184,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[183, 162, 121, 177, 151, 122, 120])).
% 1.34/1.50 tff(185,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(186,plain,
% 1.34/1.50 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[185, 150, 122, 121, 120])).
% 1.34/1.50 tff(187,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(188,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(189,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.34/1.50 tff(190,plain,
% 1.34/1.50 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[189, 47])).
% 1.34/1.50 tff(191,plain,
% 1.34/1.50 (b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[190, 143])).
% 1.34/1.50 tff(192,plain,
% 1.34/1.50 (r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[191, 186])).
% 1.34/1.50 tff(193,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.50 tff(194,assumption,(r(s(z), z)), introduced(assumption)).
% 1.34/1.50 tff(195,plain,
% 1.34/1.50 (((~![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(z), s(s(s(s(elem!1)))))) | (~r(s(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), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(196,plain,
% 1.34/1.50 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(197,plain,
% 1.34/1.50 (((~![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), 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(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[196])).
% 1.34/1.50 tff(198,plain,
% 1.34/1.50 (((~![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), 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(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[197, 195])).
% 1.34/1.50 tff(199,plain,
% 1.34/1.50 ((~![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), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(200,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.34/1.50 tff(201,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[200, 65, 194, 193, 119, 2])).
% 1.34/1.50 tff(202,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(203,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[202, 192, 176, 2, 119])).
% 1.34/1.50 tff(204,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(205,plain,
% 1.34/1.50 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[204, 118, 96, 2, 84])).
% 1.34/1.50 tff(206,assumption,(s(s(z)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.50 tff(207,plain,
% 1.34/1.50 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.34/1.50 inference(symmetry,[status(thm)],[206])).
% 1.34/1.50 tff(208,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[37, 207])).
% 1.34/1.50 tff(209,plain,(~(s(s(z)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(210,assumption,(~b(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.50 tff(211,assumption,(~r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.50 tff(212,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(213,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(214,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.34/1.50 tff(215,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[214, 47, 211, 210, 209])).
% 1.34/1.50 tff(216,plain,(b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(217,plain,
% 1.34/1.50 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[216, 205])).
% 1.34/1.50 tff(218,plain,
% 1.34/1.50 (((~![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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(219,plain,
% 1.34/1.50 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(220,plain,
% 1.34/1.50 (((~![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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), 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(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[219])).
% 1.34/1.50 tff(221,plain,
% 1.34/1.50 (((~![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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), 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(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[220, 218])).
% 1.34/1.50 tff(222,plain,
% 1.34/1.50 ((~![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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(223,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[222, 221])).
% 1.34/1.50 tff(224,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[223, 65, 54, 123, 2])).
% 1.34/1.50 tff(225,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(226,plain,
% 1.34/1.50 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[225, 2, 54])).
% 1.34/1.50 tff(227,plain,
% 1.34/1.50 (b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[149, 226])).
% 1.34/1.50 tff(228,plain,
% 1.34/1.50 (~b(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[170, 227, 96, 118, 84])).
% 1.34/1.50 tff(229,plain,
% 1.34/1.50 (r(s(z), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[175, 228])).
% 1.34/1.50 tff(230,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.34/1.50 tff(231,plain,
% 1.34/1.50 (((~![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(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(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(232,plain,
% 1.34/1.50 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(233,plain,
% 1.34/1.50 (((~![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), 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)), z)) | (~r(s(s(z)), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[232])).
% 1.34/1.50 tff(234,plain,
% 1.34/1.50 (((~![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), 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)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[233, 231])).
% 1.34/1.50 tff(235,plain,
% 1.34/1.50 ((~![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), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(236,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[235, 234])).
% 1.34/1.51 tff(237,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[236, 65, 194, 230, 2])).
% 1.34/1.51 tff(238,plain,((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(239,plain,
% 1.34/1.51 (~r(s(s(z)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[238, 229, 2])).
% 1.34/1.51 tff(240,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(241,plain,
% 1.34/1.51 (~(s(s(z)) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[240, 33])).
% 1.34/1.51 tff(242,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(243,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(244,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.34/1.51 tff(245,plain,
% 1.34/1.51 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[244, 47, 241])).
% 1.34/1.51 tff(246,plain,
% 1.34/1.51 (b(s(s(z)), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[245, 239])).
% 1.34/1.51 tff(247,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(248,plain,
% 1.34/1.51 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~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)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(249,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[248])).
% 1.34/1.51 tff(250,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[249, 247])).
% 1.34/1.51 tff(251,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(252,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.34/1.51 tff(253,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[252, 162, 118, 227, 96, 84, 246, 217])).
% 1.34/1.51 tff(254,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(255,plain,
% 1.34/1.51 (~r(s(s(z)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[254, 55, 54])).
% 1.34/1.51 tff(256,plain,
% 1.34/1.51 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.34/1.51 inference(commutativity,[status(thm)],[])).
% 1.34/1.51 tff(257,plain,
% 1.34/1.51 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[256])).
% 1.34/1.51 tff(258,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.34/1.51 tff(259,plain,
% 1.34/1.51 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[258])).
% 1.34/1.51 tff(260,plain,
% 1.34/1.51 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.34/1.51 inference(symmetry,[status(thm)],[259])).
% 1.34/1.51 tff(261,plain,
% 1.34/1.51 (s(z) = inj_0(s(s(z)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[15])).
% 1.34/1.51 tff(262,plain,
% 1.34/1.51 (s(s(z)) = s(z)),
% 1.34/1.51 inference(symmetry,[status(thm)],[258])).
% 1.34/1.51 tff(263,plain,
% 1.34/1.51 (s(s(z)) = z),
% 1.34/1.51 inference(transitivity,[status(thm)],[262, 261, 260, 13])).
% 1.34/1.51 tff(264,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[241, 263])).
% 1.34/1.51 tff(265,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(266,plain,
% 1.34/1.51 (~(s(s(z)) = s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[265, 257])).
% 1.34/1.51 tff(267,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(268,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(269,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.34/1.51 tff(270,plain,
% 1.34/1.51 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[269, 47])).
% 1.34/1.51 tff(271,plain,
% 1.34/1.51 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[270, 266])).
% 1.34/1.51 tff(272,plain,
% 1.34/1.51 (b(s(s(z)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[271, 255])).
% 1.34/1.51 tff(273,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.34/1.51 tff(274,plain,
% 1.34/1.51 (((~![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(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)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(275,plain,
% 1.34/1.51 (((~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)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(276,plain,
% 1.34/1.51 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), 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(z)))) | (~r(z, s(s(z))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[275])).
% 1.34/1.51 tff(277,plain,
% 1.34/1.51 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), 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(z)))) | (~r(z, s(s(z)))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[276, 274])).
% 1.34/1.51 tff(278,plain,
% 1.34/1.51 ((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(279,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.34/1.51 tff(280,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[279, 65, 1, 273, 55])).
% 1.34/1.51 tff(281,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(282,plain,
% 1.34/1.51 (~r(z, s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[281, 273, 55])).
% 1.34/1.51 tff(283,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 1.34/1.51 tff(284,plain,
% 1.34/1.51 (s(s(s(z))) = z),
% 1.34/1.51 inference(symmetry,[status(thm)],[283])).
% 1.34/1.51 tff(285,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(286,plain,
% 1.34/1.51 (~(s(s(s(z))) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[285, 33])).
% 1.34/1.51 tff(287,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[286, 284])).
% 1.34/1.51 tff(288,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(289,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.34/1.51 tff(290,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 1.34/1.51 tff(291,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(292,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(293,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[292, 291])).
% 1.34/1.51 tff(294,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[293, 47, 290, 289, 288])).
% 1.34/1.51 tff(295,plain,(r(z, s(s(s(z)))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(296,plain,
% 1.34/1.51 (b(z, s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[295, 282])).
% 1.34/1.51 tff(297,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.34/1.51 tff(298,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.51 tff(299,assumption,(r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.51 tff(300,plain,
% 1.34/1.51 (((~![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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(301,plain,
% 1.34/1.51 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(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(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(302,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(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(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[301])).
% 1.34/1.51 tff(303,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(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(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[302, 300])).
% 1.34/1.51 tff(304,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(305,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[304, 303])).
% 1.34/1.51 tff(306,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[305, 65, 54, 299, 273])).
% 1.34/1.51 tff(307,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(308,plain,
% 1.34/1.51 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[307, 54, 273])).
% 1.34/1.51 tff(309,assumption,(s(s(s(z))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(310,plain,
% 1.34/1.51 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[309])).
% 1.34/1.51 tff(311,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(312,plain,
% 1.34/1.51 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[311, 11])).
% 1.34/1.51 tff(313,plain,
% 1.34/1.51 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[312])).
% 1.34/1.51 tff(314,plain,
% 1.34/1.51 (s(s(z)) = s(s(s(elem!1)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[313, 310, 19])).
% 1.34/1.51 tff(315,plain,
% 1.34/1.51 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[314])).
% 1.34/1.51 tff(316,plain,
% 1.34/1.51 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[315])).
% 1.34/1.51 tff(317,plain,
% 1.34/1.51 (s(s(elem!1)) = s(z)),
% 1.34/1.51 inference(transitivity,[status(thm)],[25, 316, 15])).
% 1.34/1.51 tff(318,plain,
% 1.34/1.51 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.34/1.51 inference(commutativity,[status(thm)],[])).
% 1.34/1.51 tff(319,plain,
% 1.34/1.51 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[318])).
% 1.34/1.51 tff(320,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.51 tff(321,plain,
% 1.34/1.51 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[320])).
% 1.34/1.51 tff(322,plain,
% 1.34/1.51 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.34/1.51 inference(symmetry,[status(thm)],[321])).
% 1.34/1.51 tff(323,plain,
% 1.34/1.51 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(324,plain,
% 1.34/1.51 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[323, 11])).
% 1.34/1.51 tff(325,plain,
% 1.34/1.51 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[324])).
% 1.34/1.51 tff(326,plain,
% 1.34/1.51 (s(elem!1) = z),
% 1.34/1.51 inference(transitivity,[status(thm)],[325, 322, 13])).
% 1.34/1.51 tff(327,plain,
% 1.34/1.51 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(328,plain,
% 1.34/1.51 (~(s(elem!1) = z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[327, 33])).
% 1.34/1.51 tff(329,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[328, 326])).
% 1.34/1.51 tff(330,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(331,plain,
% 1.34/1.51 (~(s(s(elem!1)) = s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[330, 319])).
% 1.34/1.51 tff(332,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[331, 317])).
% 1.34/1.51 tff(333,plain,(~(s(s(s(z))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(334,plain,
% 1.34/1.51 (((~![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))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(335,plain,
% 1.34/1.51 ((~![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))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(336,plain,
% 1.34/1.51 ((~![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)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[335, 334])).
% 1.34/1.51 tff(337,plain,
% 1.34/1.51 ((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)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[336, 47])).
% 1.34/1.51 tff(338,plain,
% 1.34/1.51 (b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[337, 333])).
% 1.34/1.51 tff(339,plain,
% 1.34/1.51 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[338, 308])).
% 1.34/1.51 tff(340,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.51 tff(341,plain,
% 1.34/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(342,plain,
% 1.34/1.51 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(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(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(343,plain,
% 1.34/1.51 (((~![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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(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(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[342])).
% 1.34/1.51 tff(344,plain,
% 1.34/1.51 (((~![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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(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(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[343, 341])).
% 1.34/1.51 tff(345,plain,
% 1.34/1.51 ((~![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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(346,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.34/1.51 tff(347,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[346, 65, 54, 273, 340])).
% 1.34/1.51 tff(348,plain,((~r(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(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(349,plain,
% 1.34/1.51 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[348, 54, 273])).
% 1.34/1.51 tff(350,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 1.34/1.51 tff(351,plain,
% 1.34/1.51 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[350])).
% 1.34/1.51 tff(352,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[333, 351])).
% 1.34/1.51 tff(353,plain,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(354,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.51 tff(355,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.51 tff(356,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(357,plain,
% 1.34/1.51 ((~![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)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(358,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[357, 356])).
% 1.34/1.51 tff(359,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[358, 47, 355, 354, 353])).
% 1.34/1.51 tff(360,plain,(r(s(s(s(s(elem!1)))), s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(361,plain,
% 1.34/1.51 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[360, 349])).
% 1.34/1.51 tff(362,assumption,(b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.51 tff(363,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.51 tff(364,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(365,plain,
% 1.34/1.51 (((~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(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(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(366,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[365])).
% 1.34/1.51 tff(367,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[366, 364])).
% 1.34/1.52 tff(368,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(369,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.34/1.52 tff(370,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[369, 162, 122, 363, 362, 298, 297])).
% 1.34/1.52 tff(371,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(372,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[371, 361, 339, 122, 298, 297])).
% 1.34/1.52 tff(373,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(374,plain,
% 1.34/1.52 (~b(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[373, 296, 54, 96, 273])).
% 1.34/1.52 tff(375,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.52 tff(376,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.52 tff(377,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(378,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(379,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.34/1.52 tff(380,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[379, 47, 286, 376, 375])).
% 1.34/1.52 tff(381,plain,(r(s(s(s(z))), z) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(382,plain,
% 1.34/1.52 (r(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[381, 374])).
% 1.34/1.52 tff(383,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.34/1.52 tff(384,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.34/1.52 tff(385,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.52 tff(386,plain,
% 1.34/1.52 (((~![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(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(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(387,plain,
% 1.34/1.52 (((~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(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(388,plain,
% 1.34/1.52 (((~![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(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[387])).
% 1.34/1.52 tff(389,plain,
% 1.34/1.52 (((~![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(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[388, 386])).
% 1.34/1.52 tff(390,plain,
% 1.34/1.52 ((~![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)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(391,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.34/1.52 tff(392,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[391, 65, 194, 384, 55])).
% 1.34/1.52 tff(393,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(394,plain,
% 1.34/1.52 (~r(z, s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[393, 194, 384])).
% 1.34/1.52 tff(395,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.34/1.52 tff(396,plain,
% 1.34/1.52 (((~![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(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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(397,plain,
% 1.34/1.52 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), 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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(398,plain,
% 1.34/1.52 (((~![X0: $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(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), 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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[397])).
% 1.34/1.52 tff(399,plain,
% 1.34/1.52 (((~![X0: $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(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), 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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[398, 396])).
% 1.34/1.52 tff(400,plain,
% 1.34/1.52 ((~![X0: $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(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(401,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.34/1.52 tff(402,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[401, 65, 54, 193, 384])).
% 1.34/1.52 tff(403,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(404,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[403, 193, 384])).
% 1.34/1.52 tff(405,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[52, 404])).
% 1.34/1.52 tff(406,plain,
% 1.34/1.52 (((~![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), 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(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))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(407,plain,
% 1.34/1.52 (((~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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(408,plain,
% 1.34/1.52 (((~![X0: $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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[407])).
% 1.34/1.52 tff(409,plain,
% 1.34/1.52 (((~![X0: $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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[408, 406])).
% 1.34/1.52 tff(410,plain,
% 1.34/1.52 ((~![X0: $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)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(411,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.34/1.52 tff(412,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[411, 65, 193, 395, 340])).
% 1.34/1.52 tff(413,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,[]))).
% 1.34/1.52 tff(414,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[413, 395, 193])).
% 1.34/1.52 tff(415,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[360, 414])).
% 1.34/1.52 tff(416,assumption,(b(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.34/1.52 tff(417,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.34/1.52 tff(418,plain,
% 1.34/1.52 (((~![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), 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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(419,plain,
% 1.34/1.52 (((~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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(420,plain,
% 1.34/1.52 (((~![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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[419])).
% 1.34/1.52 tff(421,plain,
% 1.34/1.52 (((~![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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[420, 418])).
% 1.34/1.52 tff(422,plain,
% 1.34/1.52 ((~![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)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(423,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.34/1.52 tff(424,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[423, 65, 384, 395, 417])).
% 1.34/1.52 tff(425,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(426,plain,
% 1.34/1.52 (~r(s(s(z)), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[425, 395, 384])).
% 1.34/1.52 tff(427,plain,
% 1.34/1.52 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(428,plain,
% 1.34/1.52 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[427])).
% 1.34/1.52 tff(429,plain,
% 1.34/1.52 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[428])).
% 1.34/1.52 tff(430,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.34/1.52 tff(431,plain,
% 1.34/1.52 (s(s(z)) = s(s(s(z)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[430])).
% 1.34/1.52 tff(432,plain,
% 1.34/1.52 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[431])).
% 1.34/1.52 tff(433,plain,
% 1.34/1.52 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[432])).
% 1.34/1.52 tff(434,plain,
% 1.34/1.52 (s(s(z)) = s(z)),
% 1.34/1.52 inference(transitivity,[status(thm)],[313, 433, 15])).
% 1.34/1.52 tff(435,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[266, 434])).
% 1.34/1.52 tff(436,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(437,plain,
% 1.34/1.52 (~(s(s(z)) = s(s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[436, 429])).
% 1.34/1.52 tff(438,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(439,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(440,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.34/1.52 tff(441,plain,
% 1.34/1.52 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[440, 47])).
% 1.34/1.52 tff(442,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[441, 437])).
% 1.34/1.52 tff(443,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[442, 426])).
% 1.34/1.52 tff(444,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.34/1.52 tff(445,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.34/1.52 tff(446,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(447,plain,
% 1.34/1.52 (((~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(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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(448,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[447])).
% 1.34/1.52 tff(449,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[448, 446])).
% 1.34/1.52 tff(450,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(451,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.34/1.52 tff(452,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[451, 162, 416, 445, 444, 363, 362])).
% 1.34/1.52 tff(453,plain,((~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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(454,plain,
% 1.34/1.52 (~b(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[453, 443, 416, 362, 363])).
% 1.34/1.52 tff(455,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(456,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(457,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[456, 455])).
% 1.34/1.52 tff(458,plain,
% 1.34/1.52 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[457, 47])).
% 1.34/1.52 tff(459,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[458, 436])).
% 1.34/1.52 tff(460,plain,
% 1.34/1.52 (r(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[459, 454])).
% 1.34/1.52 tff(461,plain,
% 1.34/1.52 (((~![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), 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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(462,plain,
% 1.34/1.52 (((~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)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(463,plain,
% 1.34/1.52 (((~![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))))))) <=> ((~![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), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[462])).
% 1.34/1.52 tff(464,plain,
% 1.34/1.52 (((~![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))))))) <=> ((~![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), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[463, 461])).
% 1.34/1.52 tff(465,plain,
% 1.34/1.52 ((~![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))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(466,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[465, 464])).
% 1.34/1.52 tff(467,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[466, 65, 384, 395, 460])).
% 1.34/1.52 tff(468,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(469,plain,
% 1.34/1.52 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[468, 415, 405, 395, 384])).
% 1.34/1.52 tff(470,plain,
% 1.34/1.52 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[338, 469])).
% 1.34/1.52 tff(471,plain,
% 1.34/1.52 (((~![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(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(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(472,plain,
% 1.34/1.52 (((~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(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(473,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[472])).
% 1.34/1.53 tff(474,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[473, 471])).
% 1.34/1.53 tff(475,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(476,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.34/1.53 tff(477,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[476, 65, 193, 395, 470])).
% 1.34/1.53 tff(478,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(479,plain,
% 1.34/1.53 (~r(s(z), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[478, 193, 384])).
% 1.34/1.53 tff(480,plain,
% 1.34/1.53 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(481,plain,
% 1.34/1.53 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[480])).
% 1.34/1.53 tff(482,plain,
% 1.34/1.53 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[481])).
% 1.34/1.53 tff(483,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.34/1.53 tff(484,plain,
% 1.34/1.53 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[483])).
% 1.34/1.53 tff(485,plain,
% 1.34/1.53 (s(s(z)) = z),
% 1.34/1.53 inference(transitivity,[status(thm)],[313, 484, 13])).
% 1.34/1.53 tff(486,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[241, 485])).
% 1.34/1.53 tff(487,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(488,plain,
% 1.34/1.53 (~(s(z) = s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[487, 482])).
% 1.34/1.53 tff(489,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(490,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(491,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.34/1.53 tff(492,plain,
% 1.34/1.53 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[491, 47])).
% 1.34/1.53 tff(493,plain,
% 1.34/1.53 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[492, 488])).
% 1.34/1.53 tff(494,plain,
% 1.34/1.53 (b(s(z), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[493, 479])).
% 1.34/1.53 tff(495,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.53 tff(496,plain,
% 1.34/1.53 (((~![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(z), s(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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(497,plain,
% 1.34/1.53 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(498,plain,
% 1.34/1.53 (((~![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(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[497])).
% 1.34/1.53 tff(499,plain,
% 1.34/1.53 (((~![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(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[498, 496])).
% 1.34/1.53 tff(500,plain,
% 1.34/1.53 ((~![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(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(501,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.34/1.53 tff(502,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[501, 65, 194, 193, 495])).
% 1.34/1.53 tff(503,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(504,plain,
% 1.34/1.53 (~r(s(z), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[503, 495, 193])).
% 1.34/1.53 tff(505,plain,
% 1.34/1.53 (((~![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)))))))) <=> ((~![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)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(506,plain,
% 1.34/1.53 (((~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)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(507,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[506])).
% 1.34/1.53 tff(508,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[507, 505])).
% 1.34/1.53 tff(509,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(510,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.34/1.53 tff(511,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[510, 65, 193, 384, 119])).
% 1.34/1.53 tff(512,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,[]))).
% 1.34/1.53 tff(513,plain,
% 1.34/1.53 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[512, 193, 384])).
% 1.34/1.53 tff(514,plain,
% 1.34/1.53 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[214, 47, 513, 209])).
% 1.34/1.53 tff(515,plain,
% 1.34/1.53 (~r(z, s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[105, 97, 2])).
% 1.34/1.53 tff(516,plain,
% 1.34/1.53 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(517,plain,
% 1.34/1.53 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[516])).
% 1.34/1.53 tff(518,plain,
% 1.34/1.53 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[517])).
% 1.34/1.53 tff(519,plain,
% 1.34/1.53 (~(z = s(s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[241, 518])).
% 1.34/1.53 tff(520,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(521,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(522,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.34/1.53 tff(523,plain,
% 1.34/1.53 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[522, 47])).
% 1.34/1.53 tff(524,plain,
% 1.34/1.53 (b(z, s(s(z))) | r(z, s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[523, 519])).
% 1.34/1.53 tff(525,plain,
% 1.34/1.53 (b(z, s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[524, 515])).
% 1.34/1.53 tff(526,assumption,(b(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.53 tff(527,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(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(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(528,plain,
% 1.34/1.53 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(529,plain,
% 1.34/1.53 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[528])).
% 1.34/1.53 tff(530,plain,
% 1.34/1.53 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[529, 527])).
% 1.34/1.53 tff(531,plain,
% 1.34/1.53 ((~![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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(532,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[531, 530])).
% 1.34/1.53 tff(533,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[532, 65, 97, 193, 495])).
% 1.34/1.53 tff(534,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(535,plain,
% 1.34/1.53 (~r(z, s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[534, 97, 193])).
% 1.34/1.53 tff(536,plain,
% 1.34/1.53 (b(z, s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[83, 535])).
% 1.34/1.53 tff(537,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.34/1.53 tff(538,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.34/1.53 tff(539,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(540,plain,
% 1.34/1.53 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(541,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[540])).
% 1.34/1.53 tff(542,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[541, 539])).
% 1.34/1.53 tff(543,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(544,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.34/1.53 tff(545,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[544, 162, 416, 120, 538, 537, 526])).
% 1.34/1.53 tff(546,plain,((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(547,plain,
% 1.34/1.53 (~b(s(s(z)), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[546, 536, 416, 526, 525])).
% 1.34/1.53 tff(548,plain,
% 1.34/1.53 (r(s(s(z)), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[245, 547])).
% 1.34/1.53 tff(549,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(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(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(550,plain,
% 1.34/1.53 (((~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)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(551,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)), z)) | (~r(s(s(z)), s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[550])).
% 1.34/1.53 tff(552,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)), z)) | (~r(s(s(z)), s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[551, 549])).
% 1.34/1.53 tff(553,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(554,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[553, 552])).
% 1.34/1.53 tff(555,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[554, 65, 97, 548, 2])).
% 1.34/1.53 tff(556,plain,((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(557,plain,
% 1.34/1.53 (~r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[556, 405, 2, 514, 193])).
% 1.34/1.53 tff(558,plain,
% 1.34/1.53 (b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[117, 557])).
% 1.34/1.53 tff(559,plain,
% 1.34/1.53 (((~![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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(560,plain,
% 1.34/1.53 (((~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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(561,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[560])).
% 1.34/1.54 tff(562,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[561, 559])).
% 1.34/1.54 tff(563,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(564,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.34/1.54 tff(565,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[564, 65, 495, 1, 340])).
% 1.34/1.54 tff(566,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(567,plain,
% 1.34/1.54 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[566, 1, 495])).
% 1.34/1.54 tff(568,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[360, 567])).
% 1.34/1.54 tff(569,plain,
% 1.34/1.54 (((~![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(z))) | (~r(s(z), 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(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(570,plain,
% 1.34/1.54 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(571,plain,
% 1.34/1.54 (((~![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(z))), s(s(z)))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[570])).
% 1.34/1.54 tff(572,plain,
% 1.34/1.54 (((~![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(z))), s(s(z)))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[571, 569])).
% 1.34/1.54 tff(573,plain,
% 1.34/1.54 ((~![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(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(574,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[573, 572])).
% 1.34/1.54 tff(575,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[574, 65, 384, 385, 273])).
% 1.34/1.54 tff(576,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,[]))).
% 1.34/1.54 tff(577,plain,
% 1.34/1.54 (~r(s(s(s(z))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[576, 385, 384])).
% 1.34/1.54 tff(578,plain,
% 1.34/1.54 (b(s(s(s(z))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[459, 577])).
% 1.34/1.54 tff(579,plain,
% 1.34/1.54 (((~![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(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))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(580,plain,
% 1.34/1.54 (((~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))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(581,plain,
% 1.34/1.54 (((~![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(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)))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[580])).
% 1.34/1.54 tff(582,plain,
% 1.34/1.54 (((~![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(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))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[581, 579])).
% 1.34/1.54 tff(583,plain,
% 1.34/1.54 ((~![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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(584,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.34/1.54 tff(585,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[584, 65, 385, 417, 2])).
% 1.34/1.54 tff(586,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(587,plain,
% 1.34/1.54 (~r(s(s(z)), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[586, 385, 2])).
% 1.34/1.54 tff(588,plain,
% 1.34/1.54 (b(s(s(z)), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[442, 587])).
% 1.34/1.54 tff(589,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[453, 588, 578, 416, 362, 363])).
% 1.34/1.54 tff(590,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), 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))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(591,plain,
% 1.34/1.54 (~r(s(s(s(z))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[590, 568, 362, 405, 2, 384])).
% 1.34/1.54 tff(592,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(593,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(594,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.34/1.54 tff(595,plain,
% 1.34/1.54 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[594, 47, 487])).
% 1.34/1.54 tff(596,plain,
% 1.34/1.54 (b(s(s(s(z))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[595, 591])).
% 1.34/1.54 tff(597,plain,
% 1.34/1.54 (~r(s(z), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[468, 568, 405, 362, 384])).
% 1.34/1.54 tff(598,plain,
% 1.34/1.54 (b(s(z), s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[493, 597])).
% 1.34/1.54 tff(599,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.34/1.54 tff(600,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.54 tff(601,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(602,plain,
% 1.34/1.54 (((~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(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(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(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(603,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[602])).
% 1.34/1.54 tff(604,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[603, 601])).
% 1.34/1.54 tff(605,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(606,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.34/1.54 tff(607,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[606, 162, 151, 363, 362, 600, 599])).
% 1.34/1.54 tff(608,plain,((~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(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(609,plain,
% 1.34/1.54 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[608, 598, 362, 568, 596])).
% 1.34/1.54 tff(610,plain,
% 1.34/1.54 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[149, 609])).
% 1.34/1.54 tff(611,plain,
% 1.34/1.54 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[129, 65, 610, 2])).
% 1.34/1.54 tff(612,plain,
% 1.34/1.54 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[214, 47, 611, 209])).
% 1.34/1.54 tff(613,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(614,plain,
% 1.34/1.54 (((~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(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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(615,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[614])).
% 1.34/1.54 tff(616,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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)))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[615, 613])).
% 1.34/1.54 tff(617,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(618,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.34/1.54 tff(619,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[618, 162, 416, 363, 362, 445, 526])).
% 1.34/1.54 tff(620,plain,((~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(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(621,plain,
% 1.34/1.54 (~b(s(s(s(z))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[620, 612, 568, 362, 405])).
% 1.34/1.54 tff(622,plain,
% 1.34/1.54 (r(s(s(s(z))), s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[459, 621])).
% 1.34/1.54 tff(623,plain,
% 1.34/1.54 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.34/1.54 inference(commutativity,[status(thm)],[])).
% 1.34/1.54 tff(624,plain,
% 1.34/1.54 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[623])).
% 1.34/1.54 tff(625,plain,
% 1.34/1.54 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[624])).
% 1.34/1.54 tff(626,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.34/1.54 tff(627,plain,
% 1.34/1.54 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[626])).
% 1.34/1.54 tff(628,plain,
% 1.34/1.54 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.34/1.54 inference(symmetry,[status(thm)],[627])).
% 1.34/1.54 tff(629,plain,
% 1.34/1.54 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(630,plain,
% 1.34/1.54 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[629, 11])).
% 1.34/1.54 tff(631,plain,
% 1.34/1.54 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[630])).
% 1.34/1.54 tff(632,plain,
% 1.34/1.54 (s(s(s(z))) = s(z)),
% 1.34/1.54 inference(transitivity,[status(thm)],[631, 628, 15])).
% 1.34/1.54 tff(633,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[487, 632])).
% 1.34/1.54 tff(634,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(635,plain,
% 1.34/1.54 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[634, 625])).
% 1.34/1.54 tff(636,plain,
% 1.34/1.54 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.34/1.54 inference(commutativity,[status(thm)],[])).
% 1.34/1.54 tff(637,plain,
% 1.34/1.54 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[636])).
% 1.34/1.54 tff(638,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.34/1.54 tff(639,plain,
% 1.34/1.54 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[638])).
% 1.34/1.54 tff(640,plain,
% 1.34/1.54 (s(s(s(z))) = z),
% 1.34/1.54 inference(transitivity,[status(thm)],[631, 639, 13])).
% 1.34/1.54 tff(641,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[286, 640])).
% 1.34/1.54 tff(642,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(643,plain,
% 1.34/1.54 (~(s(z) = s(s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[642, 637])).
% 1.34/1.54 tff(644,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.34/1.54 tff(645,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.54 tff(646,plain,
% 1.34/1.54 (((~![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(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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(647,plain,
% 1.34/1.54 (((~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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(648,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[647])).
% 1.34/1.54 tff(649,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[648, 646])).
% 1.34/1.54 tff(650,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(651,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.34/1.54 tff(652,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[651, 65, 384, 644, 645])).
% 1.34/1.54 tff(653,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(654,plain,
% 1.34/1.54 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[653, 644, 384])).
% 1.34/1.54 tff(655,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(656,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(657,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[656, 655])).
% 1.34/1.54 tff(658,plain,
% 1.34/1.54 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[657, 47])).
% 1.34/1.54 tff(659,plain,
% 1.34/1.54 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[658, 654, 643])).
% 1.34/1.54 tff(660,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.34/1.54 tff(661,plain,
% 1.34/1.54 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[660])).
% 1.34/1.54 tff(662,plain,
% 1.34/1.54 (s(s(z)) = s(s(s(s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[313, 661, 630, 660])).
% 1.34/1.54 tff(663,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[634, 662])).
% 1.34/1.54 tff(664,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(665,plain,
% 1.34/1.54 (((~![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(z)))) | (~r(s(s(s(s(z)))), 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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(666,plain,
% 1.34/1.54 (((~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(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(667,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![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(s(s(z))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[666])).
% 1.34/1.54 tff(668,plain,
% 1.34/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![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(s(s(z)))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[667, 665])).
% 1.34/1.55 tff(669,plain,
% 1.34/1.55 ((~![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(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(670,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[669, 668])).
% 1.34/1.55 tff(671,plain,
% 1.34/1.55 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[670, 65, 273, 644])).
% 1.34/1.55 tff(672,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(673,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(674,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.34/1.55 tff(675,plain,
% 1.34/1.55 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[674, 47])).
% 1.34/1.55 tff(676,plain,
% 1.34/1.55 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[675, 671, 664])).
% 1.34/1.55 tff(677,plain,
% 1.34/1.55 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.34/1.55 inference(commutativity,[status(thm)],[])).
% 1.34/1.55 tff(678,plain,
% 1.34/1.55 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[677])).
% 1.34/1.55 tff(679,plain,
% 1.34/1.55 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[664, 678])).
% 1.34/1.55 tff(680,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z)))), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(681,plain,
% 1.34/1.55 (((~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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(682,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[681])).
% 1.34/1.55 tff(683,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[682, 680])).
% 1.34/1.55 tff(684,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(685,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[684, 683])).
% 1.34/1.55 tff(686,plain,
% 1.34/1.55 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[685, 65, 273, 644])).
% 1.34/1.55 tff(687,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(688,plain,
% 1.34/1.55 ((~![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)))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(689,plain,
% 1.34/1.55 ((~![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))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[688, 687])).
% 1.34/1.55 tff(690,plain,
% 1.34/1.55 ((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))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[689, 47])).
% 1.34/1.55 tff(691,plain,
% 1.34/1.55 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[690, 686, 679])).
% 1.34/1.55 tff(692,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.55 tff(693,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.55 tff(694,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.55 tff(695,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(696,plain,
% 1.34/1.55 (((~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(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(697,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[696])).
% 1.34/1.55 tff(698,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[697, 695])).
% 1.34/1.55 tff(699,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(700,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[699, 698])).
% 1.34/1.55 tff(701,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[700, 162, 600, 599, 694, 693, 692])).
% 1.34/1.55 tff(702,plain,((~b(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)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(703,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[702, 691, 676, 599, 659, 600])).
% 1.34/1.55 tff(704,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(705,plain,
% 1.34/1.55 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[704, 598, 596, 622, 384])).
% 1.34/1.55 tff(706,plain,
% 1.34/1.55 (((~![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))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(707,plain,
% 1.34/1.55 ((~![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))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(708,plain,
% 1.34/1.55 ((~![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)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.34/1.55 tff(709,plain,
% 1.34/1.55 ((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)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[708, 47])).
% 1.34/1.55 tff(710,plain,
% 1.34/1.55 (b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[709, 705, 635])).
% 1.34/1.55 tff(711,plain,
% 1.34/1.55 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[129, 65, 123, 2])).
% 1.34/1.55 tff(712,plain,
% 1.34/1.55 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[214, 47, 711, 209])).
% 1.34/1.55 tff(713,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(elem!1)))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(714,plain,
% 1.34/1.55 (((~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(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(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(s(s(elem!1)))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(715,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(elem!1))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[714])).
% 1.34/1.55 tff(716,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(elem!1)))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[715, 713])).
% 1.34/1.55 tff(717,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(718,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.34/1.55 tff(719,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[718, 162, 416, 444, 363, 362, 526])).
% 1.34/1.55 tff(720,plain,((~b(s(s(z)), s(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(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(721,plain,
% 1.34/1.55 (~b(s(s(z)), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[720, 712, 416, 362, 363])).
% 1.34/1.55 tff(722,plain,
% 1.34/1.55 (r(s(s(z)), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[442, 721])).
% 1.34/1.55 tff(723,plain,
% 1.34/1.55 (~r(s(z), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[425, 722, 384])).
% 1.34/1.55 tff(724,plain,
% 1.34/1.55 (b(s(z), s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[493, 723])).
% 1.34/1.55 tff(725,plain,
% 1.34/1.55 (~r(s(s(s(z))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[590, 363, 362, 416, 2, 384])).
% 1.34/1.55 tff(726,plain,
% 1.34/1.55 (b(s(s(s(z))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[595, 725])).
% 1.34/1.55 tff(727,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(z))))), introduced(assumption)).
% 1.34/1.55 tff(728,plain,
% 1.34/1.55 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[727])).
% 1.34/1.55 tff(729,plain,
% 1.34/1.55 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[20, 728, 630])).
% 1.34/1.55 tff(730,plain,
% 1.34/1.55 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[729])).
% 1.34/1.55 tff(731,plain,
% 1.34/1.55 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[730])).
% 1.34/1.55 tff(732,plain,
% 1.34/1.55 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[599, 731])).
% 1.34/1.55 tff(733,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 1.34/1.55 inference(monotonicity,[status(thm)],[729])).
% 1.34/1.55 tff(734,plain,
% 1.34/1.55 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(symmetry,[status(thm)],[733])).
% 1.34/1.55 tff(735,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[298, 734])).
% 1.34/1.55 tff(736,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[729])).
% 1.34/1.55 tff(737,plain,
% 1.34/1.55 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(symmetry,[status(thm)],[736])).
% 1.34/1.55 tff(738,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[600, 737])).
% 1.34/1.55 tff(739,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.55 tff(740,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.55 tff(741,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.34/1.55 tff(742,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(743,plain,
% 1.34/1.55 (((~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))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(744,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[743])).
% 1.34/1.55 tff(745,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[744, 742])).
% 1.34/1.55 tff(746,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(747,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.34/1.55 tff(748,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[747, 162, 152, 121, 741, 740, 739])).
% 1.34/1.55 tff(749,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(750,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[749, 738, 735, 152, 732, 121])).
% 1.34/1.55 tff(751,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(752,plain,
% 1.34/1.56 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[751, 724, 121, 152, 726, 298])).
% 1.34/1.56 tff(753,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.56 tff(754,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(755,plain,
% 1.34/1.56 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~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(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(756,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[755])).
% 1.34/1.56 tff(757,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[756, 754])).
% 1.34/1.56 tff(758,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), 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)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(759,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.34/1.56 tff(760,plain,
% 1.34/1.56 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[759, 162, 121, 363, 298, 600, 692])).
% 1.34/1.56 tff(761,plain,
% 1.34/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(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(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(762,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(763,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[762, 761])).
% 1.34/1.56 tff(764,plain,
% 1.34/1.56 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[763, 47, 760, 753])).
% 1.34/1.56 tff(765,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(766,plain,
% 1.34/1.56 (((~b(z, s(z))) | (~b(s(s(s(z))), s(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)))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(767,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[766])).
% 1.34/1.56 tff(768,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[767, 765])).
% 1.34/1.56 tff(769,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(770,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.34/1.56 tff(771,plain,
% 1.34/1.56 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[770, 162, 121, 298, 600, 599, 692])).
% 1.34/1.56 tff(772,plain,
% 1.34/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(773,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(774,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.34/1.56 tff(775,plain,
% 1.34/1.56 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[774, 47])).
% 1.34/1.56 tff(776,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[775, 771, 642])).
% 1.34/1.56 tff(777,plain,
% 1.34/1.56 (((~![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(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(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(778,plain,
% 1.34/1.56 (((~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(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(779,plain,
% 1.34/1.56 (((~![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(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(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[778])).
% 1.34/1.56 tff(780,plain,
% 1.34/1.56 (((~![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(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(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[779, 777])).
% 1.34/1.56 tff(781,plain,
% 1.34/1.56 ((~![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(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)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(782,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.34/1.56 tff(783,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[782, 65, 123, 776, 764])).
% 1.34/1.56 tff(784,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(785,plain,
% 1.34/1.56 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[784, 123, 752, 121, 363, 298, 726, 724])).
% 1.34/1.56 tff(786,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[690, 785, 679])).
% 1.34/1.56 tff(787,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.56 tff(788,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.56 tff(789,plain,
% 1.34/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(790,plain,
% 1.34/1.56 (((~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(791,plain,
% 1.34/1.56 (((~![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(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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[790])).
% 1.34/1.56 tff(792,plain,
% 1.34/1.56 (((~![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(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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[791, 789])).
% 1.34/1.56 tff(793,plain,
% 1.34/1.56 ((~![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(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)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(794,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.34/1.56 tff(795,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[794, 65, 417, 788, 787])).
% 1.34/1.56 tff(796,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(797,plain,
% 1.34/1.56 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[796, 786, 722])).
% 1.34/1.56 tff(798,plain,
% 1.34/1.56 (((~![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))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(799,plain,
% 1.34/1.56 ((~![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))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(800,plain,
% 1.34/1.56 ((~![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)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.34/1.56 tff(801,plain,
% 1.34/1.56 ((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)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[800, 47])).
% 1.34/1.56 tff(802,plain,
% 1.34/1.56 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[801, 797, 634])).
% 1.34/1.56 tff(803,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.56 tff(804,plain,
% 1.34/1.56 (((~![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(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(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(805,plain,
% 1.34/1.56 (((~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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(806,plain,
% 1.34/1.56 (((~![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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[805])).
% 1.34/1.56 tff(807,plain,
% 1.34/1.56 (((~![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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[806, 804])).
% 1.34/1.56 tff(808,plain,
% 1.34/1.56 ((~![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(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)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(809,plain,
% 1.34/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.34/1.56 tff(810,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[809, 65, 1, 787, 803])).
% 1.34/1.56 tff(811,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(812,plain,
% 1.34/1.56 (~r(z, s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[811, 786, 1])).
% 1.34/1.56 tff(813,plain,
% 1.34/1.56 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(814,plain,
% 1.34/1.56 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[813])).
% 1.34/1.56 tff(815,plain,
% 1.34/1.56 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[814])).
% 1.34/1.56 tff(816,plain,
% 1.34/1.56 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(817,plain,
% 1.34/1.56 (~(s(s(s(s(z)))) = z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[816, 33])).
% 1.34/1.56 tff(818,plain,
% 1.34/1.56 (~(z = s(s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[817, 815])).
% 1.34/1.56 tff(819,plain,
% 1.34/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(820,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(821,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[820, 819])).
% 1.34/1.56 tff(822,plain,
% 1.34/1.56 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[821, 47])).
% 1.34/1.56 tff(823,plain,
% 1.34/1.56 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[822, 818])).
% 1.34/1.56 tff(824,plain,
% 1.34/1.56 (b(z, s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[823, 812])).
% 1.34/1.56 tff(825,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.34/1.56 tff(826,plain,
% 1.34/1.56 (((~![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(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(z, s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(827,plain,
% 1.34/1.57 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(828,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[827])).
% 1.34/1.57 tff(829,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[828, 826])).
% 1.34/1.57 tff(830,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(831,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[830, 829])).
% 1.34/1.57 tff(832,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[831, 65, 1, 55, 417])).
% 1.34/1.57 tff(833,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(834,plain,
% 1.34/1.57 (~r(z, s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[833, 722, 1])).
% 1.34/1.57 tff(835,plain,
% 1.34/1.57 (b(z, s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[524, 834])).
% 1.34/1.57 tff(836,plain,
% 1.34/1.57 (((~![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(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(837,plain,
% 1.34/1.57 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(838,plain,
% 1.34/1.57 (((~![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(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(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[837])).
% 1.34/1.57 tff(839,plain,
% 1.34/1.57 (((~![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(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(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[838, 836])).
% 1.34/1.57 tff(840,plain,
% 1.34/1.57 ((~![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(s(elem!1)))))) | (~r(s(s(z)), z)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(841,plain,
% 1.34/1.57 ((~![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(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[840, 839])).
% 1.34/1.57 tff(842,plain,
% 1.34/1.57 (~r(s(s(z)), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[841, 65, 495, 1, 722])).
% 1.34/1.57 tff(843,plain,
% 1.34/1.57 (b(s(s(z)), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[245, 842])).
% 1.34/1.57 tff(844,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(845,plain,
% 1.34/1.57 (((~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)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(846,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[845])).
% 1.34/1.57 tff(847,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[846, 844])).
% 1.34/1.57 tff(848,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(849,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.34/1.57 tff(850,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[849, 162, 843, 835, 825, 824, 802])).
% 1.34/1.57 tff(851,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(852,plain,
% 1.34/1.57 (~b(s(s(s(z))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[851, 710, 1, 121, 568, 610, 152, 495, 384, 405, 362, 2])).
% 1.34/1.57 tff(853,plain,
% 1.34/1.57 (r(s(s(s(z))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[381, 852])).
% 1.34/1.57 tff(854,plain,
% 1.34/1.57 (~b(s(s(z)), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[720, 612, 405, 362, 568])).
% 1.34/1.57 tff(855,plain,
% 1.34/1.57 (r(s(s(z)), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[442, 854])).
% 1.34/1.57 tff(856,plain,
% 1.34/1.57 (~r(s(s(z)), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[841, 65, 495, 1, 855])).
% 1.34/1.57 tff(857,plain,
% 1.34/1.57 (b(s(s(z)), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[245, 856])).
% 1.34/1.57 tff(858,plain,
% 1.34/1.57 (~r(z, s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[833, 855, 1])).
% 1.34/1.57 tff(859,plain,
% 1.34/1.57 (b(z, s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[524, 858])).
% 1.34/1.57 tff(860,assumption,(z = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.57 tff(861,plain,
% 1.34/1.57 (s(s(s(s(s(elem!1))))) = z),
% 1.34/1.57 inference(symmetry,[status(thm)],[860])).
% 1.34/1.57 tff(862,plain,
% 1.34/1.57 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(863,plain,
% 1.34/1.57 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[862, 33])).
% 1.34/1.57 tff(864,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[863, 861])).
% 1.34/1.57 tff(865,plain,(~(z = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(866,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.34/1.57 tff(867,assumption,(r(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.57 tff(868,assumption,(r(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.57 tff(869,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), 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(z))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(870,plain,
% 1.34/1.57 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(871,plain,
% 1.34/1.57 (((~![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(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(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(z))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[870])).
% 1.34/1.57 tff(872,plain,
% 1.34/1.57 (((~![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(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(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(z))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[871, 869])).
% 1.34/1.57 tff(873,plain,
% 1.34/1.57 ((~![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(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(874,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.34/1.57 tff(875,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[874, 65, 867, 868, 866])).
% 1.34/1.57 tff(876,plain,((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(877,plain,
% 1.34/1.57 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[876, 867, 866])).
% 1.34/1.57 tff(878,assumption,(r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.34/1.57 tff(879,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), 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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(880,plain,
% 1.34/1.57 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(881,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), 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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[880])).
% 1.34/1.57 tff(882,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), 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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[881, 879])).
% 1.34/1.57 tff(883,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(884,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.34/1.57 tff(885,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[884, 65, 867, 866, 878])).
% 1.34/1.57 tff(886,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(887,plain,
% 1.34/1.57 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[886, 867, 866])).
% 1.34/1.57 tff(888,assumption,(~r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.34/1.57 tff(889,assumption,(~b(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.34/1.57 tff(890,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(891,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(892,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.34/1.57 tff(893,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[892, 47, 863, 889, 888])).
% 1.34/1.57 tff(894,plain,(r(s(s(s(s(s(elem!1))))), z) | b(s(s(s(s(s(elem!1))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(895,plain,
% 1.34/1.57 (b(s(s(s(s(s(elem!1))))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[894, 887])).
% 1.34/1.57 tff(896,assumption,(r(s(s(s(s(s(elem!1))))), s(s(z)))), introduced(assumption)).
% 1.34/1.57 tff(897,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), 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(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(898,plain,
% 1.34/1.57 (((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(899,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), 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(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[898])).
% 1.34/1.57 tff(900,plain,
% 1.34/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), 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(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[899, 897])).
% 1.34/1.57 tff(901,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(902,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[901, 900])).
% 1.34/1.57 tff(903,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[902, 65, 867, 273, 896])).
% 1.34/1.57 tff(904,plain,((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(905,plain,
% 1.34/1.57 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[904, 867, 273])).
% 1.34/1.57 tff(906,assumption,(s(s(s(s(s(elem!1))))) = s(s(z))), introduced(assumption)).
% 1.34/1.57 tff(907,plain,
% 1.34/1.57 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[906])).
% 1.34/1.57 tff(908,plain,
% 1.34/1.57 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(909,plain,
% 1.34/1.57 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[908, 11])).
% 1.34/1.57 tff(910,assumption,(s(s(z)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.57 tff(911,plain,
% 1.34/1.57 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[910])).
% 1.34/1.57 tff(912,plain,
% 1.34/1.57 (s(z) = s(s(s(s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[261, 911, 909])).
% 1.34/1.57 tff(913,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[143, 912])).
% 1.34/1.57 tff(914,plain,(~(s(s(z)) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(915,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[914, 907])).
% 1.34/1.57 tff(916,plain,(~(s(s(s(s(s(elem!1))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(917,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(z)))), introduced(assumption)).
% 1.34/1.57 tff(918,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(z)))), introduced(assumption)).
% 1.34/1.57 tff(919,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(920,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(921,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[920, 919])).
% 1.34/1.57 tff(922,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[921, 47, 918, 917, 916])).
% 1.34/1.57 tff(923,plain,(b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(924,plain,
% 1.34/1.57 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[923, 905])).
% 1.34/1.57 tff(925,assumption,(b(s(s(s(s(s(elem!1))))), s(s(z)))), introduced(assumption)).
% 1.34/1.57 tff(926,assumption,(b(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.34/1.57 tff(927,assumption,(b(s(s(z)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.57 tff(928,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(929,plain,
% 1.34/1.57 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(930,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[929])).
% 1.34/1.57 tff(931,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[930, 928])).
% 1.34/1.58 tff(932,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(933,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[932, 931])).
% 1.34/1.58 tff(934,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[933, 162, 538, 537, 927, 926, 925])).
% 1.34/1.58 tff(935,plain,((~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(936,plain,
% 1.34/1.58 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[935, 924, 537, 895, 538])).
% 1.34/1.58 tff(937,assumption,(~b(s(s(z)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.58 tff(938,assumption,(~r(s(s(z)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.58 tff(939,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), 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(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(940,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(941,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.34/1.58 tff(942,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[941, 47, 938, 937, 914])).
% 1.34/1.58 tff(943,plain,(b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(944,plain,
% 1.34/1.58 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[943, 936])).
% 1.34/1.58 tff(945,assumption,(r(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.34/1.58 tff(946,assumption,(r(s(s(z)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.58 tff(947,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), 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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(948,plain,
% 1.34/1.58 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(949,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), 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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[948])).
% 1.34/1.58 tff(950,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), 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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[949, 947])).
% 1.34/1.58 tff(951,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(952,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[951, 950])).
% 1.34/1.58 tff(953,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[952, 65, 946, 945, 2])).
% 1.34/1.58 tff(954,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(955,plain,
% 1.34/1.58 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[954, 944, 2])).
% 1.34/1.58 tff(956,assumption,(s(s(s(s(s(elem!1))))) = s(z)), introduced(assumption)).
% 1.34/1.58 tff(957,plain,
% 1.34/1.58 (s(z) = s(s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[956])).
% 1.34/1.58 tff(958,plain,
% 1.34/1.58 (inj_0(s(z)) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[957])).
% 1.34/1.58 tff(959,plain,
% 1.34/1.58 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 1.34/1.58 inference(symmetry,[status(thm)],[958])).
% 1.34/1.58 tff(960,plain,
% 1.34/1.58 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[909])).
% 1.34/1.58 tff(961,plain,
% 1.34/1.58 (s(s(s(s(elem!1)))) = z),
% 1.34/1.58 inference(transitivity,[status(thm)],[960, 959, 13])).
% 1.34/1.58 tff(962,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[77, 961])).
% 1.34/1.58 tff(963,plain,(~(s(s(s(s(s(elem!1))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(964,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(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(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(965,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(966,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[965, 964])).
% 1.34/1.58 tff(967,plain,
% 1.34/1.58 ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[966, 47])).
% 1.34/1.58 tff(968,plain,
% 1.34/1.58 (b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[967, 963])).
% 1.34/1.58 tff(969,plain,
% 1.34/1.58 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[968, 955])).
% 1.34/1.58 tff(970,assumption,(b(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.34/1.58 tff(971,assumption,(b(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.58 tff(972,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(973,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(974,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[973])).
% 1.34/1.58 tff(975,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[974, 972])).
% 1.34/1.58 tff(976,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(977,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[976, 975])).
% 1.34/1.58 tff(978,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[977, 162, 152, 121, 971, 970, 926])).
% 1.34/1.58 tff(979,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(980,plain,
% 1.34/1.58 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[979, 969, 121, 152, 895])).
% 1.34/1.58 tff(981,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(982,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(983,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[982, 981])).
% 1.34/1.58 tff(984,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[983, 47, 980, 877, 865])).
% 1.34/1.58 tff(985,plain,((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(986,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[985, 859, 152, 2, 121, 857, 853, 622])).
% 1.34/1.58 tff(987,plain,
% 1.34/1.58 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(988,plain,
% 1.34/1.58 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[987])).
% 1.34/1.58 tff(989,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(z)))), introduced(assumption)).
% 1.34/1.58 tff(990,plain,
% 1.34/1.58 (s(s(s(z))) = s(s(s(s(s(elem!1)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[989])).
% 1.34/1.58 tff(991,plain,
% 1.34/1.58 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[990])).
% 1.34/1.58 tff(992,plain,
% 1.34/1.58 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(z))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[991])).
% 1.34/1.58 tff(993,plain,
% 1.34/1.58 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.34/1.58 inference(transitivity,[status(thm)],[960, 992, 312])).
% 1.34/1.58 tff(994,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[37, 993])).
% 1.34/1.58 tff(995,plain,(~(s(s(s(s(s(elem!1))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(996,plain,
% 1.34/1.58 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[995, 988])).
% 1.34/1.58 tff(997,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), 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(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(998,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(999,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[998, 997])).
% 1.34/1.58 tff(1000,plain,
% 1.34/1.58 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[999, 47])).
% 1.34/1.58 tff(1001,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1000, 996])).
% 1.34/1.58 tff(1002,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1001, 986])).
% 1.34/1.58 tff(1003,assumption,(b(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.58 tff(1004,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.58 tff(1005,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[590, 363, 362, 405, 2, 384])).
% 1.34/1.58 tff(1006,plain,
% 1.34/1.58 (b(s(s(s(z))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[595, 1005])).
% 1.34/1.58 tff(1007,plain,
% 1.34/1.58 (~b(s(s(z)), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[453, 445, 405, 362, 363])).
% 1.34/1.58 tff(1008,plain,
% 1.34/1.58 (r(s(s(z)), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[442, 1007])).
% 1.34/1.58 tff(1009,plain,
% 1.34/1.58 (~r(s(z), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[425, 1008, 384])).
% 1.34/1.58 tff(1010,plain,
% 1.34/1.58 (b(s(z), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[493, 1009])).
% 1.34/1.58 tff(1011,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1012,plain,
% 1.34/1.58 (((~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(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(s(elem!1)))), s(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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1013,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[1012])).
% 1.34/1.58 tff(1014,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[1013, 1011])).
% 1.34/1.58 tff(1015,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(1016,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 1.34/1.58 tff(1017,plain,
% 1.34/1.58 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1016, 162, 405, 363, 362, 445, 1010])).
% 1.34/1.58 tff(1018,plain,
% 1.34/1.58 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[149, 1017])).
% 1.34/1.58 tff(1019,plain,
% 1.34/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(1020,plain,
% 1.34/1.58 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1021,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1020])).
% 1.34/1.59 tff(1022,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1021, 1019])).
% 1.34/1.59 tff(1023,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1024,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.34/1.59 tff(1025,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1024, 65, 123, 1004, 945])).
% 1.34/1.59 tff(1026,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1027,plain,
% 1.34/1.59 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1026, 1018, 1004])).
% 1.34/1.59 tff(1028,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[968, 1027])).
% 1.34/1.59 tff(1029,assumption,(b(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.59 tff(1030,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1031,plain,
% 1.34/1.59 (((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1032,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1031])).
% 1.34/1.59 tff(1033,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1032, 1030])).
% 1.34/1.59 tff(1034,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1035,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 1.34/1.59 tff(1036,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1035, 162, 1029, 600, 970, 1003, 599])).
% 1.34/1.59 tff(1037,plain,((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1038,plain,
% 1.34/1.59 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1037, 1028, 1003, 600, 1010])).
% 1.34/1.59 tff(1039,plain,
% 1.34/1.59 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(commutativity,[status(thm)],[])).
% 1.34/1.59 tff(1040,plain,
% 1.34/1.59 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1039])).
% 1.34/1.59 tff(1041,plain,
% 1.34/1.59 (~(s(z) = s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[963, 1040])).
% 1.34/1.59 tff(1042,assumption,(~b(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.59 tff(1043,assumption,(~(s(z) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.59 tff(1044,assumption,(~r(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.59 tff(1045,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), 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(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1046,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1047,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 1.34/1.59 tff(1048,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1047, 47, 1044, 1043, 1042])).
% 1.34/1.59 tff(1049,plain,(b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1)))))) | (s(z) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1050,plain,
% 1.34/1.59 (b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1049, 1041])).
% 1.34/1.59 tff(1051,plain,
% 1.34/1.59 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1050, 1038])).
% 1.34/1.59 tff(1052,plain,
% 1.34/1.59 (((~![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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), 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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1053,plain,
% 1.34/1.59 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1054,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1053])).
% 1.34/1.59 tff(1055,plain,
% 1.34/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1054, 1052])).
% 1.34/1.59 tff(1056,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1057,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 1.34/1.59 tff(1058,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1057, 65, 193, 1018, 1004, 1051])).
% 1.34/1.59 tff(1059,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1060,plain,
% 1.34/1.59 (~b(s(s(s(z))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1059, 1006, 1004, 1003, 193, 363, 362, 384])).
% 1.34/1.59 tff(1061,plain,
% 1.34/1.59 (r(s(s(s(z))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[459, 1060])).
% 1.34/1.59 tff(1062,plain,
% 1.34/1.59 (~r(s(z), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[466, 65, 384, 1061])).
% 1.34/1.59 tff(1063,plain,
% 1.34/1.59 (b(s(z), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[493, 1062])).
% 1.34/1.59 tff(1064,plain,
% 1.34/1.59 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[608, 363, 362, 1006, 1063])).
% 1.34/1.59 tff(1065,plain,
% 1.34/1.59 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[149, 1064])).
% 1.34/1.59 tff(1066,plain,
% 1.34/1.59 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1026, 1065, 1004])).
% 1.34/1.59 tff(1067,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[968, 1066])).
% 1.34/1.59 tff(1068,plain,
% 1.34/1.59 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1037, 1067, 1003, 1006, 1063])).
% 1.34/1.59 tff(1069,plain,
% 1.34/1.59 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1050, 1068])).
% 1.34/1.59 tff(1070,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1057, 65, 193, 1065, 1004, 1069])).
% 1.34/1.59 tff(1071,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1072,plain,
% 1.34/1.59 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1071, 1002, 568, 193, 362, 384, 2])).
% 1.34/1.59 tff(1073,plain,
% 1.34/1.59 (~r(z, s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[811, 787, 1])).
% 1.34/1.59 tff(1074,plain,
% 1.34/1.59 (b(z, s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[823, 1073])).
% 1.34/1.59 tff(1075,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.59 tff(1076,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.34/1.59 tff(1077,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1078,plain,
% 1.34/1.59 (((~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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(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)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1079,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1078])).
% 1.34/1.59 tff(1080,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1079, 1077])).
% 1.34/1.59 tff(1081,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1082,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 1.34/1.59 tff(1083,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1082, 162, 538, 537, 1076, 825, 1075])).
% 1.34/1.59 tff(1084,plain,((~b(s(s(s(s(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))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1085,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1084, 1074, 825, 538, 537])).
% 1.34/1.59 tff(1086,plain,
% 1.34/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1087,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1088,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.34/1.59 tff(1089,plain,
% 1.34/1.59 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1088, 47, 817])).
% 1.34/1.59 tff(1090,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1089, 1085])).
% 1.34/1.59 tff(1091,plain,
% 1.34/1.59 (((~![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(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1092,plain,
% 1.34/1.59 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1093,plain,
% 1.34/1.59 (((~![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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1092])).
% 1.34/1.59 tff(1094,plain,
% 1.34/1.59 (((~![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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[1093, 1091])).
% 1.34/1.59 tff(1095,plain,
% 1.34/1.59 ((~![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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(1096,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 1.34/1.59 tff(1097,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1096, 65, 495, 1, 787, 1090])).
% 1.34/1.59 tff(1098,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(1099,plain,
% 1.34/1.59 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1098, 1, 495, 710, 857, 859])).
% 1.34/1.59 tff(1100,plain,
% 1.34/1.59 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[690, 1099, 679])).
% 1.34/1.59 tff(1101,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(1102,plain,
% 1.34/1.59 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(1103,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[1102])).
% 1.34/1.60 tff(1104,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.60 inference(transitivity,[status(thm)],[1103, 1101])).
% 1.34/1.60 tff(1105,plain,
% 1.34/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(1106,plain,
% 1.34/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 1.34/1.60 tff(1107,plain,
% 1.34/1.60 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1106, 162, 600, 970, 1003, 599, 692])).
% 1.34/1.60 tff(1108,plain,
% 1.34/1.60 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[775, 1107, 642])).
% 1.34/1.60 tff(1109,plain,
% 1.34/1.60 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[782, 65, 123, 1108])).
% 1.34/1.60 tff(1110,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1111,plain,
% 1.43/1.60 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1112,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1111])).
% 1.43/1.60 tff(1113,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1112, 1110])).
% 1.43/1.60 tff(1114,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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)))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1115,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 1.43/1.60 tff(1116,plain,
% 1.43/1.60 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1115, 162, 363, 600, 970, 1003, 692])).
% 1.43/1.60 tff(1117,plain,
% 1.43/1.60 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[763, 47, 1116])).
% 1.43/1.60 tff(1118,plain,
% 1.43/1.60 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1117, 1109])).
% 1.43/1.60 tff(1119,plain,
% 1.43/1.60 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1118])).
% 1.43/1.60 tff(1120,plain,
% 1.43/1.60 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[20, 1119, 630])).
% 1.43/1.60 tff(1121,plain,
% 1.43/1.60 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1120])).
% 1.43/1.60 tff(1122,plain,
% 1.43/1.60 (s(s(elem!1)) = s(s(z))),
% 1.43/1.60 inference(transitivity,[status(thm)],[25, 1121, 312])).
% 1.43/1.60 tff(1123,plain,
% 1.43/1.60 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1122])).
% 1.43/1.60 tff(1124,plain,
% 1.43/1.60 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.43/1.60 inference(symmetry,[status(thm)],[1123])).
% 1.43/1.60 tff(1125,plain,
% 1.43/1.60 (b(s(s(elem!1)), z)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[538, 1124])).
% 1.43/1.60 tff(1126,plain,
% 1.43/1.60 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1122])).
% 1.43/1.60 tff(1127,plain,
% 1.43/1.60 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1126])).
% 1.43/1.60 tff(1128,plain,
% 1.43/1.60 (b(z, s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[537, 1127])).
% 1.43/1.60 tff(1129,plain,
% 1.43/1.60 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1122, 1118])).
% 1.43/1.60 tff(1130,plain,
% 1.43/1.60 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1129])).
% 1.43/1.60 tff(1131,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.43/1.60 tff(1132,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(s(z)), s(z))) | (~r(s(s(z)), s(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(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1133,plain,
% 1.43/1.60 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1134,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(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![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(s(s(s(z)))), s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1133])).
% 1.43/1.60 tff(1135,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(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![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(s(s(s(z)))), s(z))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1134, 1132])).
% 1.43/1.60 tff(1136,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(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1137,plain,
% 1.43/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 1.43/1.60 tff(1138,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1137, 65, 2, 788, 1131])).
% 1.43/1.60 tff(1139,plain,((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1140,plain,
% 1.43/1.60 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1139, 1108, 2])).
% 1.43/1.60 tff(1141,plain,
% 1.43/1.60 (b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[801, 1140, 634])).
% 1.43/1.60 tff(1142,plain,
% 1.43/1.60 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1141, 1130])).
% 1.43/1.60 tff(1143,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1118, 1122])).
% 1.43/1.60 tff(1144,plain,
% 1.43/1.60 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1143])).
% 1.43/1.60 tff(1145,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[825, 1144])).
% 1.43/1.60 tff(1146,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.60 tff(1147,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.60 tff(1148,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.43/1.60 tff(1149,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.43/1.60 tff(1150,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1151,plain,
% 1.43/1.60 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1152,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1151])).
% 1.43/1.60 tff(1153,plain,
% 1.43/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1152, 1150])).
% 1.43/1.60 tff(1154,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1155,plain,
% 1.43/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.43/1.60 tff(1156,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1155, 162, 1149, 1148, 1147, 122, 1146])).
% 1.43/1.60 tff(1157,plain,((~b(s(s(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1158,plain,
% 1.43/1.60 (~b(s(s(s(s(elem!1)))), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1157, 1145, 1142, 1128, 1125])).
% 1.43/1.60 tff(1159,plain,
% 1.43/1.60 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1120])).
% 1.43/1.60 tff(1160,plain,
% 1.43/1.60 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 1.43/1.60 inference(symmetry,[status(thm)],[1159])).
% 1.43/1.60 tff(1161,plain,
% 1.43/1.60 (r(s(s(s(elem!1))), z)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[866, 1160])).
% 1.43/1.60 tff(1162,plain,
% 1.43/1.60 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(commutativity,[status(thm)],[])).
% 1.43/1.60 tff(1163,plain,
% 1.43/1.60 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.60 inference(symmetry,[status(thm)],[1162])).
% 1.43/1.60 tff(1164,plain,
% 1.43/1.60 ((elem!1 = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1118])).
% 1.43/1.60 tff(1165,plain,
% 1.43/1.60 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1164])).
% 1.43/1.60 tff(1166,plain,
% 1.43/1.60 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1122])).
% 1.43/1.60 tff(1167,plain,
% 1.43/1.60 (s(elem!1) = s(z)),
% 1.43/1.60 inference(transitivity,[status(thm)],[325, 1166, 15])).
% 1.43/1.60 tff(1168,plain,
% 1.43/1.60 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1167])).
% 1.43/1.60 tff(1169,plain,
% 1.43/1.60 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.43/1.60 inference(quant_inst,[status(thm)],[])).
% 1.43/1.60 tff(1170,plain,
% 1.43/1.60 (inj_0(s(elem!1)) = elem!1),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1169, 11])).
% 1.43/1.60 tff(1171,plain,
% 1.43/1.60 (elem!1 = inj_0(s(elem!1))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1170])).
% 1.43/1.60 tff(1172,plain,
% 1.43/1.60 (elem!1 = z),
% 1.43/1.60 inference(transitivity,[status(thm)],[1171, 1168, 13])).
% 1.43/1.60 tff(1173,plain,
% 1.43/1.60 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1172])).
% 1.43/1.60 tff(1174,plain,
% 1.43/1.60 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.43/1.60 inference(transitivity,[status(thm)],[1173, 813])).
% 1.43/1.60 tff(1175,plain,
% 1.43/1.60 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1174])).
% 1.43/1.60 tff(1176,plain,
% 1.43/1.60 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.60 inference(transitivity,[status(thm)],[1175, 1165, 1163])).
% 1.43/1.60 tff(1177,plain,
% 1.43/1.60 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1176])).
% 1.43/1.60 tff(1178,plain,
% 1.43/1.60 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[817, 1177])).
% 1.43/1.60 tff(1179,plain,
% 1.43/1.60 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.43/1.60 inference(commutativity,[status(thm)],[])).
% 1.43/1.60 tff(1180,plain,
% 1.43/1.60 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.43/1.60 inference(symmetry,[status(thm)],[1179])).
% 1.43/1.60 tff(1181,plain,
% 1.43/1.60 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1168])).
% 1.43/1.60 tff(1182,plain,
% 1.43/1.60 (z = inj_0(s(z))),
% 1.43/1.60 inference(symmetry,[status(thm)],[13])).
% 1.43/1.60 tff(1183,plain,
% 1.43/1.60 (z = elem!1),
% 1.43/1.60 inference(transitivity,[status(thm)],[1182, 1181, 1170])).
% 1.43/1.60 tff(1184,plain,
% 1.43/1.60 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1183])).
% 1.43/1.60 tff(1185,plain,
% 1.43/1.60 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1184, 1179])).
% 1.43/1.60 tff(1186,plain,
% 1.43/1.60 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.43/1.60 inference(transitivity,[status(thm)],[1185, 1180])).
% 1.43/1.60 tff(1187,plain,
% 1.43/1.60 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1186])).
% 1.43/1.60 tff(1188,plain,
% 1.43/1.60 (~(s(z) = elem!1)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[111, 1187])).
% 1.43/1.60 tff(1189,plain,
% 1.43/1.60 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1122])).
% 1.43/1.60 tff(1190,plain,
% 1.43/1.60 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1189])).
% 1.43/1.60 tff(1191,plain,
% 1.43/1.60 (r(s(z), s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[384, 1190])).
% 1.43/1.60 tff(1192,plain,
% 1.43/1.60 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1122, 1118])).
% 1.43/1.60 tff(1193,plain,
% 1.43/1.60 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1192])).
% 1.43/1.60 tff(1194,plain,
% 1.43/1.60 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1193])).
% 1.43/1.60 tff(1195,plain,
% 1.43/1.60 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[634, 1194])).
% 1.43/1.60 tff(1196,plain,
% 1.43/1.60 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1122])).
% 1.43/1.60 tff(1197,plain,
% 1.43/1.60 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1196])).
% 1.43/1.60 tff(1198,plain,
% 1.43/1.60 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1172])).
% 1.43/1.60 tff(1199,plain,
% 1.43/1.60 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1198])).
% 1.43/1.60 tff(1200,plain,
% 1.43/1.60 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1199, 1197])).
% 1.43/1.60 tff(1201,plain,
% 1.43/1.60 (b(elem!1, s(s(elem!1)))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[537, 1200])).
% 1.43/1.60 tff(1202,plain,
% 1.43/1.60 ((elem!1 = z) <=> (z = elem!1)),
% 1.43/1.60 inference(commutativity,[status(thm)],[])).
% 1.43/1.60 tff(1203,plain,
% 1.43/1.60 ((z = elem!1) <=> (elem!1 = z)),
% 1.43/1.60 inference(symmetry,[status(thm)],[1202])).
% 1.43/1.60 tff(1204,assumption,(z = elem!1), introduced(assumption)).
% 1.43/1.60 tff(1205,plain,
% 1.43/1.60 (elem!1 = z),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 1.43/1.60 tff(1206,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.43/1.60 tff(1207,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1206, 1205])).
% 1.43/1.60 tff(1208,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1209,plain,
% 1.43/1.60 (elem!1 = z),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1208, 1183])).
% 1.43/1.60 tff(1210,plain,
% 1.43/1.60 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 1.43/1.60 inference(commutativity,[status(thm)],[])).
% 1.43/1.60 tff(1211,assumption,(elem!1 = z), introduced(assumption)).
% 1.43/1.60 tff(1212,plain,
% 1.43/1.60 (s(elem!1) = s(z)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.60 tff(1213,plain,
% 1.43/1.60 (s(s(elem!1)) = s(s(z))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1212])).
% 1.43/1.60 tff(1214,plain,
% 1.43/1.60 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1213])).
% 1.43/1.60 tff(1215,plain,
% 1.43/1.60 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1214])).
% 1.43/1.60 tff(1216,plain,
% 1.43/1.60 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1215])).
% 1.43/1.60 tff(1217,plain,
% 1.43/1.60 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.60 tff(1218,plain,
% 1.43/1.60 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1217, 1210])).
% 1.43/1.60 tff(1219,plain,
% 1.43/1.60 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1218])).
% 1.43/1.60 tff(1220,plain,
% 1.43/1.60 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1219])).
% 1.43/1.60 tff(1221,plain,
% 1.43/1.60 (~(s(s(z)) = s(s(s(s(z)))))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[37, 1220])).
% 1.43/1.60 tff(1222,plain,
% 1.43/1.60 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.43/1.60 inference(symmetry,[status(thm)],[636])).
% 1.43/1.60 tff(1223,plain,
% 1.43/1.60 ((s(z) = s(s(s(s(z))))) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.60 tff(1224,plain,
% 1.43/1.60 ((s(z) = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(z)))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1223])).
% 1.43/1.60 tff(1225,plain,
% 1.43/1.60 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1224, 1222])).
% 1.43/1.60 tff(1226,plain,
% 1.43/1.60 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1225])).
% 1.43/1.60 tff(1227,plain,
% 1.43/1.60 (~(s(s(s(s(z)))) = s(z))),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[143, 1226])).
% 1.43/1.60 tff(1228,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1215])).
% 1.43/1.60 tff(1229,assumption,(~b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.43/1.60 tff(1230,plain,
% 1.43/1.60 (r(s(s(s(s(elem!1)))), z)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[95, 1229])).
% 1.43/1.60 tff(1231,plain,
% 1.43/1.60 (r(s(s(s(s(z)))), z)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1230, 1228])).
% 1.43/1.60 tff(1232,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.60 tff(1233,plain,
% 1.43/1.60 (z = elem!1),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1211, 1202])).
% 1.43/1.60 tff(1234,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.43/1.60 tff(1235,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1234, 1233])).
% 1.43/1.60 tff(1236,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1237,plain,
% 1.43/1.60 (z = elem!1),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1236, 1211])).
% 1.43/1.60 tff(1238,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1204])).
% 1.43/1.60 tff(1239,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.43/1.60 inference(symmetry,[status(thm)],[1238])).
% 1.43/1.60 tff(1240,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.43/1.60 tff(1241,plain,
% 1.43/1.60 (b(s(s(s(s(elem!1)))), z)),
% 1.43/1.60 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 1.43/1.60 tff(1242,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1229, 1241])).
% 1.43/1.60 tff(1243,plain,((~(z = elem!1)) | b(s(s(s(s(elem!1)))), z) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1244,plain,
% 1.43/1.60 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1243, 1237, 1229])).
% 1.43/1.60 tff(1245,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.43/1.60 tff(1246,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.60 tff(1247,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.43/1.60 tff(1248,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.43/1.60 tff(1249,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.43/1.60 tff(1250,plain,
% 1.43/1.60 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.43/1.60 inference(symmetry,[status(thm)],[1249])).
% 1.43/1.60 tff(1251,plain,
% 1.43/1.60 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.43/1.60 inference(monotonicity,[status(thm)],[1250])).
% 1.43/1.60 tff(1252,plain,
% 1.43/1.60 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.43/1.60 inference(transitivity,[status(thm)],[25, 1251, 19])).
% 1.43/1.60 tff(1253,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.60 tff(1254,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1253, 1252])).
% 1.43/1.60 tff(1255,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1256,plain,
% 1.43/1.60 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1255, 1249])).
% 1.43/1.60 tff(1257,plain,
% 1.43/1.60 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.43/1.60 inference(transitivity,[status(thm)],[1256, 1250])).
% 1.43/1.60 tff(1258,plain,
% 1.43/1.60 ($false),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1232, 1257])).
% 1.43/1.60 tff(1259,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.60 tff(1260,plain,
% 1.43/1.60 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.43/1.60 inference(unit_resolution,[status(thm)],[1259, 1232])).
% 1.43/1.60 tff(1261,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.43/1.60 tff(1262,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(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.60 tff(1263,plain,
% 1.43/1.60 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.43/1.60 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1264,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)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, 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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1263])).
% 1.43/1.61 tff(1265,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)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, 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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1264, 1262])).
% 1.43/1.61 tff(1266,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)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1267,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)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 1.43/1.61 tff(1268,plain,
% 1.43/1.61 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1267, 65, 1261, 1230])).
% 1.43/1.61 tff(1269,plain,
% 1.43/1.61 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.43/1.61 inference(commutativity,[status(thm)],[])).
% 1.43/1.61 tff(1270,plain,
% 1.43/1.61 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1214])).
% 1.43/1.61 tff(1271,plain,
% 1.43/1.61 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1270])).
% 1.43/1.61 tff(1272,plain,
% 1.43/1.61 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1271, 1269])).
% 1.43/1.61 tff(1273,plain,
% 1.43/1.61 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1272])).
% 1.43/1.61 tff(1274,plain,
% 1.43/1.61 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1273])).
% 1.43/1.61 tff(1275,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.61 tff(1276,plain,
% 1.43/1.61 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 1.43/1.61 tff(1277,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)],[1270])).
% 1.43/1.61 tff(1278,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)],[1277])).
% 1.43/1.61 tff(1279,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)],[1278])).
% 1.43/1.61 tff(1280,assumption,(~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.61 tff(1281,plain,
% 1.43/1.61 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.43/1.61 tff(1282,assumption,(~b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.61 tff(1283,plain,
% 1.43/1.61 ((s(s(s(z))) = s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[336, 47, 1282])).
% 1.43/1.61 tff(1284,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1283, 1281, 1276])).
% 1.43/1.61 tff(1285,plain,(b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1286,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1285, 1211, 1268, 1260])).
% 1.43/1.61 tff(1287,plain,
% 1.43/1.61 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.61 tff(1288,plain,
% 1.43/1.61 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.43/1.61 inference(symmetry,[status(thm)],[1287])).
% 1.43/1.61 tff(1289,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1214])).
% 1.43/1.61 tff(1290,plain,
% 1.43/1.61 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), elem!1)),
% 1.43/1.61 inference(transitivity,[status(thm)],[1289, 1288])).
% 1.43/1.61 tff(1291,plain,
% 1.43/1.61 (r(s(s(s(z))), elem!1)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1261, 1290])).
% 1.43/1.61 tff(1292,plain,
% 1.43/1.61 (r(s(s(s(z))), z)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1261, 1289])).
% 1.43/1.61 tff(1293,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1214])).
% 1.43/1.61 tff(1294,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)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(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(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1295,plain,
% 1.43/1.61 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1296,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(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(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(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1295])).
% 1.43/1.61 tff(1297,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(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(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(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1296, 1294])).
% 1.43/1.61 tff(1298,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(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1299,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)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 1.43/1.61 tff(1300,plain,
% 1.43/1.61 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1299, 65, 1261, 1230])).
% 1.43/1.61 tff(1301,plain,
% 1.43/1.61 (((~![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)))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1302,plain,
% 1.43/1.61 ((~![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)))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1303,plain,
% 1.43/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.43/1.61 tff(1304,plain,
% 1.43/1.61 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1303, 47])).
% 1.43/1.61 tff(1305,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1304, 1300, 1260])).
% 1.43/1.61 tff(1306,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1305, 1293])).
% 1.43/1.61 tff(1307,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.43/1.61 tff(1308,plain,
% 1.43/1.61 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1213])).
% 1.43/1.61 tff(1309,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1308])).
% 1.43/1.61 tff(1310,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.61 tff(1311,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1310, 1309])).
% 1.43/1.61 tff(1312,plain,
% 1.43/1.61 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1311])).
% 1.43/1.61 tff(1313,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.43/1.61 tff(1314,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 1.43/1.61 tff(1315,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1314, 1213])).
% 1.43/1.61 tff(1316,plain,((~(elem!1 = z)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1317,plain,
% 1.43/1.61 (s(s(elem!1)) = s(s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1316, 1211])).
% 1.43/1.61 tff(1318,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.43/1.61 tff(1319,plain,
% 1.43/1.61 (s(s(z)) = s(s(elem!1))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1318])).
% 1.43/1.61 tff(1320,plain,
% 1.43/1.61 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1319])).
% 1.43/1.61 tff(1321,plain,
% 1.43/1.61 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1320])).
% 1.43/1.61 tff(1322,plain,
% 1.43/1.61 (r(s(z), s(s(z)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1246, 1321])).
% 1.43/1.61 tff(1323,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.43/1.61 tff(1324,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1323, 1322])).
% 1.43/1.61 tff(1325,plain,((~(s(s(elem!1)) = s(s(z)))) | r(s(z), s(s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1326,plain,
% 1.43/1.61 (r(s(z), s(s(z)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1325, 1317, 1246])).
% 1.43/1.61 tff(1327,plain,
% 1.43/1.61 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1213])).
% 1.43/1.61 tff(1328,plain,
% 1.43/1.61 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.61 tff(1329,plain,
% 1.43/1.61 (b(z, s(s(elem!1)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1248, 1328])).
% 1.43/1.61 tff(1330,plain,
% 1.43/1.61 (b(z, s(s(z)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1329, 1327])).
% 1.43/1.61 tff(1331,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.61 tff(1332,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1331])).
% 1.43/1.61 tff(1333,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[362, 1332])).
% 1.43/1.61 tff(1334,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.43/1.61 tff(1335,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1334, 1333])).
% 1.43/1.61 tff(1336,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(z))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1337,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1336, 362, 1211])).
% 1.43/1.61 tff(1338,plain,
% 1.43/1.61 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.61 tff(1339,plain,
% 1.43/1.61 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1338])).
% 1.43/1.61 tff(1340,plain,
% 1.43/1.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[363, 1339])).
% 1.43/1.61 tff(1341,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.43/1.61 tff(1342,plain,
% 1.43/1.61 (~r(s(s(s(z))), s(s(z)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[576, 385, 1326])).
% 1.43/1.61 tff(1343,plain,
% 1.43/1.61 (b(s(s(s(z))), s(s(z)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[459, 1342])).
% 1.43/1.61 tff(1344,plain,
% 1.43/1.61 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.61 tff(1345,plain,
% 1.43/1.61 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.61 inference(symmetry,[status(thm)],[1344])).
% 1.43/1.61 tff(1346,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(z))), s(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))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1347,plain,
% 1.43/1.61 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), 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)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1348,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(z))), z)) | (~r(s(s(z)), 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)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1347])).
% 1.43/1.61 tff(1349,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(z))), z)) | (~r(s(s(z)), 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)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1348, 1346])).
% 1.43/1.61 tff(1350,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(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1351,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 1.43/1.61 tff(1352,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1351, 65, 230, 385, 417, 866])).
% 1.43/1.61 tff(1353,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1354,plain,
% 1.43/1.61 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1353, 230, 866, 385])).
% 1.43/1.61 tff(1355,plain,
% 1.43/1.61 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[442, 1354])).
% 1.43/1.61 tff(1356,plain,
% 1.43/1.61 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[453, 1355, 362, 363, 445])).
% 1.43/1.61 tff(1357,plain,
% 1.43/1.61 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[52, 1356])).
% 1.43/1.61 tff(1358,plain,
% 1.43/1.61 (r(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1357, 1345])).
% 1.43/1.61 tff(1359,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(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1360,plain,
% 1.43/1.61 (((~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)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1361,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(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)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1360])).
% 1.43/1.61 tff(1362,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(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)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1361, 1359])).
% 1.43/1.61 tff(1363,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(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1364,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 1.43/1.61 tff(1365,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1364, 65, 230, 1358, 1341])).
% 1.43/1.61 tff(1366,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~(elem!1 = 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(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1367,plain,
% 1.43/1.61 (~r(s(s(z)), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1366, 1343, 1211, 362, 363, 1341, 866, 385])).
% 1.43/1.61 tff(1368,plain,
% 1.43/1.61 (b(s(s(z)), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[245, 1367])).
% 1.43/1.61 tff(1369,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.43/1.61 tff(1370,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(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1371,plain,
% 1.43/1.61 (((~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))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1372,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(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))), s(z))) | (~r(s(s(s(z))), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1371])).
% 1.43/1.61 tff(1373,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(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))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.43/1.61 tff(1374,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(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1375,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.43/1.61 tff(1376,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1375, 65, 97, 385, 866])).
% 1.43/1.61 tff(1377,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1378,plain,
% 1.43/1.61 (~r(z, s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1377, 385, 866])).
% 1.43/1.61 tff(1379,plain,
% 1.43/1.61 (b(z, s(z))),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[117, 1378])).
% 1.43/1.61 tff(1380,plain,
% 1.43/1.61 (z = elem!1),
% 1.43/1.61 inference(symmetry,[status(thm)],[1211])).
% 1.43/1.61 tff(1381,plain,
% 1.43/1.61 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1380])).
% 1.43/1.61 tff(1382,plain,
% 1.43/1.61 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.43/1.61 inference(symmetry,[status(thm)],[1381])).
% 1.43/1.61 tff(1383,plain,
% 1.43/1.61 (r(s(s(s(z))), z)),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1313, 1382])).
% 1.43/1.61 tff(1384,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(z), z)) | (~r(s(s(s(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(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1385,plain,
% 1.43/1.61 (((~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))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.43/1.61 inference(rewrite,[status(thm)],[])).
% 1.43/1.61 tff(1386,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(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))), s(z))) | (~r(s(s(s(z))), z))))),
% 1.43/1.61 inference(monotonicity,[status(thm)],[1385])).
% 1.43/1.61 tff(1387,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(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))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.43/1.61 inference(transitivity,[status(thm)],[1386, 1384])).
% 1.43/1.61 tff(1388,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(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.43/1.61 inference(quant_inst,[status(thm)],[])).
% 1.43/1.61 tff(1389,plain,
% 1.43/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.43/1.61 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.43/1.61 tff(1390,plain,
% 1.43/1.61 (~r(s(s(s(z))), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1389, 65, 194, 385])).
% 1.43/1.61 tff(1391,plain,
% 1.43/1.61 ($false),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1390, 1383])).
% 1.43/1.61 tff(1392,plain,((~r(s(s(s(z))), elem!1)) | (~(elem!1 = z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.61 tff(1393,plain,
% 1.43/1.61 (~r(s(z), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[1392, 385, 1313, 1211])).
% 1.43/1.61 tff(1394,plain,
% 1.43/1.61 (b(s(z), z)),
% 1.43/1.61 inference(unit_resolution,[status(thm)],[175, 1393])).
% 1.43/1.61 tff(1395,plain,
% 1.43/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1396,plain,
% 1.43/1.62 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1397,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1396])).
% 1.43/1.62 tff(1398,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1397, 1395])).
% 1.43/1.62 tff(1399,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1400,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 1.43/1.62 tff(1401,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1400, 162, 152, 121, 538, 537, 383])).
% 1.43/1.62 tff(1402,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1403,plain,
% 1.43/1.62 (~b(s(s(z)), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1402, 1394, 538, 1379, 537])).
% 1.43/1.62 tff(1404,plain,
% 1.43/1.62 (r(s(s(z)), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[271, 1403])).
% 1.43/1.62 tff(1405,plain,
% 1.43/1.62 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[586, 1404, 385])).
% 1.43/1.62 tff(1406,plain,
% 1.43/1.62 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[442, 1405])).
% 1.43/1.62 tff(1407,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1408,plain,
% 1.43/1.62 (((~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(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(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))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1409,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1408])).
% 1.43/1.62 tff(1410,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1409, 1407])).
% 1.43/1.62 tff(1411,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1412,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.43/1.62 tff(1413,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1412, 162, 1406, 578, 693, 692, 1369])).
% 1.43/1.62 tff(1414,plain,((~r(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))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~(elem!1 = z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1415,plain,
% 1.43/1.62 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1414, 1368, 1340, 1337, 385, 1330, 1326, 1313, 1211, 866])).
% 1.43/1.62 tff(1416,plain,
% 1.43/1.62 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1415, 1312])).
% 1.43/1.62 tff(1417,plain,
% 1.43/1.62 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.62 tff(1418,plain,
% 1.43/1.62 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[1417])).
% 1.43/1.62 tff(1419,plain,
% 1.43/1.62 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[534, 97, 495])).
% 1.43/1.62 tff(1420,plain,
% 1.43/1.62 (b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[191, 1419])).
% 1.43/1.62 tff(1421,plain,
% 1.43/1.62 (b(s(z), s(s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1420, 1418])).
% 1.43/1.62 tff(1422,plain,
% 1.43/1.62 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.62 tff(1423,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.43/1.62 inference(symmetry,[status(thm)],[1422])).
% 1.43/1.62 tff(1424,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(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1425,plain,
% 1.43/1.62 (((~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(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1426,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(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(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1425])).
% 1.43/1.62 tff(1427,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(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(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1426, 1424])).
% 1.43/1.62 tff(1428,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(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)))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1429,plain,
% 1.43/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 1.43/1.62 tff(1430,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1429, 65, 97, 123, 495])).
% 1.43/1.62 tff(1431,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1432,plain,
% 1.43/1.62 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1431, 97, 495])).
% 1.43/1.62 tff(1433,plain,
% 1.43/1.62 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[149, 1432])).
% 1.43/1.62 tff(1434,plain,
% 1.43/1.62 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1433, 1423])).
% 1.43/1.62 tff(1435,plain,
% 1.43/1.62 (~r(s(s(s(z))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1377, 97, 866])).
% 1.43/1.62 tff(1436,plain,
% 1.43/1.62 (b(s(s(s(z))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[595, 1435])).
% 1.43/1.62 tff(1437,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.43/1.62 tff(1438,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1439,plain,
% 1.43/1.62 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1440,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1439])).
% 1.43/1.62 tff(1441,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1440, 1438])).
% 1.43/1.62 tff(1442,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(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))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1443,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.43/1.62 tff(1444,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1443, 162, 600, 694, 1437, 693, 692])).
% 1.43/1.62 tff(1445,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1446,plain,
% 1.43/1.62 (~b(s(s(s(s(z)))), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1445, 1436, 694, 693, 692])).
% 1.43/1.62 tff(1447,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1446, 1434])).
% 1.43/1.62 tff(1448,plain,((~r(z, s(z))) | (~(elem!1 = z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1449,plain,
% 1.43/1.62 (~b(s(z), s(s(s(s(z)))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1448, 97, 1211, 693, 692, 866, 495])).
% 1.43/1.62 tff(1450,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1449, 1421])).
% 1.43/1.62 tff(1451,plain,((~r(z, s(z))) | (~(elem!1 = z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1452,plain,
% 1.43/1.62 (~r(z, s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1451, 1211, 1337, 1340, 866, 495])).
% 1.43/1.62 tff(1453,plain,
% 1.43/1.62 (b(z, s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[117, 1452])).
% 1.43/1.62 tff(1454,plain,
% 1.43/1.62 (~b(s(s(z)), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1402, 1368, 1453, 1394, 1330])).
% 1.43/1.62 tff(1455,plain,
% 1.43/1.62 (r(s(s(z)), s(z))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[271, 1454])).
% 1.43/1.62 tff(1456,plain,
% 1.43/1.62 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[586, 1455, 385])).
% 1.43/1.62 tff(1457,plain,
% 1.43/1.62 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[442, 1456])).
% 1.43/1.62 tff(1458,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1459,plain,
% 1.43/1.62 (((~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(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.62 inference(rewrite,[status(thm)],[])).
% 1.43/1.62 tff(1460,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1459])).
% 1.43/1.62 tff(1461,plain,
% 1.43/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1460, 1458])).
% 1.43/1.62 tff(1462,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.43/1.62 inference(quant_inst,[status(thm)],[])).
% 1.43/1.62 tff(1463,plain,
% 1.43/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 1.43/1.62 tff(1464,plain,
% 1.43/1.62 ($false),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1463, 162, 538, 537, 444, 445, 297])).
% 1.43/1.62 tff(1465,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.62 tff(1466,plain,
% 1.43/1.62 (~b(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[1465, 1368, 1330, 1457, 1343])).
% 1.43/1.62 tff(1467,plain,
% 1.43/1.62 (r(z, s(s(s(z))))),
% 1.43/1.62 inference(unit_resolution,[status(thm)],[293, 47, 1466, 288])).
% 1.43/1.62 tff(1468,plain,
% 1.43/1.62 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.43/1.62 inference(commutativity,[status(thm)],[])).
% 1.43/1.62 tff(1469,plain,
% 1.43/1.62 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.62 tff(1470,plain,
% 1.43/1.62 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.43/1.62 inference(transitivity,[status(thm)],[1469, 1468])).
% 1.43/1.62 tff(1471,plain,
% 1.43/1.62 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[1470])).
% 1.43/1.62 tff(1472,plain,
% 1.43/1.62 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1471])).
% 1.43/1.62 tff(1473,plain,
% 1.43/1.62 (~(elem!1 = s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[141, 1472])).
% 1.43/1.62 tff(1474,plain,
% 1.43/1.62 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.62 tff(1475,plain,
% 1.43/1.62 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.43/1.62 inference(symmetry,[status(thm)],[1474])).
% 1.43/1.62 tff(1476,plain,
% 1.43/1.62 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1270])).
% 1.43/1.62 tff(1477,plain,
% 1.43/1.62 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.43/1.62 inference(transitivity,[status(thm)],[1476, 1475])).
% 1.43/1.62 tff(1478,plain,
% 1.43/1.62 ((~b(z, s(s(s(z))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.43/1.62 inference(monotonicity,[status(thm)],[1477])).
% 1.43/1.62 tff(1479,plain,
% 1.43/1.62 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.62 inference(modus_ponens,[status(thm)],[1466, 1478])).
% 1.43/1.63 tff(1480,plain,
% 1.43/1.63 (((~![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)))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1481,plain,
% 1.43/1.63 ((~![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)))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1482,plain,
% 1.43/1.63 ((~![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))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 1.43/1.63 tff(1483,plain,
% 1.43/1.63 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1482, 47])).
% 1.43/1.63 tff(1484,plain,
% 1.43/1.63 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1483, 1479, 1473])).
% 1.43/1.63 tff(1485,plain,
% 1.43/1.63 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.63 tff(1486,plain,
% 1.43/1.63 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1219, 624])).
% 1.43/1.63 tff(1487,plain,
% 1.43/1.63 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1486])).
% 1.43/1.63 tff(1488,plain,
% 1.43/1.63 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[37, 1487])).
% 1.43/1.63 tff(1489,assumption,(~b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.63 tff(1490,plain,
% 1.43/1.63 (((~![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))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1491,plain,
% 1.43/1.63 ((~![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))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1492,plain,
% 1.43/1.63 ((~![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)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.43/1.63 tff(1493,plain,
% 1.43/1.63 ((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)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1492, 47])).
% 1.43/1.63 tff(1494,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)],[1493, 1489, 1232])).
% 1.43/1.63 tff(1495,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.63 tff(1496,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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1497,plain,
% 1.43/1.63 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1498,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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1497])).
% 1.43/1.63 tff(1499,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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1498, 1496])).
% 1.43/1.63 tff(1500,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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1501,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.43/1.63 tff(1502,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1501, 65, 1246, 193, 1495])).
% 1.43/1.63 tff(1503,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1504,plain,
% 1.43/1.63 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1503, 1494, 1246])).
% 1.43/1.63 tff(1505,plain,
% 1.43/1.63 (b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[191, 1504])).
% 1.43/1.63 tff(1506,plain,
% 1.43/1.63 (b(s(z), s(s(s(s(z)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1505, 1418])).
% 1.43/1.63 tff(1507,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.63 tff(1508,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.63 tff(1509,plain,
% 1.43/1.63 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1508])).
% 1.43/1.63 tff(1510,plain,
% 1.43/1.63 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1509])).
% 1.43/1.63 tff(1511,plain,
% 1.43/1.63 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1508])).
% 1.43/1.63 tff(1512,plain,
% 1.43/1.63 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1511])).
% 1.43/1.63 tff(1513,plain,
% 1.43/1.63 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1508])).
% 1.43/1.63 tff(1514,plain,
% 1.43/1.63 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1513, 960, 1512, 19])).
% 1.43/1.63 tff(1515,plain,
% 1.43/1.63 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1514, 1510])).
% 1.43/1.63 tff(1516,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1275, 1515])).
% 1.43/1.63 tff(1517,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1518,plain,
% 1.43/1.63 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1517, 1260])).
% 1.43/1.63 tff(1519,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.43/1.63 tff(1520,plain,
% 1.43/1.63 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1519])).
% 1.43/1.63 tff(1521,plain,
% 1.43/1.63 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1520])).
% 1.43/1.63 tff(1522,plain,
% 1.43/1.63 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[25, 1521, 909])).
% 1.43/1.63 tff(1523,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1232, 1522])).
% 1.43/1.63 tff(1524,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1525,plain,
% 1.43/1.63 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1524, 1232])).
% 1.43/1.63 tff(1526,plain,
% 1.43/1.63 (((~![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))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1527,plain,
% 1.43/1.63 ((~![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))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1528,plain,
% 1.43/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 1.43/1.63 tff(1529,plain,
% 1.43/1.63 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1528, 47])).
% 1.43/1.63 tff(1530,plain,
% 1.43/1.63 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1529, 1245, 1307])).
% 1.43/1.63 tff(1531,plain,
% 1.43/1.63 ((~(s(s(s(s(elem!1)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1162])).
% 1.43/1.63 tff(1532,plain,
% 1.43/1.63 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1245, 1531])).
% 1.43/1.63 tff(1533,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.63 tff(1534,plain,
% 1.43/1.63 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1533])).
% 1.43/1.63 tff(1535,plain,
% 1.43/1.63 (s(elem!1) = s(s(s(elem!1)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[325, 1534, 19])).
% 1.43/1.63 tff(1536,plain,
% 1.43/1.63 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1535])).
% 1.43/1.63 tff(1537,plain,
% 1.43/1.63 (elem!1 = s(s(s(s(elem!1))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1171, 1536, 24, 1533])).
% 1.43/1.63 tff(1538,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.63 tff(1539,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1538, 1537])).
% 1.43/1.63 tff(1540,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1541,plain,
% 1.43/1.63 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1540, 1532])).
% 1.43/1.63 tff(1542,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)],[1493, 1541, 1489])).
% 1.43/1.63 tff(1543,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.43/1.63 tff(1544,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.43/1.63 tff(1545,plain,
% 1.43/1.63 (s(elem!1) = s(s(s(elem!1)))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1544])).
% 1.43/1.63 tff(1546,plain,
% 1.43/1.63 (s(s(s(elem!1))) = s(elem!1)),
% 1.43/1.63 inference(symmetry,[status(thm)],[1545])).
% 1.43/1.63 tff(1547,plain,
% 1.43/1.63 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1546])).
% 1.43/1.63 tff(1548,plain,
% 1.43/1.63 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1547])).
% 1.43/1.63 tff(1549,plain,
% 1.43/1.63 (s(s(elem!1)) = elem!1),
% 1.43/1.63 inference(symmetry,[status(thm)],[1544])).
% 1.43/1.63 tff(1550,plain,
% 1.43/1.63 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1549])).
% 1.43/1.63 tff(1551,plain,
% 1.43/1.63 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1550])).
% 1.43/1.63 tff(1552,plain,
% 1.43/1.63 ((~(elem!1 = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1551])).
% 1.43/1.63 tff(1553,plain,
% 1.43/1.63 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1538, 1552])).
% 1.43/1.63 tff(1554,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1553, 1548])).
% 1.43/1.63 tff(1555,plain,((~(elem!1 = s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1556,plain,
% 1.43/1.63 (~(elem!1 = s(s(elem!1)))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1555, 1532])).
% 1.43/1.63 tff(1557,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.43/1.63 tff(1558,plain,
% 1.43/1.63 (elem!1 = s(s(elem!1))),
% 1.43/1.63 inference(symmetry,[status(thm)],[1557])).
% 1.43/1.63 tff(1559,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.43/1.63 tff(1560,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1559, 1558])).
% 1.43/1.63 tff(1561,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1562,plain,
% 1.43/1.63 (~(s(s(elem!1)) = elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1561, 1556])).
% 1.43/1.63 tff(1563,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.43/1.63 tff(1564,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.43/1.63 tff(1565,plain,
% 1.43/1.63 (((~![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))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1566,plain,
% 1.43/1.63 ((~![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))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1567,plain,
% 1.43/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 1.43/1.63 tff(1568,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1567, 47, 1543, 1564, 1563])).
% 1.43/1.63 tff(1569,plain,(r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1570,plain,
% 1.43/1.63 (r(s(s(elem!1)), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1569, 1562, 1543])).
% 1.43/1.63 tff(1571,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.43/1.63 tff(1572,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.43/1.63 tff(1573,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)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1574,plain,
% 1.43/1.63 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1575,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)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1574])).
% 1.43/1.63 tff(1576,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)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1575, 1573])).
% 1.43/1.63 tff(1577,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)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1578,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 1.43/1.63 tff(1579,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1578, 65, 1495, 1572, 1571])).
% 1.43/1.63 tff(1580,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1581,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1580, 1570, 1542, 1530])).
% 1.43/1.63 tff(1582,plain,((s(s(s(s(elem!1)))) = elem!1) | b(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1583,plain,
% 1.43/1.63 (b(s(s(elem!1)), elem!1)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1582, 1489, 1245, 1307])).
% 1.43/1.63 tff(1584,plain,
% 1.43/1.63 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(commutativity,[status(thm)],[])).
% 1.43/1.63 tff(1585,plain,
% 1.43/1.63 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1380])).
% 1.43/1.63 tff(1586,plain,
% 1.43/1.63 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1585, 1584])).
% 1.43/1.63 tff(1587,plain,
% 1.43/1.63 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1586])).
% 1.43/1.63 tff(1588,plain,
% 1.43/1.63 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[863, 1587])).
% 1.43/1.63 tff(1589,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(z), s(s(z)))) | (~r(s(s(s(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1590,plain,
% 1.43/1.63 (((~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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1591,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(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1590])).
% 1.43/1.63 tff(1592,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(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1591, 1589])).
% 1.43/1.63 tff(1593,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(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))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1594,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.43/1.63 tff(1595,plain,
% 1.43/1.63 (~r(s(s(s(s(z)))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1594, 65, 384, 644])).
% 1.43/1.63 tff(1596,plain,
% 1.43/1.63 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[775, 1595, 1227])).
% 1.43/1.63 tff(1597,plain,
% 1.43/1.63 (~b(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1445, 1596, 694, 693, 692])).
% 1.43/1.63 tff(1598,plain,
% 1.43/1.63 (r(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[595, 1597])).
% 1.43/1.63 tff(1599,plain,
% 1.43/1.63 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1213])).
% 1.43/1.63 tff(1600,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.43/1.63 tff(1601,plain,
% 1.43/1.63 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.63 tff(1602,plain,
% 1.43/1.63 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.43/1.63 inference(symmetry,[status(thm)],[1601])).
% 1.43/1.63 tff(1603,plain,
% 1.43/1.63 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1602])).
% 1.43/1.63 tff(1604,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.43/1.63 tff(1605,plain,
% 1.43/1.63 (~b(s(s(elem!1)), elem!1)),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.43/1.63 tff(1606,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1600, 1605])).
% 1.43/1.63 tff(1607,plain,((~(elem!1 = z)) | (~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1608,plain,
% 1.43/1.63 (b(s(s(elem!1)), z)),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1607, 1600, 1211])).
% 1.43/1.63 tff(1609,plain,
% 1.43/1.63 (b(s(s(z)), z)),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1608, 1599])).
% 1.43/1.63 tff(1610,plain,
% 1.43/1.63 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.63 tff(1611,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.43/1.63 tff(1612,plain,
% 1.43/1.63 (s(z) = elem!1),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1611, 1180])).
% 1.43/1.63 tff(1613,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1247, 1612])).
% 1.43/1.63 tff(1614,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1615,plain,
% 1.43/1.63 (~(elem!1 = s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1614, 1247])).
% 1.43/1.63 tff(1616,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.43/1.63 tff(1617,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(z))) | (~r(s(s(s(z))), s(z))) | (~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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1618,plain,
% 1.43/1.63 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1619,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(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1618])).
% 1.43/1.63 tff(1620,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(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1619, 1617])).
% 1.43/1.63 tff(1621,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(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1622,plain,
% 1.43/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 1.43/1.63 tff(1623,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1622, 65, 1616, 1313, 385])).
% 1.43/1.63 tff(1624,plain,((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1625,plain,
% 1.43/1.63 (~r(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1624, 1616, 1313])).
% 1.43/1.63 tff(1626,plain,
% 1.43/1.63 (b(s(s(s(z))), s(z))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[595, 1625])).
% 1.43/1.63 tff(1627,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1628,plain,
% 1.43/1.63 (((~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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.63 inference(rewrite,[status(thm)],[])).
% 1.43/1.63 tff(1629,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1628])).
% 1.43/1.63 tff(1630,plain,
% 1.43/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.63 inference(transitivity,[status(thm)],[1629, 1627])).
% 1.43/1.63 tff(1631,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(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))))),
% 1.43/1.63 inference(quant_inst,[status(thm)],[])).
% 1.43/1.63 tff(1632,plain,
% 1.43/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 1.43/1.63 tff(1633,plain,
% 1.43/1.63 ($false),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1632, 162, 600, 599, 1437, 693, 692])).
% 1.43/1.63 tff(1634,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.63 tff(1635,plain,
% 1.43/1.63 (~b(s(z), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[1634, 1626, 693, 692, 1437])).
% 1.43/1.63 tff(1636,plain,
% 1.43/1.63 (r(s(z), s(s(s(z))))),
% 1.43/1.63 inference(unit_resolution,[status(thm)],[493, 1635])).
% 1.43/1.63 tff(1637,plain,
% 1.43/1.63 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.43/1.63 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.63 tff(1638,plain,
% 1.43/1.63 (r(z, s(z))),
% 1.43/1.63 inference(modus_ponens,[status(thm)],[1616, 1637])).
% 1.43/1.64 tff(1639,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(z), s(s(s(z))))) | (~r(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(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1640,plain,
% 1.43/1.64 (((~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(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1641,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(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(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1640])).
% 1.43/1.64 tff(1642,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(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(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1641, 1639])).
% 1.43/1.64 tff(1643,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(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1644,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 1.43/1.64 tff(1645,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1644, 65, 1638, 1, 1636])).
% 1.43/1.64 tff(1646,plain,((~r(elem!1, s(z))) | (~r(z, s(s(s(z))))) | (~(elem!1 = 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))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1647,plain,
% 1.43/1.64 (~r(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1646, 1596, 1211, 693, 692, 1, 1313])).
% 1.43/1.64 tff(1648,plain,
% 1.43/1.64 (((~![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)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1649,plain,
% 1.43/1.64 ((~![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)))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1650,plain,
% 1.43/1.64 ((~![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))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 1.43/1.64 tff(1651,plain,
% 1.43/1.64 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1650, 47])).
% 1.43/1.64 tff(1652,plain,
% 1.43/1.64 (b(elem!1, s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1651, 1647, 1615])).
% 1.43/1.64 tff(1653,plain,
% 1.43/1.64 (b(z, s(z))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1652, 1610])).
% 1.43/1.64 tff(1654,plain,
% 1.43/1.64 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.64 tff(1655,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.43/1.64 tff(1656,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(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~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(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1657,plain,
% 1.43/1.64 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1658,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(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~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), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1657])).
% 1.43/1.64 tff(1659,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(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~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), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1658, 1656])).
% 1.43/1.64 tff(1660,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(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1661,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 1.43/1.64 tff(1662,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1661, 65, 1655, 1313, 385])).
% 1.43/1.64 tff(1663,plain,((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1664,plain,
% 1.43/1.64 (~r(s(s(s(z))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1663, 1655, 1313])).
% 1.43/1.64 tff(1665,plain,
% 1.43/1.64 (b(s(s(s(z))), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[595, 1664])).
% 1.43/1.64 tff(1666,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(z), s(s(s(z))))) | (~r(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(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1667,plain,
% 1.43/1.64 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1668,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(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), 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(z), elem!1)) | (~r(s(s(s(z))), elem!1))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1667])).
% 1.43/1.64 tff(1669,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(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), 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(z), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1668, 1666])).
% 1.43/1.64 tff(1670,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(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1671,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 1.43/1.64 tff(1672,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1671, 65, 1655, 1313, 395])).
% 1.43/1.64 tff(1673,plain,((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1674,plain,
% 1.43/1.64 (~r(s(z), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1673, 1655, 1313])).
% 1.43/1.64 tff(1675,plain,
% 1.43/1.64 (b(s(z), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[493, 1674])).
% 1.43/1.64 tff(1676,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1634, 1675, 1665, 693, 692, 1437])).
% 1.43/1.64 tff(1677,plain,((~r(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(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1678,plain,
% 1.43/1.64 (~r(s(z), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1677, 1596, 692, 693, 1313])).
% 1.43/1.64 tff(1679,plain,
% 1.43/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1680,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1681,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 1.43/1.64 tff(1682,plain,
% 1.43/1.64 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1681, 47])).
% 1.43/1.64 tff(1683,plain,
% 1.43/1.64 (b(s(z), elem!1)),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1682, 1678, 1247])).
% 1.43/1.64 tff(1684,plain,
% 1.43/1.64 (b(s(z), z)),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1683, 1654])).
% 1.43/1.64 tff(1685,plain,
% 1.43/1.64 (~b(s(s(z)), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1402, 1684, 1653, 1609, 1330])).
% 1.43/1.64 tff(1686,plain,
% 1.43/1.64 (r(s(s(z)), s(z))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[271, 1685])).
% 1.43/1.64 tff(1687,plain,
% 1.43/1.64 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[586, 1686, 1598])).
% 1.43/1.64 tff(1688,plain,
% 1.43/1.64 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[442, 1687])).
% 1.43/1.64 tff(1689,plain,
% 1.43/1.64 (~r(s(s(s(z))), s(s(z)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[576, 1598, 384])).
% 1.43/1.64 tff(1690,plain,
% 1.43/1.64 (b(s(s(s(z))), s(s(z)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[459, 1689])).
% 1.43/1.64 tff(1691,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.64 tff(1692,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.64 tff(1693,plain,
% 1.43/1.64 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1215])).
% 1.43/1.64 tff(1694,assumption,(s(s(s(s(s(elem!1))))) = s(s(elem!1))), introduced(assumption)).
% 1.43/1.64 tff(1695,plain,
% 1.43/1.64 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1694])).
% 1.43/1.64 tff(1696,plain,
% 1.43/1.64 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1695])).
% 1.43/1.64 tff(1697,plain,
% 1.43/1.64 (s(z) = s(elem!1)),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1204])).
% 1.43/1.64 tff(1698,plain,
% 1.43/1.64 (s(z) = s(s(s(s(elem!1))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1697, 325, 1696, 909])).
% 1.43/1.64 tff(1699,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[143, 1698])).
% 1.43/1.64 tff(1700,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1701,plain,
% 1.43/1.64 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1700, 1237])).
% 1.43/1.64 tff(1702,plain,
% 1.43/1.64 (b(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1213])).
% 1.43/1.64 tff(1703,plain,
% 1.43/1.64 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1702])).
% 1.43/1.64 tff(1704,plain,
% 1.43/1.64 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1215])).
% 1.43/1.64 tff(1705,plain,
% 1.43/1.64 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1704])).
% 1.43/1.64 tff(1706,plain,
% 1.43/1.64 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1705])).
% 1.43/1.64 tff(1707,plain,
% 1.43/1.64 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1706, 1703])).
% 1.43/1.64 tff(1708,plain,
% 1.43/1.64 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1707])).
% 1.43/1.64 tff(1709,assumption,(r(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.64 tff(1710,plain,
% 1.43/1.64 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1317])).
% 1.43/1.64 tff(1711,plain,
% 1.43/1.64 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1710])).
% 1.43/1.64 tff(1712,plain,
% 1.43/1.64 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1711])).
% 1.43/1.64 tff(1713,plain,
% 1.43/1.64 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1712])).
% 1.43/1.64 tff(1714,plain,
% 1.43/1.64 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1713])).
% 1.43/1.64 tff(1715,plain,
% 1.43/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1714])).
% 1.43/1.64 tff(1716,plain,
% 1.43/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1710])).
% 1.43/1.64 tff(1717,plain,
% 1.43/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1716, 1715])).
% 1.43/1.64 tff(1718,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.64 tff(1719,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(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, 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(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1720,plain,
% 1.43/1.64 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1721,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(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, 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(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1720])).
% 1.43/1.64 tff(1722,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(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, 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(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1721, 1719])).
% 1.43/1.64 tff(1723,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(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1724,plain,
% 1.43/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 1.43/1.64 tff(1725,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1724, 65, 1718, 1507, 1709])).
% 1.43/1.64 tff(1726,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1727,plain,
% 1.43/1.64 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1726, 1709, 1507])).
% 1.43/1.64 tff(1728,plain,
% 1.43/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1729,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(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(1730,plain,
% 1.43/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 1.43/1.64 tff(1731,plain,
% 1.43/1.64 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1730, 47])).
% 1.43/1.64 tff(1732,plain,
% 1.43/1.64 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1731, 1727, 1691])).
% 1.43/1.64 tff(1733,plain,
% 1.43/1.64 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1732, 1717])).
% 1.43/1.64 tff(1734,plain,
% 1.43/1.64 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1713])).
% 1.43/1.64 tff(1735,plain,
% 1.43/1.64 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1734])).
% 1.43/1.64 tff(1736,plain,
% 1.43/1.64 (r(z, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1380])).
% 1.43/1.64 tff(1737,plain,
% 1.43/1.64 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(symmetry,[status(thm)],[1736])).
% 1.43/1.64 tff(1738,plain,
% 1.43/1.64 (r(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1709, 1737])).
% 1.43/1.64 tff(1739,assumption,(~r(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.64 tff(1740,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1739, 1738])).
% 1.43/1.64 tff(1741,plain,(r(z, s(s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1742,plain,
% 1.43/1.64 (r(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1741, 1709, 1211])).
% 1.43/1.64 tff(1743,plain,
% 1.43/1.64 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[876, 1742, 866])).
% 1.43/1.64 tff(1744,plain,
% 1.43/1.64 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1001, 1743])).
% 1.43/1.64 tff(1745,plain,
% 1.43/1.64 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1744, 1735])).
% 1.43/1.64 tff(1746,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.43/1.64 tff(1747,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1748,plain,
% 1.43/1.64 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.64 tff(1749,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.43/1.64 inference(monotonicity,[status(thm)],[1748])).
% 1.43/1.64 tff(1750,plain,
% 1.43/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.64 inference(transitivity,[status(thm)],[1749, 1747])).
% 1.43/1.64 tff(1751,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.43/1.64 inference(quant_inst,[status(thm)],[])).
% 1.43/1.64 tff(1752,plain,
% 1.43/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 1.43/1.64 tff(1753,plain,
% 1.43/1.64 ($false),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1752, 162, 444, 445, 1746, 1745, 1733])).
% 1.43/1.64 tff(1754,plain,((~r(elem!1, s(s(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(s(s(z))))), s(s(z)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.64 tff(1755,plain,
% 1.43/1.64 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.64 inference(unit_resolution,[status(thm)],[1754, 1709, 1211, 445, 1691, 866, 1507, 444])).
% 1.43/1.64 tff(1756,plain,
% 1.43/1.64 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.64 inference(modus_ponens,[status(thm)],[1755, 1708])).
% 1.43/1.64 tff(1757,plain,
% 1.43/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(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(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.43/1.64 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1758,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1759,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 1.43/1.65 tff(1760,plain,
% 1.43/1.65 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1759, 47])).
% 1.43/1.65 tff(1761,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1760, 1756, 1701])).
% 1.43/1.65 tff(1762,plain,
% 1.43/1.65 (s(s(z)) = s(s(elem!1))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1213])).
% 1.43/1.65 tff(1763,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1762])).
% 1.43/1.65 tff(1764,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1763])).
% 1.43/1.65 tff(1765,assumption,(r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.65 tff(1766,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.43/1.65 tff(1767,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[918, 1766])).
% 1.43/1.65 tff(1768,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(z))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1769,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1768, 1761, 1211])).
% 1.43/1.65 tff(1770,plain,
% 1.43/1.65 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.65 tff(1771,plain,
% 1.43/1.65 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1770])).
% 1.43/1.65 tff(1772,plain,
% 1.43/1.65 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1004, 1771])).
% 1.43/1.65 tff(1773,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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), 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(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1774,plain,
% 1.43/1.65 (((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1775,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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), 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(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1774])).
% 1.43/1.65 tff(1776,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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), 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(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1775, 1773])).
% 1.43/1.65 tff(1777,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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1778,plain,
% 1.43/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.43/1.65 tff(1779,plain,
% 1.43/1.65 ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1778, 65, 644])).
% 1.43/1.65 tff(1780,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1779, 1772, 896])).
% 1.43/1.65 tff(1781,plain,((~r(s(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(s(s(s(elem!1))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1782,plain,
% 1.43/1.65 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1781, 1769, 1211, 644])).
% 1.43/1.65 tff(1783,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.65 tff(1784,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.65 tff(1785,plain,
% 1.43/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1786,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1787,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.43/1.65 tff(1788,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1787, 47, 1784, 1692, 1783])).
% 1.43/1.65 tff(1789,plain,(b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1790,plain,
% 1.43/1.65 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1789, 1782, 1692])).
% 1.43/1.65 tff(1791,plain,
% 1.43/1.65 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1790, 1693])).
% 1.43/1.65 tff(1792,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1732, 1716])).
% 1.43/1.65 tff(1793,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.65 tff(1794,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 1.43/1.65 tff(1795,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(elem!1))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1796,plain,
% 1.43/1.65 (((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(elem!1))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1797,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(elem!1)))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1796])).
% 1.43/1.65 tff(1798,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(elem!1))))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1797, 1795])).
% 1.43/1.65 tff(1799,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1))))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1800,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 1.43/1.65 tff(1801,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1800, 162, 1794, 1003, 693, 692, 1793])).
% 1.43/1.65 tff(1802,plain,((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(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(z)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1803,plain,
% 1.43/1.65 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1802, 1744, 693, 692, 1793])).
% 1.43/1.65 tff(1804,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1803, 1792])).
% 1.43/1.65 tff(1805,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1806,plain,
% 1.43/1.65 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1805, 1709, 692, 693, 1691, 866, 1507, 1211])).
% 1.43/1.65 tff(1807,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1806, 1791])).
% 1.43/1.65 tff(1808,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(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)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1809,plain,
% 1.43/1.65 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1808, 644, 1692, 1211, 692, 693, 1691, 866, 1507, 1690, 1688])).
% 1.43/1.65 tff(1810,plain,
% 1.43/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, 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(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1811,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1812,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 1.43/1.65 tff(1813,plain,
% 1.43/1.65 ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1812, 47])).
% 1.43/1.65 tff(1814,plain,
% 1.43/1.65 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1813, 1809, 1588])).
% 1.43/1.65 tff(1815,plain,
% 1.43/1.65 (b(z, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1380])).
% 1.43/1.65 tff(1816,plain,
% 1.43/1.65 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1815])).
% 1.43/1.65 tff(1817,assumption,(b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.65 tff(1818,plain,
% 1.43/1.65 (b(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 1.43/1.65 tff(1819,assumption,(~b(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.65 tff(1820,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1819, 1818])).
% 1.43/1.65 tff(1821,plain,(b(z, s(s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1822,plain,
% 1.43/1.65 (b(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1821, 1814, 1211])).
% 1.43/1.65 tff(1823,plain,
% 1.43/1.65 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1705])).
% 1.43/1.65 tff(1824,plain,
% 1.43/1.65 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(s(elem!1))))), z))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1823])).
% 1.43/1.65 tff(1825,plain,
% 1.43/1.65 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1705, 1270])).
% 1.43/1.65 tff(1826,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1825])).
% 1.43/1.65 tff(1827,plain,
% 1.43/1.65 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1705])).
% 1.43/1.65 tff(1828,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1827])).
% 1.43/1.65 tff(1829,plain,
% 1.43/1.65 (b(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1821, 1817, 1211])).
% 1.43/1.65 tff(1830,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.65 tff(1831,plain,
% 1.43/1.65 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.43/1.65 inference(symmetry,[status(thm)],[1584])).
% 1.43/1.65 tff(1832,plain,
% 1.43/1.65 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.43/1.65 inference(transitivity,[status(thm)],[1586, 1831])).
% 1.43/1.65 tff(1833,plain,
% 1.43/1.65 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1832])).
% 1.43/1.65 tff(1834,plain,
% 1.43/1.65 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[863, 1833])).
% 1.43/1.65 tff(1835,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1214])).
% 1.43/1.65 tff(1836,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.65 tff(1837,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 1.43/1.65 tff(1838,plain,
% 1.43/1.65 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1705])).
% 1.43/1.65 tff(1839,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1838])).
% 1.43/1.65 tff(1840,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1835, 1839])).
% 1.43/1.65 tff(1841,plain,
% 1.43/1.65 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1836, 1840])).
% 1.43/1.65 tff(1842,plain,
% 1.43/1.65 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1705])).
% 1.43/1.65 tff(1843,plain,
% 1.43/1.65 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1842])).
% 1.43/1.65 tff(1844,assumption,(b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.65 tff(1845,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.43/1.65 tff(1846,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1847,plain,
% 1.43/1.65 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1848,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1847])).
% 1.43/1.65 tff(1849,plain,
% 1.43/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.43/1.65 inference(transitivity,[status(thm)],[1848, 1846])).
% 1.43/1.65 tff(1850,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1851,plain,
% 1.43/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 1.43/1.65 tff(1852,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1851, 162, 1600, 1248, 1817, 1845, 1844])).
% 1.43/1.65 tff(1853,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1854,plain,
% 1.43/1.65 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1853, 1844, 1248, 1817, 1600])).
% 1.43/1.65 tff(1855,plain,
% 1.43/1.65 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(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(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.65 inference(rewrite,[status(thm)],[])).
% 1.43/1.65 tff(1856,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.65 inference(quant_inst,[status(thm)],[])).
% 1.43/1.65 tff(1857,plain,
% 1.43/1.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1856, 1855])).
% 1.43/1.65 tff(1858,plain,
% 1.43/1.65 ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1857, 47])).
% 1.43/1.65 tff(1859,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1858, 1854, 1834])).
% 1.43/1.65 tff(1860,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.65 inference(monotonicity,[status(thm)],[1380])).
% 1.43/1.65 tff(1861,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.65 inference(symmetry,[status(thm)],[1860])).
% 1.43/1.65 tff(1862,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.43/1.65 tff(1863,plain,
% 1.43/1.65 (r(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.43/1.65 tff(1864,plain,
% 1.43/1.65 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[884, 65, 867, 866])).
% 1.43/1.65 tff(1865,plain,
% 1.43/1.65 ($false),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1864, 1863])).
% 1.43/1.65 tff(1866,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~(elem!1 = z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.65 tff(1867,plain,
% 1.43/1.65 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1866, 1859, 866, 1211])).
% 1.43/1.65 tff(1868,plain,
% 1.43/1.65 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.65 inference(unit_resolution,[status(thm)],[1001, 1867])).
% 1.43/1.65 tff(1869,plain,
% 1.43/1.65 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.43/1.65 inference(modus_ponens,[status(thm)],[1868, 1843])).
% 1.43/1.65 tff(1870,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.43/1.65 tff(1871,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.65 inference(symmetry,[status(thm)],[1706])).
% 1.43/1.65 tff(1872,plain,
% 1.43/1.65 (b(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1702, 1871])).
% 1.43/1.66 tff(1873,plain,
% 1.43/1.66 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1844, 1872])).
% 1.43/1.66 tff(1874,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1752, 162, 444, 445, 1873, 1870, 1869])).
% 1.43/1.66 tff(1875,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1876,plain,
% 1.43/1.66 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1875, 1841, 445, 444, 1211, 866, 1248, 1817, 1600])).
% 1.43/1.66 tff(1877,plain,
% 1.43/1.66 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1760, 1876, 1701])).
% 1.43/1.66 tff(1878,plain,
% 1.43/1.66 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1768, 1877, 1211])).
% 1.43/1.66 tff(1879,plain,
% 1.43/1.66 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1781, 1878, 1211, 644])).
% 1.43/1.66 tff(1880,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1789, 1879, 1692])).
% 1.43/1.66 tff(1881,plain,
% 1.43/1.66 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1880, 1693])).
% 1.43/1.66 tff(1882,plain,
% 1.43/1.66 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1802, 1881, 693, 692, 1837])).
% 1.43/1.66 tff(1883,plain,
% 1.43/1.66 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1001, 1882])).
% 1.43/1.66 tff(1884,plain,
% 1.43/1.66 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1866, 1883, 866, 1211])).
% 1.43/1.66 tff(1885,plain,
% 1.43/1.66 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1858, 1884, 1834])).
% 1.43/1.66 tff(1886,plain,
% 1.43/1.66 (b(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1885, 1830])).
% 1.43/1.66 tff(1887,plain,
% 1.43/1.66 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[979, 1886, 121, 152, 1829])).
% 1.43/1.66 tff(1888,plain,
% 1.43/1.66 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[968, 1887])).
% 1.43/1.66 tff(1889,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), s(z))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1888, 1828])).
% 1.43/1.66 tff(1890,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1705])).
% 1.43/1.66 tff(1891,plain,
% 1.43/1.66 (r(s(s(s(s(s(elem!1))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.66 inference(symmetry,[status(thm)],[1890])).
% 1.43/1.66 tff(1892,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1878, 1891])).
% 1.43/1.66 tff(1893,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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1894,plain,
% 1.43/1.66 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1895,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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1894])).
% 1.43/1.66 tff(1896,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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1895, 1893])).
% 1.43/1.66 tff(1897,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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1898,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 1.43/1.66 tff(1899,plain,
% 1.43/1.66 ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1898, 65, 384])).
% 1.43/1.66 tff(1900,plain,
% 1.43/1.66 (~r(s(s(s(s(s(z))))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1899, 1892])).
% 1.43/1.66 tff(1901,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1900, 1889])).
% 1.43/1.66 tff(1902,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(elem!1 = z)) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(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))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1903,plain,
% 1.43/1.66 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1902, 1653, 384, 1211, 1684, 866, 693, 692, 1692, 644, 1690, 1688, 1248, 1814, 1600])).
% 1.43/1.66 tff(1904,plain,
% 1.43/1.66 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1731, 1903, 1691])).
% 1.43/1.66 tff(1905,plain,
% 1.43/1.66 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1904, 1826])).
% 1.43/1.66 tff(1906,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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1907,plain,
% 1.43/1.66 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1908,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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(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(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1907])).
% 1.43/1.66 tff(1909,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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(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(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1908, 1906])).
% 1.43/1.66 tff(1910,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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1911,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(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.43/1.66 tff(1912,plain,
% 1.43/1.66 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1911, 65, 1])).
% 1.43/1.66 tff(1913,plain,
% 1.43/1.66 (~r(s(s(s(s(s(z))))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1912, 1905])).
% 1.43/1.66 tff(1914,plain,
% 1.43/1.66 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1913, 1824])).
% 1.43/1.66 tff(1915,plain,
% 1.43/1.66 (b(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[894, 1914])).
% 1.43/1.66 tff(1916,plain,
% 1.43/1.66 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[979, 1915, 1653, 1684, 1822])).
% 1.43/1.66 tff(1917,plain,
% 1.43/1.66 ((s(s(s(s(s(elem!1))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(commutativity,[status(thm)],[])).
% 1.43/1.66 tff(1918,plain,
% 1.43/1.66 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 1.43/1.66 inference(symmetry,[status(thm)],[1917])).
% 1.43/1.66 tff(1919,plain,
% 1.43/1.66 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(z))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1918])).
% 1.43/1.66 tff(1920,plain,
% 1.43/1.66 (~(s(s(s(s(s(elem!1))))) = s(s(z)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[914, 1919])).
% 1.43/1.66 tff(1921,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(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), 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(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1922,plain,
% 1.43/1.66 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1923,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(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), 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(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1922])).
% 1.43/1.66 tff(1924,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(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), 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(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1923, 1921])).
% 1.43/1.66 tff(1925,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(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1926,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(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.43/1.66 tff(1927,plain,
% 1.43/1.66 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1926, 65, 1718, 945, 2])).
% 1.43/1.66 tff(1928,plain,
% 1.43/1.66 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[943, 1927])).
% 1.43/1.66 tff(1929,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1930,plain,
% 1.43/1.66 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1931,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1930])).
% 1.43/1.66 tff(1932,plain,
% 1.43/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1931, 1929])).
% 1.43/1.66 tff(1933,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1934,plain,
% 1.43/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1933, 1932])).
% 1.43/1.66 tff(1935,plain,
% 1.43/1.66 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1934, 162, 538, 971, 1928, 926])).
% 1.43/1.66 tff(1936,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(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1937,plain,
% 1.43/1.66 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1938,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(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1937])).
% 1.43/1.66 tff(1939,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(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.43/1.66 tff(1940,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(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1941,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.43/1.66 tff(1942,plain,
% 1.43/1.66 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1941, 65, 945, 2])).
% 1.43/1.66 tff(1943,plain,
% 1.43/1.66 ((s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[921, 47, 1942])).
% 1.43/1.66 tff(1944,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1943, 1935, 1920])).
% 1.43/1.66 tff(1945,plain,((~r(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1946,plain,
% 1.43/1.66 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1945, 1915, 1609, 1686, 1822, 1904])).
% 1.43/1.66 tff(1947,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[968, 1946, 1916])).
% 1.43/1.66 tff(1948,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = z)) | (~r(z, s(s(s(z))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(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))))) | (s(s(s(s(elem!1)))) = s(s(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), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1949,plain,
% 1.43/1.66 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1948, 1583, 1, 1525, 1326, 866, 1337, 1340, 1518, 1248, 1211, 1507, 1506, 1313, 1247])).
% 1.43/1.66 tff(1950,plain,
% 1.43/1.66 (b(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[709, 1949, 1488])).
% 1.43/1.66 tff(1951,plain,
% 1.43/1.66 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1950, 1485])).
% 1.43/1.66 tff(1952,plain,
% 1.43/1.66 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.66 tff(1953,plain,
% 1.43/1.66 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.66 inference(symmetry,[status(thm)],[1952])).
% 1.43/1.66 tff(1954,plain,
% 1.43/1.66 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1213])).
% 1.43/1.66 tff(1955,plain,
% 1.43/1.66 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1954, 1953])).
% 1.43/1.66 tff(1956,plain,
% 1.43/1.66 (r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1494, 1955])).
% 1.43/1.66 tff(1957,plain,
% 1.43/1.66 (b(s(s(elem!1)), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1607, 1583, 1211])).
% 1.43/1.66 tff(1958,plain,
% 1.43/1.66 (b(s(s(z)), z)),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1957, 1599])).
% 1.43/1.66 tff(1959,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(z), z)) | (~r(s(z), 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(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1960,plain,
% 1.43/1.66 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.43/1.66 inference(rewrite,[status(thm)],[])).
% 1.43/1.66 tff(1961,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(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(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.43/1.66 inference(monotonicity,[status(thm)],[1960])).
% 1.43/1.66 tff(1962,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(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(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.43/1.66 inference(transitivity,[status(thm)],[1961, 1959])).
% 1.43/1.66 tff(1963,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(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 1.43/1.66 inference(quant_inst,[status(thm)],[])).
% 1.43/1.66 tff(1964,plain,
% 1.43/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.43/1.66 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 1.43/1.66 tff(1965,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1964, 65, 194, 1, 395])).
% 1.43/1.66 tff(1966,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1967,plain,
% 1.43/1.66 (~r(s(z), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1966, 194, 1])).
% 1.43/1.66 tff(1968,plain,
% 1.43/1.66 (b(s(z), s(s(s(z))))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[493, 1967])).
% 1.43/1.66 tff(1969,plain,
% 1.43/1.66 (~r(s(s(s(z))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1392, 194, 1313, 1211])).
% 1.43/1.66 tff(1970,plain,
% 1.43/1.66 (b(s(s(s(z))), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[595, 1969])).
% 1.43/1.66 tff(1971,plain,
% 1.43/1.66 ($false),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[702, 1970, 1968, 693, 692, 694])).
% 1.43/1.66 tff(1972,plain,((~r(s(z), 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)))))) | (~r(s(s(s(z))), elem!1)) | (~(elem!1 = z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.66 tff(1973,plain,
% 1.43/1.66 (~r(s(z), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1972, 1506, 1340, 1337, 1313, 1211, 1])).
% 1.43/1.66 tff(1974,plain,
% 1.43/1.66 (b(s(z), z)),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[175, 1973])).
% 1.43/1.66 tff(1975,plain,
% 1.43/1.66 (~r(z, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1448, 1506, 1211, 1337, 1340, 866, 495])).
% 1.43/1.66 tff(1976,plain,
% 1.43/1.66 (b(z, s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[117, 1975])).
% 1.43/1.66 tff(1977,plain,
% 1.43/1.66 (~b(s(s(z)), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[1402, 1976, 1974, 1958, 1330])).
% 1.43/1.66 tff(1978,plain,
% 1.43/1.66 (r(s(s(z)), s(z))),
% 1.43/1.66 inference(unit_resolution,[status(thm)],[271, 1977])).
% 1.43/1.67 tff(1979,plain,
% 1.43/1.67 (~r(s(s(s(s(z)))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1139, 1978, 1956])).
% 1.43/1.67 tff(1980,plain,
% 1.43/1.67 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[775, 1979, 1227])).
% 1.43/1.67 tff(1981,plain,
% 1.43/1.67 (~b(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1445, 1980, 1506, 1337, 1340])).
% 1.43/1.67 tff(1982,plain,
% 1.43/1.67 (r(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[595, 1981])).
% 1.43/1.67 tff(1983,plain,
% 1.43/1.67 (~r(s(s(s(z))), s(s(z)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[576, 1982, 1326])).
% 1.43/1.67 tff(1984,plain,
% 1.43/1.67 (b(s(s(s(z))), s(s(z)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[459, 1983])).
% 1.43/1.67 tff(1985,plain,
% 1.43/1.67 (~r(s(s(z)), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[586, 1982, 1978])).
% 1.43/1.67 tff(1986,plain,
% 1.43/1.67 (b(s(s(z)), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[442, 1985])).
% 1.43/1.67 tff(1987,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[453, 1986, 1984, 362, 363, 1951])).
% 1.43/1.67 tff(1988,plain,(b(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))))) | (~(elem!1 = z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (s(z) = elem!1) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(1989,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1988, 1484, 1467, 363, 1211, 866, 495, 1313, 362, 1248, 1416, 1247, 1246, 1245, 1307, 1232])).
% 1.43/1.67 tff(1990,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (s(z) = elem!1) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(1991,plain,
% 1.43/1.67 (~r(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1990, 1306, 1211, 1292, 495, 1291, 1286, 1248, 1247, 1246, 1245, 1244, 1232, 1231])).
% 1.43/1.67 tff(1992,plain,
% 1.43/1.67 (b(s(s(s(z))), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[595, 1991])).
% 1.43/1.67 tff(1993,plain,
% 1.43/1.67 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1306, 1339])).
% 1.43/1.67 tff(1994,plain,
% 1.43/1.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1336, 1286, 1211])).
% 1.43/1.67 tff(1995,plain,
% 1.43/1.67 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1215])).
% 1.43/1.67 tff(1996,plain,
% 1.43/1.67 (r(z, s(s(s(s(z)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[495, 1995])).
% 1.43/1.67 tff(1997,plain,
% 1.43/1.67 (~r(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1451, 1211, 1994, 1993, 1292, 495])).
% 1.43/1.67 tff(1998,plain,
% 1.43/1.67 (b(z, s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[117, 1997])).
% 1.43/1.67 tff(1999,plain,
% 1.43/1.67 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1224])).
% 1.43/1.67 tff(2000,plain,
% 1.43/1.67 (~(s(z) = s(s(s(s(z)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[143, 1999])).
% 1.43/1.67 tff(2001,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.67 tff(2002,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1304, 2001, 1260])).
% 1.43/1.67 tff(2003,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2002, 1293])).
% 1.43/1.67 tff(2004,plain,
% 1.43/1.67 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2003, 1339])).
% 1.43/1.67 tff(2005,plain,
% 1.43/1.67 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1285, 1211, 1280, 1260])).
% 1.43/1.67 tff(2006,plain,
% 1.43/1.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1336, 2005, 1211])).
% 1.43/1.67 tff(2007,plain,
% 1.43/1.67 (~r(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[466, 65, 1326, 273])).
% 1.43/1.67 tff(2008,plain,
% 1.43/1.67 (b(s(z), s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[493, 2007])).
% 1.43/1.67 tff(2009,plain,
% 1.43/1.67 (~b(s(z), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[702, 2008, 2006, 2004, 600])).
% 1.43/1.67 tff(2010,plain,
% 1.43/1.67 (r(s(z), s(s(s(s(z)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[658, 2009, 2000])).
% 1.43/1.67 tff(2011,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(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)))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2012,plain,
% 1.43/1.67 (((~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)))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2013,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(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))))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2012])).
% 1.43/1.67 tff(2014,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(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)))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[2013, 2011])).
% 1.43/1.67 tff(2015,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(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)))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(2016,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(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 1.43/1.67 tff(2017,plain,
% 1.43/1.67 (~r(s(z), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2016, 65, 803, 2010])).
% 1.43/1.67 tff(2018,plain,
% 1.43/1.67 (b(s(z), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[175, 2017])).
% 1.43/1.67 tff(2019,plain,
% 1.43/1.67 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.43/1.67 inference(symmetry,[status(thm)],[1599])).
% 1.43/1.67 tff(2020,plain,
% 1.43/1.67 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.43/1.67 inference(transitivity,[status(thm)],[2019, 1602])).
% 1.43/1.67 tff(2021,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(z)), z)) | (~r(s(s(s(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(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2022,plain,
% 1.43/1.67 (((~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(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2023,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(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(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2022])).
% 1.43/1.67 tff(2024,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(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(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.43/1.67 inference(transitivity,[status(thm)],[2023, 2021])).
% 1.43/1.67 tff(2025,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(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(2026,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 1.43/1.67 tff(2027,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2026, 65, 230, 273, 866])).
% 1.43/1.67 tff(2028,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(2029,plain,
% 1.43/1.67 (~r(s(s(z)), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2028, 273, 866])).
% 1.43/1.67 tff(2030,plain,
% 1.43/1.67 (b(s(s(z)), z)),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[245, 2029])).
% 1.43/1.67 tff(2031,plain,
% 1.43/1.67 (b(s(s(elem!1)), elem!1)),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2030, 2020])).
% 1.43/1.67 tff(2032,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2033,plain,
% 1.43/1.67 (((~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(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2034,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2033])).
% 1.43/1.67 tff(2035,plain,
% 1.43/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[2034, 2032])).
% 1.43/1.67 tff(2036,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(2037,plain,
% 1.43/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 1.43/1.67 tff(2038,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2037, 162, 152, 121, 600, 599, 297])).
% 1.43/1.67 tff(2039,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(2040,plain,
% 1.43/1.67 (~b(z, s(s(s(z))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2039, 2018, 121, 600, 2008])).
% 1.43/1.67 tff(2041,plain,
% 1.43/1.67 (~b(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2040, 1478])).
% 1.43/1.67 tff(2042,plain,
% 1.43/1.67 (r(elem!1, s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1483, 2041, 1473])).
% 1.43/1.67 tff(2043,plain,
% 1.43/1.67 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1705])).
% 1.43/1.67 tff(2044,plain,
% 1.43/1.67 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[2043])).
% 1.43/1.67 tff(2045,plain,
% 1.43/1.67 (r(z, s(s(s(s(s(z))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1742, 2044])).
% 1.43/1.67 tff(2046,plain,
% 1.43/1.67 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1216, 1705])).
% 1.43/1.67 tff(2047,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[2046])).
% 1.43/1.67 tff(2048,plain,
% 1.43/1.67 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[1693])).
% 1.43/1.67 tff(2049,plain,
% 1.43/1.67 ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2048])).
% 1.43/1.67 tff(2050,plain,
% 1.43/1.67 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[1806, 2049])).
% 1.43/1.67 tff(2051,plain,
% 1.43/1.67 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1789, 2050, 1692])).
% 1.43/1.67 tff(2052,plain,
% 1.43/1.67 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2051, 2047])).
% 1.43/1.67 tff(2053,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(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), 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(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2054,plain,
% 1.43/1.67 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2055,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(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(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(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2054])).
% 1.43/1.67 tff(2056,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(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(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(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[2055, 2053])).
% 1.43/1.67 tff(2057,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(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(2058,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 1.43/1.67 tff(2059,plain,
% 1.43/1.67 (~r(z, s(s(s(s(s(z))))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2058, 65, 803, 2052])).
% 1.43/1.67 tff(2060,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2059, 2045])).
% 1.43/1.67 tff(2061,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~(elem!1 = z)) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(2062,plain,
% 1.43/1.67 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2061, 2042, 803, 1518, 2004, 2006, 1525, 866, 1211])).
% 1.43/1.67 tff(2063,plain,
% 1.43/1.67 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1813, 2062, 1588])).
% 1.43/1.67 tff(2064,plain,
% 1.43/1.67 (~b(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1402, 2018, 121, 2030, 1330])).
% 1.43/1.67 tff(2065,plain,
% 1.43/1.67 (r(s(s(z)), s(z))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[271, 2064])).
% 1.43/1.67 tff(2066,plain,
% 1.43/1.67 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1213, 1214])).
% 1.43/1.67 tff(2067,plain,
% 1.43/1.67 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[1216])).
% 1.43/1.67 tff(2068,plain,
% 1.43/1.67 (r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2010, 2067])).
% 1.43/1.67 tff(2069,plain,
% 1.43/1.67 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1503, 2068, 1246])).
% 1.43/1.67 tff(2070,plain,
% 1.43/1.67 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1493, 2069, 1232])).
% 1.43/1.67 tff(2071,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.43/1.67 tff(2072,plain,
% 1.43/1.67 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.43/1.67 inference(symmetry,[status(thm)],[2071])).
% 1.43/1.67 tff(2073,plain,
% 1.43/1.67 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2072])).
% 1.43/1.67 tff(2074,plain,
% 1.43/1.67 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[2073])).
% 1.43/1.67 tff(2075,plain,
% 1.43/1.67 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[2071, 2074])).
% 1.43/1.67 tff(2076,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1232, 2075])).
% 1.43/1.67 tff(2077,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(2078,plain,
% 1.43/1.67 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2077, 1232])).
% 1.43/1.67 tff(2079,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.43/1.67 tff(2080,plain,
% 1.43/1.67 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[2079])).
% 1.43/1.67 tff(2081,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1232, 2080])).
% 1.43/1.67 tff(2082,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(2083,plain,
% 1.43/1.67 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2082, 1232])).
% 1.43/1.67 tff(2084,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.67 tff(2085,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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2086,plain,
% 1.43/1.67 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2087,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(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2086])).
% 1.43/1.67 tff(2088,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(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.43/1.67 inference(transitivity,[status(thm)],[2087, 2085])).
% 1.43/1.67 tff(2089,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(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(2090,plain,
% 1.43/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 1.43/1.67 tff(2091,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2090, 65, 1246, 193, 2084])).
% 1.43/1.67 tff(2092,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(2093,plain,
% 1.43/1.67 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2092, 2068, 1246])).
% 1.43/1.67 tff(2094,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.43/1.67 tff(2095,assumption,(~r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.67 tff(2096,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.43/1.67 tff(2097,plain,
% 1.43/1.67 (((~![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))))),
% 1.43/1.67 inference(rewrite,[status(thm)],[])).
% 1.43/1.67 tff(2098,plain,
% 1.43/1.67 ((~![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))))),
% 1.43/1.67 inference(quant_inst,[status(thm)],[])).
% 1.43/1.67 tff(2099,plain,
% 1.43/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 1.43/1.67 tff(2100,plain,
% 1.43/1.67 ($false),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2099, 47, 2096, 2095, 2094])).
% 1.43/1.67 tff(2101,plain,(r(s(s(s(s(elem!1)))), s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.67 tff(2102,plain,
% 1.43/1.67 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[2101, 2093, 2083])).
% 1.43/1.67 tff(2103,plain,
% 1.43/1.67 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(symmetry,[status(thm)],[1269])).
% 1.43/1.67 tff(2104,plain,
% 1.43/1.67 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 1.43/1.67 inference(monotonicity,[status(thm)],[2103])).
% 1.43/1.67 tff(2105,plain,
% 1.43/1.67 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.43/1.67 inference(unit_resolution,[status(thm)],[1255, 1253])).
% 1.43/1.67 tff(2106,plain,
% 1.43/1.67 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.43/1.67 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 1.43/1.68 tff(2107,plain,
% 1.43/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2108,plain,
% 1.43/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(2109,plain,
% 1.43/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2108, 2107])).
% 1.43/1.68 tff(2110,plain,
% 1.43/1.68 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2109, 47, 1280])).
% 1.43/1.68 tff(2111,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2110, 2106])).
% 1.43/1.68 tff(2112,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.68 tff(2113,plain,
% 1.43/1.68 (((~![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)))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2114,plain,
% 1.43/1.68 ((~![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)))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(2115,plain,
% 1.43/1.68 ((~![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))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2114, 2113])).
% 1.43/1.68 tff(2116,plain,
% 1.43/1.68 ((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))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2115, 47])).
% 1.43/1.68 tff(2117,plain,
% 1.43/1.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2116, 1253, 2112])).
% 1.43/1.68 tff(2118,plain,
% 1.43/1.68 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1304, 2105, 2001])).
% 1.43/1.68 tff(2119,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2120,plain,
% 1.43/1.68 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2121,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[2120])).
% 1.43/1.68 tff(2122,plain,
% 1.43/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[2121, 2119])).
% 1.43/1.68 tff(2123,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(2124,plain,
% 1.43/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.43/1.68 tff(2125,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2124, 162, 1147, 2118, 2117, 1146, 2111])).
% 1.43/1.68 tff(2126,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(2127,plain,
% 1.43/1.68 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2126, 2102, 2001, 1280, 2078, 2070])).
% 1.43/1.68 tff(2128,plain,
% 1.43/1.68 (r(s(s(z)), s(s(s(z))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2127, 2066])).
% 1.43/1.68 tff(2129,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.43/1.68 tff(2130,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2129, 1824])).
% 1.43/1.68 tff(2131,plain,
% 1.43/1.68 (b(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[894, 2130])).
% 1.43/1.68 tff(2132,plain,
% 1.43/1.68 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[979, 2131, 121, 152, 1829])).
% 1.43/1.68 tff(2133,plain,
% 1.43/1.68 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[968, 2132])).
% 1.43/1.68 tff(2134,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), s(z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2133, 1828])).
% 1.43/1.68 tff(2135,plain,
% 1.43/1.68 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1211])).
% 1.43/1.68 tff(2136,plain,
% 1.43/1.68 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(symmetry,[status(thm)],[2135])).
% 1.43/1.68 tff(2137,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(transitivity,[status(thm)],[1823, 2136])).
% 1.43/1.68 tff(2138,plain,
% 1.43/1.68 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[2137])).
% 1.43/1.68 tff(2139,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2129, 2138])).
% 1.43/1.68 tff(2140,plain,
% 1.43/1.68 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1858, 2139, 1834])).
% 1.43/1.68 tff(2141,plain,
% 1.43/1.68 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1853, 2140, 1248, 1817, 1600])).
% 1.43/1.68 tff(2142,plain,
% 1.43/1.68 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1760, 2141, 1701])).
% 1.43/1.68 tff(2143,plain,
% 1.43/1.68 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1768, 2142, 1211])).
% 1.43/1.68 tff(2144,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2143, 1891])).
% 1.43/1.68 tff(2145,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(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2146,plain,
% 1.43/1.68 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2147,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(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(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(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[2146])).
% 1.43/1.68 tff(2148,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(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(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(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[2147, 2145])).
% 1.43/1.68 tff(2149,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(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(2150,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 1.43/1.68 tff(2151,plain,
% 1.43/1.68 (~r(s(s(s(s(s(z))))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2150, 65, 417, 2, 2144])).
% 1.43/1.68 tff(2152,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2151, 2134])).
% 1.43/1.68 tff(2153,plain,(r(s(s(s(s(s(z))))), z) | (~(elem!1 = z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(2154,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), z)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2153, 2128, 1211, 2065, 1248, 2063, 2031, 121, 2018])).
% 1.43/1.68 tff(2155,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.43/1.68 tff(2156,plain,
% 1.43/1.68 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[1004, 2047])).
% 1.43/1.68 tff(2157,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(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2158,plain,
% 1.43/1.68 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2159,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(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[2158])).
% 1.43/1.68 tff(2160,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(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[2159, 2157])).
% 1.43/1.68 tff(2161,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(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(2162,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 1.43/1.68 tff(2163,plain,
% 1.43/1.68 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2162, 65, 1341])).
% 1.43/1.68 tff(2164,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2163, 2156, 2155])).
% 1.43/1.68 tff(2165,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(2166,plain,
% 1.43/1.68 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2165, 2154, 1341, 1211])).
% 1.43/1.68 tff(2167,plain,
% 1.43/1.68 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1789, 2166, 1518])).
% 1.43/1.68 tff(2168,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1214])).
% 1.43/1.68 tff(2169,plain,
% 1.43/1.68 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(symmetry,[status(thm)],[2168])).
% 1.43/1.68 tff(2170,plain,
% 1.43/1.68 ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1763])).
% 1.43/1.68 tff(2171,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[905, 2170])).
% 1.43/1.68 tff(2172,plain,
% 1.43/1.68 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1760, 2171, 1701])).
% 1.43/1.68 tff(2173,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1866, 867, 1211, 866])).
% 1.43/1.68 tff(2174,plain,
% 1.43/1.68 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1858, 2173, 1834])).
% 1.43/1.68 tff(2175,plain,
% 1.43/1.68 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1853, 2174, 1248, 2172, 1600])).
% 1.43/1.68 tff(2176,plain,
% 1.43/1.68 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1813, 2175, 1588])).
% 1.43/1.68 tff(2177,plain,
% 1.43/1.68 (r(z, s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1741, 2176, 1211])).
% 1.43/1.68 tff(2178,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[874, 65, 867, 2177, 866])).
% 1.43/1.68 tff(2179,plain,((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~(elem!1 = z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(2180,plain,
% 1.43/1.68 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2179, 2031, 1248, 1211, 273, 866])).
% 1.43/1.68 tff(2181,plain,
% 1.43/1.68 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1001, 2180])).
% 1.43/1.68 tff(2182,plain,
% 1.43/1.68 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2181, 2169])).
% 1.43/1.68 tff(2183,plain,
% 1.43/1.68 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1825])).
% 1.43/1.68 tff(2184,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(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2185,plain,
% 1.43/1.68 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2186,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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[2185])).
% 1.43/1.68 tff(2187,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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.68 inference(transitivity,[status(thm)],[2186, 2184])).
% 1.43/1.68 tff(2188,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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(2189,plain,
% 1.43/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.43/1.68 tff(2190,plain,
% 1.43/1.68 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2189, 65, 273, 866, 2154])).
% 1.43/1.68 tff(2191,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2190, 2183])).
% 1.43/1.68 tff(2192,plain,
% 1.43/1.68 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1731, 2191, 1525])).
% 1.43/1.68 tff(2193,plain,
% 1.43/1.68 ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(commutativity,[status(thm)],[])).
% 1.43/1.68 tff(2194,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.68 tff(2195,plain,
% 1.43/1.68 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 1.43/1.68 tff(2196,plain,
% 1.43/1.68 ($false),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1692, 2195])).
% 1.43/1.68 tff(2197,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.68 tff(2198,plain,
% 1.43/1.68 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2197, 1518])).
% 1.43/1.68 tff(2199,plain,
% 1.43/1.68 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[1705, 1216])).
% 1.43/1.68 tff(2200,plain,
% 1.43/1.68 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[2199])).
% 1.43/1.68 tff(2201,plain,
% 1.43/1.68 (~b(s(s(s(s(z)))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[1634, 2008, 2006, 2004, 600])).
% 1.43/1.68 tff(2202,plain,
% 1.43/1.68 (r(s(s(s(s(z)))), s(z))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[775, 2201, 1227])).
% 1.43/1.68 tff(2203,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(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2204,plain,
% 1.43/1.68 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.68 inference(rewrite,[status(thm)],[])).
% 1.43/1.68 tff(2205,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(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.43/1.68 inference(monotonicity,[status(thm)],[2204])).
% 1.43/1.68 tff(2206,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(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.43/1.68 inference(transitivity,[status(thm)],[2205, 2203])).
% 1.43/1.68 tff(2207,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(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.43/1.68 inference(quant_inst,[status(thm)],[])).
% 1.43/1.68 tff(2208,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(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.43/1.68 tff(2209,plain,
% 1.43/1.68 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.43/1.68 inference(unit_resolution,[status(thm)],[2208, 65, 2202, 1341, 2154])).
% 1.43/1.68 tff(2210,plain,
% 1.43/1.68 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.68 inference(modus_ponens,[status(thm)],[2209, 2200])).
% 1.43/1.68 tff(2211,plain,
% 1.43/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2212,plain,
% 1.43/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2213,plain,
% 1.43/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 1.43/1.69 tff(2214,plain,
% 1.43/1.69 ((s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2213, 47])).
% 1.43/1.69 tff(2215,plain,
% 1.43/1.69 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2214, 2210, 2198])).
% 1.43/1.69 tff(2216,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.69 tff(2217,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.43/1.69 tff(2218,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.43/1.69 tff(2219,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.69 tff(2220,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2221,plain,
% 1.43/1.69 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2222,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2221])).
% 1.43/1.69 tff(2223,plain,
% 1.43/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2222, 2220])).
% 1.43/1.69 tff(2224,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2225,plain,
% 1.43/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2224, 2223])).
% 1.43/1.69 tff(2226,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2225, 162, 1836, 2219, 2218, 2217, 2216])).
% 1.43/1.69 tff(2227,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2228,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2227, 2215, 2192, 2002, 2182, 2167])).
% 1.43/1.69 tff(2229,plain,((~r(s(s(s(z))), s(s(z)))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2230,plain,
% 1.43/1.69 (~r(s(s(s(z))), s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2229, 1211, 1231, 1292, 1248, 1998, 1996, 1992, 1300, 1268, 1232, 1246])).
% 1.43/1.69 tff(2231,plain,
% 1.43/1.69 (b(s(s(s(z))), s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[459, 2230])).
% 1.43/1.69 tff(2232,plain,
% 1.43/1.69 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[453, 443, 362, 363, 445])).
% 1.43/1.69 tff(2233,plain,
% 1.43/1.69 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[52, 2232])).
% 1.43/1.69 tff(2234,plain,
% 1.43/1.69 (r(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2233, 1345])).
% 1.43/1.69 tff(2235,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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2236,plain,
% 1.43/1.69 (((~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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2237,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(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2236])).
% 1.43/1.69 tff(2238,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(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2237, 2235])).
% 1.43/1.69 tff(2239,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(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))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2240,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 1.43/1.69 tff(2241,plain,
% 1.43/1.69 (~r(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2240, 65, 384, 395, 2234])).
% 1.43/1.69 tff(2242,plain,
% 1.43/1.69 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[403, 2233, 384])).
% 1.43/1.69 tff(2243,plain,
% 1.43/1.69 (b(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[191, 2242])).
% 1.43/1.69 tff(2244,plain,
% 1.43/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2243, 1418])).
% 1.43/1.69 tff(2245,plain,
% 1.43/1.69 (~b(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1445, 2244, 600, 1337, 1340])).
% 1.43/1.69 tff(2246,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[775, 2245, 2241, 1227])).
% 1.43/1.69 tff(2247,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~(elem!1 = 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(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2248,plain,
% 1.43/1.69 (~r(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2247, 1992, 1326, 1211, 1286, 1306, 2231])).
% 1.43/1.69 tff(2249,plain,
% 1.43/1.69 (b(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[493, 2248])).
% 1.43/1.69 tff(2250,plain,
% 1.43/1.69 (~b(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1634, 2249, 1994, 1993, 1992])).
% 1.43/1.69 tff(2251,plain,
% 1.43/1.69 (r(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[775, 2250, 1227])).
% 1.43/1.69 tff(2252,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.43/1.69 tff(2253,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(z), z)) | (~r(s(s(s(s(elem!1)))), 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), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2254,plain,
% 1.43/1.69 (((~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(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2255,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(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(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2254])).
% 1.43/1.69 tff(2256,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(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(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2255, 2253])).
% 1.43/1.69 tff(2257,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(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2258,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 1.43/1.69 tff(2259,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2258, 65, 194, 123, 2252])).
% 1.43/1.69 tff(2260,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2261,plain,
% 1.43/1.69 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2260, 194, 2252])).
% 1.43/1.69 tff(2262,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[149, 2261])).
% 1.43/1.69 tff(2263,plain,
% 1.43/1.69 (b(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2262, 1423])).
% 1.43/1.69 tff(2264,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(z), z)) | (~r(s(z), 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(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2265,plain,
% 1.43/1.69 (((~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), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2266,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(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), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2265])).
% 1.43/1.69 tff(2267,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(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), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2266, 2264])).
% 1.43/1.69 tff(2268,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(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2269,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 1.43/1.69 tff(2270,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2269, 65, 194, 395, 866])).
% 1.43/1.69 tff(2271,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2272,plain,
% 1.43/1.69 (~r(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2271, 194, 866])).
% 1.43/1.69 tff(2273,plain,
% 1.43/1.69 (b(s(z), s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[493, 2272])).
% 1.43/1.69 tff(2274,plain,
% 1.43/1.69 (~b(s(s(s(s(z)))), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1634, 2273, 693, 692, 600])).
% 1.43/1.69 tff(2275,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2274, 2263])).
% 1.43/1.69 tff(2276,plain,((~r(s(z), z)) | (~(elem!1 = 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(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2277,plain,
% 1.43/1.69 (~r(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2276, 1211, 1994, 1993, 1992, 1292, 1230])).
% 1.43/1.69 tff(2278,plain,
% 1.43/1.69 (b(s(z), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[175, 2277])).
% 1.43/1.69 tff(2279,plain,
% 1.43/1.69 (~b(s(z), s(s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[702, 2249, 1994, 1993, 1992])).
% 1.43/1.69 tff(2280,plain,
% 1.43/1.69 (r(s(z), s(s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[658, 2279, 2000])).
% 1.43/1.69 tff(2281,plain,
% 1.43/1.69 (r(s(z), s(s(s(s(elem!1)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2280, 2067])).
% 1.43/1.69 tff(2282,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)],[1503, 2281, 1246])).
% 1.43/1.69 tff(2283,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)],[1493, 2282, 1232])).
% 1.43/1.69 tff(2284,plain,
% 1.43/1.69 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[403, 2281, 1326])).
% 1.43/1.69 tff(2285,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[52, 2284])).
% 1.43/1.69 tff(2286,plain,
% 1.43/1.69 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[1476])).
% 1.43/1.69 tff(2287,plain,
% 1.43/1.69 (~b(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2039, 2249, 1998, 1992, 2278])).
% 1.43/1.69 tff(2288,plain,
% 1.43/1.69 (~b(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 1.43/1.69 tff(2289,plain,
% 1.43/1.69 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[1468])).
% 1.43/1.69 tff(2290,plain,
% 1.43/1.69 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2289])).
% 1.43/1.69 tff(2291,plain,
% 1.43/1.69 (~(z = s(s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[141, 2290])).
% 1.43/1.69 tff(2292,plain,
% 1.43/1.69 (((~![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)))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2293,plain,
% 1.43/1.69 ((~![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)))))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2294,plain,
% 1.43/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 1.43/1.69 tff(2295,plain,
% 1.43/1.69 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2294, 47])).
% 1.43/1.69 tff(2296,plain,
% 1.43/1.69 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2295, 2291])).
% 1.43/1.69 tff(2297,plain,
% 1.43/1.69 (r(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2296, 2288])).
% 1.43/1.69 tff(2298,plain,
% 1.43/1.69 (s(s(z)) = s(s(elem!1))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[1697])).
% 1.43/1.69 tff(2299,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2298])).
% 1.43/1.69 tff(2300,plain,
% 1.43/1.69 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[416, 2299])).
% 1.43/1.69 tff(2301,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2096, 2300])).
% 1.43/1.69 tff(2302,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2303,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)],[2302, 1237, 416])).
% 1.43/1.69 tff(2304,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.69 tff(2305,plain,
% 1.43/1.69 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[1270])).
% 1.43/1.69 tff(2306,plain,
% 1.43/1.69 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[2305])).
% 1.43/1.69 tff(2307,plain,
% 1.43/1.69 (r(z, s(s(s(z))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2304, 2306])).
% 1.43/1.69 tff(2308,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[290, 2307])).
% 1.43/1.69 tff(2309,plain,((~r(z, s(s(s(elem!1))))) | r(z, s(s(s(z)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2310,plain,
% 1.43/1.69 (r(z, s(s(s(z))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2309, 1211, 2304])).
% 1.43/1.69 tff(2311,plain,
% 1.43/1.69 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[1762, 1270])).
% 1.43/1.69 tff(2312,plain,
% 1.43/1.69 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.43/1.69 inference(symmetry,[status(thm)],[2311])).
% 1.43/1.69 tff(2313,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.43/1.69 tff(2314,plain,
% 1.43/1.69 (r(s(s(z)), s(s(s(z))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 1.43/1.69 tff(2315,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(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2316,plain,
% 1.43/1.69 (((~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)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.69 inference(rewrite,[status(thm)],[])).
% 1.43/1.69 tff(2317,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(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)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.43/1.69 inference(monotonicity,[status(thm)],[2316])).
% 1.43/1.69 tff(2318,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(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)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.43/1.69 inference(transitivity,[status(thm)],[2317, 2315])).
% 1.43/1.69 tff(2319,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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.43/1.69 inference(quant_inst,[status(thm)],[])).
% 1.43/1.69 tff(2320,plain,
% 1.43/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.43/1.69 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 1.43/1.69 tff(2321,plain,
% 1.43/1.69 ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2320, 65, 230])).
% 1.43/1.69 tff(2322,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2321, 2314, 1])).
% 1.43/1.69 tff(2323,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2324,plain,
% 1.43/1.69 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2323, 2310, 230, 1211])).
% 1.43/1.69 tff(2325,plain,
% 1.43/1.69 ($false),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2126, 2324, 2303, 2001, 1280, 1253, 1147])).
% 1.43/1.69 tff(2326,plain,((~(elem!1 = z)) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.43/1.69 tff(2327,plain,
% 1.43/1.69 (~r(s(s(z)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[2326, 2297, 1268, 2078, 1300, 1211, 2285, 2283])).
% 1.43/1.69 tff(2328,plain,
% 1.43/1.69 (b(s(s(z)), z)),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[245, 2327])).
% 1.43/1.69 tff(2329,plain,
% 1.43/1.69 (~b(s(s(z)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[1402, 2328, 1998, 2278, 1330])).
% 1.43/1.69 tff(2330,plain,
% 1.43/1.69 (r(s(s(z)), s(z))),
% 1.43/1.69 inference(unit_resolution,[status(thm)],[271, 2329])).
% 1.43/1.69 tff(2331,plain,
% 1.43/1.69 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[1139, 2330, 2251])).
% 1.43/1.70 tff(2332,plain,
% 1.43/1.70 (b(s(s(z)), s(s(s(s(z)))))),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[801, 2331, 1221])).
% 1.43/1.70 tff(2333,plain,
% 1.43/1.70 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.70 inference(symmetry,[status(thm)],[1485])).
% 1.43/1.70 tff(2334,plain,
% 1.43/1.70 (b(s(s(s(s(z)))), s(s(z)))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[2285, 2333])).
% 1.43/1.70 tff(2335,plain,
% 1.43/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(2336,plain,
% 1.43/1.70 (((~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(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.70 inference(rewrite,[status(thm)],[])).
% 1.43/1.70 tff(2337,plain,
% 1.43/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.43/1.70 inference(monotonicity,[status(thm)],[2336])).
% 1.43/1.70 tff(2338,plain,
% 1.43/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.43/1.70 inference(transitivity,[status(thm)],[2337, 2335])).
% 1.43/1.70 tff(2339,plain,
% 1.43/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(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)))))),
% 1.43/1.70 inference(quant_inst,[status(thm)],[])).
% 1.43/1.70 tff(2340,plain,
% 1.43/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.43/1.70 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 1.43/1.70 tff(2341,plain,
% 1.43/1.70 ($false),
% 1.43/1.70 inference(unit_resolution,[status(thm)],[2340, 162, 2231, 2334, 1994, 1993, 2332])).
% 1.43/1.70 tff(2342,plain,((~(elem!1 = z)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (s(z) = elem!1) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(s(elem!1)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2343,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2342, 1209, 1201, 1195, 1191, 495, 1188, 1178, 1161, 1158])).
% 1.53/1.70 tff(2344,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2345,plain,
% 1.53/1.70 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2344, 859, 495, 710, 857, 384, 853, 610, 2, 568, 596, 1002, 1100, 598])).
% 1.53/1.70 tff(2346,plain,
% 1.53/1.70 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[968, 2345])).
% 1.53/1.70 tff(2347,plain,
% 1.53/1.70 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[954, 2346, 2])).
% 1.53/1.70 tff(2348,plain,
% 1.53/1.70 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[943, 2347])).
% 1.53/1.70 tff(2349,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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(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(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2350,plain,
% 1.53/1.70 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2351,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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(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(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2350])).
% 1.53/1.70 tff(2352,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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(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(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2351, 2349])).
% 1.53/1.70 tff(2353,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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2354,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(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 1.53/1.70 tff(2355,plain,
% 1.53/1.70 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2354, 65, 610, 2346])).
% 1.53/1.70 tff(2356,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(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2357,plain,
% 1.53/1.70 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2358,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(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2357])).
% 1.53/1.70 tff(2359,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(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2358, 2356])).
% 1.53/1.70 tff(2360,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(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2361,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(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 1.53/1.70 tff(2362,plain,
% 1.53/1.70 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2361, 65, 2346, 855, 2])).
% 1.53/1.70 tff(2363,plain,
% 1.53/1.70 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[923, 2362])).
% 1.53/1.70 tff(2364,plain,
% 1.53/1.70 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[935, 2363, 859, 2348, 857])).
% 1.53/1.70 tff(2365,plain,
% 1.53/1.70 (r(s(s(s(s(s(elem!1))))), z)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[894, 2364])).
% 1.53/1.70 tff(2366,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(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(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(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2367,plain,
% 1.53/1.70 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2368,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))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(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(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2367])).
% 1.53/1.70 tff(2369,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))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(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(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2368, 2366])).
% 1.53/1.70 tff(2370,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))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2371,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(elem!1))))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 1.53/1.70 tff(2372,plain,
% 1.53/1.70 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2371, 65, 622, 853, 2365])).
% 1.53/1.70 tff(2373,plain,
% 1.53/1.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(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(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2374,plain,
% 1.53/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2375,plain,
% 1.53/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.53/1.70 tff(2376,plain,
% 1.53/1.70 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2375, 47, 995, 2372])).
% 1.53/1.70 tff(2377,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.53/1.70 tff(2378,plain,
% 1.53/1.70 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2197, 1692])).
% 1.53/1.70 tff(2379,plain,
% 1.53/1.70 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2214, 2378, 2377])).
% 1.53/1.70 tff(2380,plain,
% 1.53/1.70 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1789, 1692, 1783])).
% 1.53/1.70 tff(2381,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2382,plain,
% 1.53/1.70 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2383,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2382])).
% 1.53/1.70 tff(2384,plain,
% 1.53/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2383, 2381])).
% 1.53/1.70 tff(2385,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(2386,plain,
% 1.53/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 1.53/1.70 tff(2387,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2386, 162, 416, 2380, 1794, 363, 927, 2379])).
% 1.53/1.70 tff(2388,plain,((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2389,plain,
% 1.53/1.70 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2388, 2376, 405, 2355, 568, 2348, 1072])).
% 1.53/1.70 tff(2390,plain,
% 1.53/1.70 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 1.53/1.70 inference(symmetry,[status(thm)],[2389])).
% 1.53/1.70 tff(2391,plain,
% 1.53/1.70 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2390])).
% 1.53/1.70 tff(2392,plain,
% 1.53/1.70 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.53/1.70 inference(symmetry,[status(thm)],[2391])).
% 1.53/1.70 tff(2393,plain,
% 1.53/1.70 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1517, 2389])).
% 1.53/1.70 tff(2394,plain,
% 1.53/1.70 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1259, 2393])).
% 1.53/1.70 tff(2395,plain,
% 1.53/1.70 (elem!1 = s(s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1540, 2394])).
% 1.53/1.70 tff(2396,plain,
% 1.53/1.70 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2395])).
% 1.53/1.70 tff(2397,plain,
% 1.53/1.70 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1255, 2393])).
% 1.53/1.70 tff(2398,plain,
% 1.53/1.70 (elem!1 = s(s(s(s(elem!1))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1540, 1533])).
% 1.53/1.70 tff(2399,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.53/1.70 tff(2400,plain,
% 1.53/1.70 (s(s(s(s(z)))) = elem!1),
% 1.53/1.70 inference(symmetry,[status(thm)],[2399])).
% 1.53/1.70 tff(2401,plain,
% 1.53/1.70 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2400, 2398])).
% 1.53/1.70 tff(2402,plain,
% 1.53/1.70 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2401])).
% 1.53/1.70 tff(2403,plain,
% 1.53/1.70 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[631, 2402, 19, 2072, 1533])).
% 1.53/1.70 tff(2404,plain,
% 1.53/1.70 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.53/1.70 inference(symmetry,[status(thm)],[1533])).
% 1.53/1.70 tff(2405,plain,
% 1.53/1.70 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2404])).
% 1.53/1.70 tff(2406,plain,
% 1.53/1.70 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2405, 2072, 1533])).
% 1.53/1.70 tff(2407,plain,
% 1.53/1.70 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2406])).
% 1.53/1.70 tff(2408,plain,
% 1.53/1.70 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2407])).
% 1.53/1.70 tff(2409,plain,
% 1.53/1.70 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[996, 2408])).
% 1.53/1.70 tff(2410,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2409, 2403])).
% 1.53/1.70 tff(2411,plain,((~(elem!1 = s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(2412,plain,
% 1.53/1.70 (~(elem!1 = s(s(s(s(z)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[2411, 2397, 2394])).
% 1.53/1.70 tff(2413,plain,
% 1.53/1.70 (elem!1 = s(s(s(s(s(elem!1)))))),
% 1.53/1.70 inference(transitivity,[status(thm)],[2395, 2389])).
% 1.53/1.70 tff(2414,plain,
% 1.53/1.70 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2413])).
% 1.53/1.70 tff(2415,plain,
% 1.53/1.70 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.53/1.70 inference(symmetry,[status(thm)],[2414])).
% 1.53/1.70 tff(2416,plain,
% 1.53/1.70 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[2415])).
% 1.53/1.70 tff(2417,plain,
% 1.53/1.70 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1139, 788, 2])).
% 1.53/1.70 tff(2418,plain,
% 1.53/1.70 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[775, 2417, 642])).
% 1.53/1.70 tff(2419,plain,
% 1.53/1.70 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[1634, 2418, 599, 692, 600])).
% 1.53/1.70 tff(2420,plain,
% 1.53/1.70 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[675, 2419, 664])).
% 1.53/1.70 tff(2421,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(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2422,plain,
% 1.53/1.70 (((~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(2423,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(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(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2422])).
% 1.53/1.71 tff(2424,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(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(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2423, 2421])).
% 1.53/1.71 tff(2425,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(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)))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2426,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 1.53/1.71 tff(2427,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2426, 65, 273, 788, 2420])).
% 1.53/1.71 tff(2428,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2429,plain,
% 1.53/1.71 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2428, 622, 598, 1100, 596, 2])).
% 1.53/1.71 tff(2430,plain,
% 1.53/1.71 (b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[801, 2429, 634])).
% 1.53/1.71 tff(2431,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.53/1.71 tff(2432,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2433,plain,
% 1.53/1.71 (((~b(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(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2434,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))))), s(s(s(s(z))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2433])).
% 1.53/1.71 tff(2435,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2434, 2432])).
% 1.53/1.71 tff(2436,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2437,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.53/1.71 tff(2438,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2437, 162, 927, 825, 925, 1369, 2431])).
% 1.53/1.71 tff(2439,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2440,plain,
% 1.53/1.71 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2439, 2348, 710, 2363, 2430])).
% 1.53/1.71 tff(2441,plain,
% 1.53/1.71 (~b(elem!1, s(s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2440, 2416])).
% 1.53/1.71 tff(2442,plain,
% 1.53/1.71 (((~![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))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2443,plain,
% 1.53/1.71 ((~![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))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2444,plain,
% 1.53/1.71 ((~![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)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 1.53/1.71 tff(2445,plain,
% 1.53/1.71 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2444, 47])).
% 1.53/1.71 tff(2446,plain,
% 1.53/1.71 (r(elem!1, s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2445, 2441, 2412])).
% 1.53/1.71 tff(2447,plain,
% 1.53/1.71 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2446, 2396])).
% 1.53/1.71 tff(2448,plain,
% 1.53/1.71 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2447, 2392])).
% 1.53/1.71 tff(2449,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.53/1.71 tff(2450,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(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(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(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2451,plain,
% 1.53/1.71 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2452,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(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(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(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2451])).
% 1.53/1.71 tff(2453,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(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(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(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2452, 2450])).
% 1.53/1.71 tff(2454,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(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2455,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 1.53/1.71 tff(2456,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2455, 65, 945, 1131, 2449])).
% 1.53/1.71 tff(2457,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2458,plain,
% 1.53/1.71 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2457, 2346, 2448])).
% 1.53/1.71 tff(2459,plain,
% 1.53/1.71 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[775, 2458, 642])).
% 1.53/1.71 tff(2460,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2461,plain,
% 1.53/1.71 (((~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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2462,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2461])).
% 1.53/1.71 tff(2463,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2462, 2460])).
% 1.53/1.71 tff(2464,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2465,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2464, 2463])).
% 1.53/1.71 tff(2466,plain,
% 1.53/1.71 (~b(s(z), s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2465, 162, 596, 598, 2459, 1100])).
% 1.53/1.71 tff(2467,plain,
% 1.53/1.71 (r(s(z), s(s(s(s(z)))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[658, 2466, 643])).
% 1.53/1.71 tff(2468,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(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(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(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2469,plain,
% 1.53/1.71 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2470,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(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2469])).
% 1.53/1.71 tff(2471,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(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(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(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2470, 2468])).
% 1.53/1.71 tff(2472,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(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2473,plain,
% 1.53/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 1.53/1.71 tff(2474,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2473, 65, 2346, 2467, 2448])).
% 1.53/1.71 tff(2475,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(2476,plain,
% 1.53/1.71 (~r(z, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[2475, 362, 495, 384, 193, 2, 152, 121])).
% 1.53/1.71 tff(2477,plain,
% 1.53/1.71 (b(z, s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[295, 2476])).
% 1.53/1.71 tff(2478,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)],[590, 385, 362, 405, 2, 384])).
% 1.53/1.71 tff(2479,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)],[360, 2478])).
% 1.53/1.71 tff(2480,plain,
% 1.53/1.71 (~r(s(z), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[413, 2479, 193])).
% 1.53/1.71 tff(2481,plain,
% 1.53/1.71 (b(s(z), s(s(s(z))))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[493, 2480])).
% 1.53/1.71 tff(2482,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2483,plain,
% 1.53/1.71 (((~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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(2484,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[2483])).
% 1.53/1.71 tff(2485,plain,
% 1.53/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.53/1.71 inference(transitivity,[status(thm)],[2484, 2482])).
% 1.53/1.71 tff(2486,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(2487,plain,
% 1.53/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.53/1.72 tff(2488,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2487, 162, 152, 405, 362, 578, 2481, 297])).
% 1.53/1.72 tff(2489,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2490,plain,
% 1.53/1.72 (~r(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2489, 362, 152, 2477, 193, 2, 384])).
% 1.53/1.72 tff(2491,plain,
% 1.53/1.72 (b(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[595, 2490])).
% 1.53/1.72 tff(2492,plain,
% 1.53/1.72 (~b(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2039, 2491, 121, 2477, 152])).
% 1.53/1.72 tff(2493,plain,
% 1.53/1.72 (r(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[493, 2492])).
% 1.53/1.72 tff(2494,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)],[468, 2493, 405, 362, 384])).
% 1.53/1.72 tff(2495,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)],[413, 2493, 193])).
% 1.53/1.72 tff(2496,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[360, 2495, 2494])).
% 1.53/1.72 tff(2497,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2498,plain,
% 1.53/1.72 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2497, 495, 384, 121, 152, 2, 193])).
% 1.53/1.72 tff(2499,plain,
% 1.53/1.72 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[338, 2498])).
% 1.53/1.72 tff(2500,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(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2501,plain,
% 1.53/1.72 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2502,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(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z)))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2501])).
% 1.53/1.72 tff(2503,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(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2502, 2500])).
% 1.53/1.72 tff(2504,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(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2505,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z)))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 1.53/1.72 tff(2506,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2505, 65, 495, 1, 299])).
% 1.53/1.72 tff(2507,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2508,plain,
% 1.53/1.72 (~r(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2507, 2499, 495])).
% 1.53/1.72 tff(2509,plain,
% 1.53/1.72 (b(z, s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[295, 2508])).
% 1.53/1.72 tff(2510,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(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2511,plain,
% 1.53/1.72 (((~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(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~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(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2512,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(z), s(s(s(s(elem!1)))))) | (~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(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2511])).
% 1.53/1.72 tff(2513,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(z), s(s(s(s(elem!1)))))) | (~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(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2512, 2510])).
% 1.53/1.72 tff(2514,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(z), s(s(s(s(elem!1)))))) | (~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(z))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2515,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 1.53/1.72 tff(2516,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2515, 65, 193, 385, 299])).
% 1.53/1.72 tff(2517,plain,((~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(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2518,plain,
% 1.53/1.72 (~r(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2517, 2499, 193])).
% 1.53/1.72 tff(2519,plain,
% 1.53/1.72 (b(s(s(s(z))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[595, 2518])).
% 1.53/1.72 tff(2520,plain,
% 1.53/1.72 (~b(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2039, 2519, 121, 2509, 152])).
% 1.53/1.72 tff(2521,plain,
% 1.53/1.72 (r(s(z), s(s(s(z))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[493, 2520])).
% 1.53/1.72 tff(2522,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[476, 65, 193, 2521, 2499])).
% 1.53/1.72 tff(2523,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2524,plain,
% 1.53/1.72 (~b(s(z), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2523, 495, 558, 193, 384, 2])).
% 1.53/1.72 tff(2525,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[175, 2524, 504])).
% 1.53/1.72 tff(2526,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2527,plain,
% 1.53/1.72 (~r(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2526, 193, 384, 2])).
% 1.53/1.72 tff(2528,plain,
% 1.53/1.72 (b(z, s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[83, 2527])).
% 1.53/1.72 tff(2529,plain,
% 1.53/1.72 (b(z, s(s(z)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[524, 394])).
% 1.53/1.72 tff(2530,plain,
% 1.53/1.72 (~b(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[546, 2529, 416, 526, 120])).
% 1.53/1.72 tff(2531,plain,
% 1.53/1.72 (r(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[245, 2530])).
% 1.53/1.72 tff(2532,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(z), z)) | (~r(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(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2533,plain,
% 1.53/1.72 (((~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(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2534,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(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(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2533])).
% 1.53/1.72 tff(2535,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(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(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2534, 2532])).
% 1.53/1.72 tff(2536,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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2537,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 1.53/1.72 tff(2538,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2537, 65, 194, 384, 2531])).
% 1.53/1.72 tff(2539,plain,((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2540,plain,
% 1.53/1.72 (~r(s(z), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2539, 2528, 405, 514, 384])).
% 1.53/1.72 tff(2541,plain,
% 1.53/1.72 (b(s(z), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[175, 2540])).
% 1.53/1.72 tff(2542,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(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2543,plain,
% 1.53/1.72 (((~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(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2544,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(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(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2543])).
% 1.53/1.72 tff(2545,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(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(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2544, 2542])).
% 1.53/1.72 tff(2546,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(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))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2547,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 1.53/1.72 tff(2548,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2547, 65, 123, 385, 340])).
% 1.53/1.72 tff(2549,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,[]))).
% 1.53/1.72 tff(2550,plain,
% 1.53/1.72 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2549, 385, 340])).
% 1.53/1.72 tff(2551,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[149, 2550])).
% 1.53/1.72 tff(2552,plain,
% 1.53/1.72 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2517, 385, 193])).
% 1.53/1.72 tff(2553,plain,
% 1.53/1.72 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[338, 2552])).
% 1.53/1.72 tff(2554,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(z), z)) | (~r(s(z), s(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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2555,plain,
% 1.53/1.72 (((~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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2556,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(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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2555])).
% 1.53/1.72 tff(2557,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(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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2556, 2554])).
% 1.53/1.72 tff(2558,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(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)))))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2559,plain,
% 1.53/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 1.53/1.72 tff(2560,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2559, 65, 194, 193, 2252])).
% 1.53/1.72 tff(2561,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2562,plain,
% 1.53/1.72 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2561, 194, 193])).
% 1.53/1.72 tff(2563,plain,
% 1.53/1.72 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[95, 2562])).
% 1.53/1.72 tff(2564,plain,
% 1.53/1.72 (~r(z, s(s(z)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[105, 2, 97])).
% 1.53/1.72 tff(2565,plain,
% 1.53/1.72 (b(z, s(s(z)))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[524, 2564])).
% 1.53/1.72 tff(2566,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2567,plain,
% 1.53/1.72 (((~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(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2568,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2567])).
% 1.53/1.72 tff(2569,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2568, 2566])).
% 1.53/1.72 tff(2570,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2571,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 1.53/1.72 tff(2572,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2571, 162, 416, 122, 120, 538, 537])).
% 1.53/1.72 tff(2573,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2574,plain,
% 1.53/1.72 (~b(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2573, 2565, 122, 416, 120])).
% 1.53/1.72 tff(2575,plain,
% 1.53/1.72 (r(s(s(z)), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[245, 2574])).
% 1.53/1.72 tff(2576,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[554, 65, 97, 2575, 2])).
% 1.53/1.72 tff(2577,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(2578,plain,
% 1.53/1.72 (~r(z, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2577, 2563, 2, 120, 416])).
% 1.53/1.72 tff(2579,plain,
% 1.53/1.72 (b(z, s(z))),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[117, 2578])).
% 1.53/1.72 tff(2580,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2581,plain,
% 1.53/1.72 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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)))))))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(2582,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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))))))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[2581])).
% 1.53/1.72 tff(2583,plain,
% 1.53/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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)))))))),
% 1.53/1.72 inference(transitivity,[status(thm)],[2582, 2580])).
% 1.53/1.72 tff(2584,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(2585,plain,
% 1.53/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 1.53/1.72 tff(2586,plain,
% 1.53/1.72 (~b(s(s(s(z))), z)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[2585, 162, 2579, 151, 2563, 120, 2553])).
% 1.53/1.72 tff(2587,plain,
% 1.53/1.72 (r(s(s(s(z))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[381, 2586])).
% 1.53/1.73 tff(2588,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1389, 65, 194, 385, 2587])).
% 1.53/1.73 tff(2589,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2590,plain,
% 1.53/1.73 (~r(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2589, 120, 2551, 385, 2, 405, 193])).
% 1.53/1.73 tff(2591,plain,
% 1.53/1.73 (b(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[175, 2590])).
% 1.53/1.73 tff(2592,plain,
% 1.53/1.73 (~b(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2489, 2591, 385, 2553, 193, 2, 384])).
% 1.53/1.73 tff(2593,plain,
% 1.53/1.73 (r(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[295, 2592])).
% 1.53/1.73 tff(2594,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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2595,plain,
% 1.53/1.73 (((~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(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2596,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(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(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2595])).
% 1.53/1.73 tff(2597,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(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(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2596, 2594])).
% 1.53/1.73 tff(2598,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(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)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2599,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 1.53/1.73 tff(2600,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2599, 65, 2252, 1, 340])).
% 1.53/1.73 tff(2601,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2602,plain,
% 1.53/1.73 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2601, 2593, 340])).
% 1.53/1.73 tff(2603,plain,
% 1.53/1.73 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[95, 2602])).
% 1.53/1.73 tff(2604,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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2605,plain,
% 1.53/1.73 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2606,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(z))) | (~r(z, 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(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2605])).
% 1.53/1.73 tff(2607,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(z))) | (~r(z, 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(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2606, 2604])).
% 1.53/1.73 tff(2608,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(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2609,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2608, 2607])).
% 1.53/1.73 tff(2610,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2609, 65, 97, 1, 385])).
% 1.53/1.73 tff(2611,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2612,plain,
% 1.53/1.73 (~r(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2611, 2593, 385])).
% 1.53/1.73 tff(2613,plain,
% 1.53/1.73 (b(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[117, 2612])).
% 1.53/1.73 tff(2614,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[170, 2613, 2603, 2551, 2591, 120])).
% 1.53/1.73 tff(2615,plain,((~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2616,plain,
% 1.53/1.73 (~b(z, s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2615, 385, 340, 193, 2, 384])).
% 1.53/1.73 tff(2617,plain,
% 1.53/1.73 (r(z, s(s(s(s(elem!1)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[83, 2616])).
% 1.53/1.73 tff(2618,plain,
% 1.53/1.73 (~r(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[534, 2617, 193])).
% 1.53/1.73 tff(2619,plain,
% 1.53/1.73 (b(z, s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[117, 2618])).
% 1.53/1.73 tff(2620,plain,
% 1.53/1.73 (~r(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[503, 2617, 193])).
% 1.53/1.73 tff(2621,plain,
% 1.53/1.73 (b(s(z), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[175, 2620])).
% 1.53/1.73 tff(2622,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2497, 2621, 2619, 384, 2553, 2617, 2, 193])).
% 1.53/1.73 tff(2623,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), 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,[]))).
% 1.53/1.73 tff(2624,plain,
% 1.53/1.73 (~r(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2623, 340, 2, 193, 384])).
% 1.53/1.73 tff(2625,plain,
% 1.53/1.73 (b(s(s(s(z))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[595, 2624])).
% 1.53/1.73 tff(2626,plain,
% 1.53/1.73 (~b(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2039, 2625, 494, 558, 2541])).
% 1.53/1.73 tff(2627,plain,
% 1.53/1.73 (r(z, s(s(s(z))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[295, 2626])).
% 1.53/1.73 tff(2628,plain,
% 1.53/1.73 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2601, 2627, 340])).
% 1.53/1.73 tff(2629,plain,
% 1.53/1.73 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[95, 2628])).
% 1.53/1.73 tff(2630,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2631,plain,
% 1.53/1.73 (((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z, s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2632,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2631])).
% 1.53/1.73 tff(2633,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2632, 2630])).
% 1.53/1.73 tff(2634,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z, s(s(z)))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2635,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 1.53/1.73 tff(2636,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2635, 162, 416, 122, 120, 537, 526])).
% 1.53/1.73 tff(2637,plain,((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2638,plain,
% 1.53/1.73 (~b(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2637, 2629, 405, 2528, 514])).
% 1.53/1.73 tff(2639,plain,
% 1.53/1.73 (r(z, s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[524, 2638])).
% 1.53/1.73 tff(2640,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(z, s(s(z)))) | (~r(z, 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(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2641,plain,
% 1.53/1.73 (((~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(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2642,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(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(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2641])).
% 1.53/1.73 tff(2643,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(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(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2642, 2640])).
% 1.53/1.73 tff(2644,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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2645,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 1.53/1.73 tff(2646,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2645, 65, 55, 803, 644])).
% 1.53/1.73 tff(2647,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2648,plain,
% 1.53/1.73 (~r(z, s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2647, 644, 55])).
% 1.53/1.73 tff(2649,plain,
% 1.53/1.73 (b(z, s(s(s(s(z)))))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[823, 2648])).
% 1.53/1.73 tff(2650,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2651,plain,
% 1.53/1.73 (((~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)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2652,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2651])).
% 1.53/1.73 tff(2653,plain,
% 1.53/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2652, 2650])).
% 1.53/1.73 tff(2654,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2655,plain,
% 1.53/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 1.53/1.73 tff(2656,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2655, 162, 152, 121, 694, 1437, 1075])).
% 1.53/1.73 tff(2657,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2658,plain,
% 1.53/1.73 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2657, 659, 121, 152, 2649])).
% 1.53/1.73 tff(2659,plain,
% 1.53/1.73 (r(s(s(s(s(z)))), s(z))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[775, 2658, 642])).
% 1.53/1.73 tff(2660,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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2661,plain,
% 1.53/1.73 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(2662,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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[2661])).
% 1.53/1.73 tff(2663,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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.53/1.73 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.53/1.73 tff(2664,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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(2665,plain,
% 1.53/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.53/1.73 tff(2666,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2665, 65, 193, 384, 2659, 644])).
% 1.53/1.73 tff(2667,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(2668,plain,
% 1.53/1.73 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[2667, 2639, 384, 558, 2541, 193])).
% 1.53/1.73 tff(2669,plain,
% 1.53/1.73 (b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[709, 2668, 635])).
% 1.53/1.73 tff(2670,plain,
% 1.53/1.73 (~r(s(s(s(z))), s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[281, 2627, 2639])).
% 1.53/1.74 tff(2671,plain,
% 1.53/1.74 (b(s(s(s(z))), s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[459, 2670])).
% 1.53/1.74 tff(2672,plain,
% 1.53/1.74 (~r(z, s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[833, 417, 1])).
% 1.53/1.74 tff(2673,plain,
% 1.53/1.74 (b(z, s(s(z)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[524, 2672])).
% 1.53/1.74 tff(2674,plain,
% 1.53/1.74 (~b(s(s(z)), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[546, 2673, 416, 526, 120])).
% 1.53/1.74 tff(2675,plain,
% 1.53/1.74 (r(s(s(z)), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[245, 2674])).
% 1.53/1.74 tff(2676,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2320, 65, 1, 2675, 417])).
% 1.53/1.74 tff(2677,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2678,plain,
% 1.53/1.74 (~r(s(s(z)), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2677, 2627, 405, 514, 2528])).
% 1.53/1.74 tff(2679,plain,
% 1.53/1.74 (b(s(s(z)), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[442, 2678])).
% 1.53/1.74 tff(2680,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2681,plain,
% 1.53/1.74 (((~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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2682,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2681])).
% 1.53/1.74 tff(2683,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.53/1.74 tff(2684,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2685,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.53/1.74 tff(2686,plain,
% 1.53/1.74 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2685, 162, 444, 445, 825, 692])).
% 1.53/1.74 tff(2687,plain,
% 1.53/1.74 (r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[801, 2686, 634])).
% 1.53/1.74 tff(2688,plain,
% 1.53/1.74 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1139, 2687, 2])).
% 1.53/1.74 tff(2689,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[775, 2688, 642])).
% 1.53/1.74 tff(2690,plain,
% 1.53/1.74 (~b(s(z), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2465, 162, 600, 599, 2689, 692])).
% 1.53/1.74 tff(2691,plain,
% 1.53/1.74 (r(s(z), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[658, 2690, 643])).
% 1.53/1.74 tff(2692,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(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)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2693,plain,
% 1.53/1.74 (((~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)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2694,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(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))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2693])).
% 1.53/1.74 tff(2695,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(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)))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2694, 2692])).
% 1.53/1.74 tff(2696,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(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))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2697,plain,
% 1.53/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 1.53/1.74 tff(2698,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2697, 65, 2, 2687, 2691])).
% 1.53/1.74 tff(2699,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), 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(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2700,plain,
% 1.53/1.74 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2699, 2625, 2, 494, 2679, 2671, 2669])).
% 1.53/1.74 tff(2701,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[690, 2700, 679])).
% 1.53/1.74 tff(2702,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(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)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2703,plain,
% 1.53/1.74 (((~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)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2704,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(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))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2703])).
% 1.53/1.74 tff(2705,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(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)))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2704, 2702])).
% 1.53/1.74 tff(2706,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(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)))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2707,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(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))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 1.53/1.74 tff(2708,plain,
% 1.53/1.74 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2707, 65, 787, 340])).
% 1.53/1.74 tff(2709,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[763, 47, 753, 2708])).
% 1.53/1.74 tff(2710,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(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2711,plain,
% 1.53/1.74 (((~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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2712,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(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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2711])).
% 1.53/1.74 tff(2713,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(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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2712, 2710])).
% 1.53/1.74 tff(2714,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(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)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2715,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(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 1.53/1.74 tff(2716,plain,
% 1.53/1.74 (~r(s(s(s(s(z)))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2715, 65, 1, 787])).
% 1.53/1.74 tff(2717,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1089, 2716])).
% 1.53/1.74 tff(2718,plain,
% 1.53/1.74 (~r(s(s(s(s(elem!1)))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2601, 1, 340])).
% 1.53/1.74 tff(2719,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), z)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[95, 2718])).
% 1.53/1.74 tff(2720,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~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(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2721,plain,
% 1.53/1.74 (((~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(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~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(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2722,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~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(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2721])).
% 1.53/1.74 tff(2723,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2722, 2720])).
% 1.53/1.74 tff(2724,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2725,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2724, 2723])).
% 1.53/1.74 tff(2726,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2725, 162, 2719, 120, 2717, 1074, 2709])).
% 1.53/1.74 tff(2727,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2728,plain,
% 1.53/1.74 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2727, 2701, 2528, 2627, 340])).
% 1.53/1.74 tff(2729,plain,
% 1.53/1.74 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2728])).
% 1.53/1.74 tff(2730,plain,
% 1.53/1.74 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2729])).
% 1.53/1.74 tff(2731,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2730])).
% 1.53/1.74 tff(2732,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2731])).
% 1.53/1.74 tff(2733,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2728])).
% 1.53/1.74 tff(2734,plain,
% 1.53/1.74 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2728])).
% 1.53/1.74 tff(2735,plain,
% 1.53/1.74 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[20, 2734, 630])).
% 1.53/1.74 tff(2736,plain,
% 1.53/1.74 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2735])).
% 1.53/1.74 tff(2737,plain,
% 1.53/1.74 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2736, 987])).
% 1.53/1.74 tff(2738,plain,
% 1.53/1.74 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2737])).
% 1.53/1.74 tff(2739,plain,
% 1.53/1.74 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2738])).
% 1.53/1.74 tff(2740,plain,
% 1.53/1.74 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[996, 2739])).
% 1.53/1.74 tff(2741,plain,
% 1.53/1.74 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1513])).
% 1.53/1.74 tff(2742,plain,
% 1.53/1.74 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2741])).
% 1.53/1.74 tff(2743,plain,
% 1.53/1.74 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1517, 1508])).
% 1.53/1.74 tff(2744,plain,
% 1.53/1.74 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 1.53/1.74 tff(2745,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1691, 2744])).
% 1.53/1.74 tff(2746,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2747,plain,
% 1.53/1.74 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2746, 2740])).
% 1.53/1.74 tff(2748,plain,
% 1.53/1.74 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[170, 2629, 558, 2541, 2528])).
% 1.53/1.74 tff(2749,plain,
% 1.53/1.74 (r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[149, 2748])).
% 1.53/1.74 tff(2750,plain,
% 1.53/1.74 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2735])).
% 1.53/1.74 tff(2751,plain,
% 1.53/1.74 (s(s(elem!1)) = s(s(z))),
% 1.53/1.74 inference(transitivity,[status(thm)],[25, 2750, 312])).
% 1.53/1.74 tff(2752,plain,
% 1.53/1.74 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2751])).
% 1.53/1.74 tff(2753,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2751, 2728])).
% 1.53/1.74 tff(2754,plain,
% 1.53/1.74 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2753])).
% 1.53/1.74 tff(2755,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2756,plain,
% 1.53/1.74 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(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(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(2757,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2756])).
% 1.53/1.74 tff(2758,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.53/1.74 inference(transitivity,[status(thm)],[2757, 2755])).
% 1.53/1.74 tff(2759,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(2760,plain,
% 1.53/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 1.53/1.74 tff(2761,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2760, 162, 152, 121, 2717, 1437, 1074])).
% 1.53/1.74 tff(2762,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(2763,plain,
% 1.53/1.74 (~b(s(s(s(s(z)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[2762, 2701, 558, 2541, 2627])).
% 1.53/1.74 tff(2764,plain,
% 1.53/1.74 (r(s(s(s(s(z)))), s(z))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[775, 2763, 642])).
% 1.53/1.74 tff(2765,plain,
% 1.53/1.74 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1139, 2764, 2])).
% 1.53/1.74 tff(2766,plain,
% 1.53/1.74 (b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[801, 2765, 634])).
% 1.53/1.74 tff(2767,plain,
% 1.53/1.74 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2766, 2754])).
% 1.53/1.74 tff(2768,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[2728, 2751])).
% 1.53/1.74 tff(2769,plain,
% 1.53/1.74 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.74 inference(symmetry,[status(thm)],[2768])).
% 1.53/1.74 tff(2770,plain,
% 1.53/1.74 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[2669, 2769])).
% 1.53/1.74 tff(2771,plain,
% 1.53/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2772,plain,
% 1.53/1.75 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2773,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2772])).
% 1.53/1.75 tff(2774,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2773, 2771])).
% 1.53/1.75 tff(2775,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2776,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 1.53/1.75 tff(2777,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2776, 162, 1148, 1147, 122, 120, 1146])).
% 1.53/1.75 tff(2778,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2779,plain,
% 1.53/1.75 (~b(s(s(elem!1)), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2778, 2770, 2528, 2629, 2767])).
% 1.53/1.75 tff(2780,plain,
% 1.53/1.75 (((~![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))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2781,plain,
% 1.53/1.75 ((~![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))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2782,plain,
% 1.53/1.75 ((~![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)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2781, 2780])).
% 1.53/1.75 tff(2783,plain,
% 1.53/1.75 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2782, 47, 35])).
% 1.53/1.75 tff(2784,plain,
% 1.53/1.75 (r(s(s(elem!1)), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2783, 2779])).
% 1.53/1.75 tff(2785,plain,
% 1.53/1.75 (r(s(s(z)), z)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2784, 2752])).
% 1.53/1.75 tff(2786,plain,
% 1.53/1.75 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[727])).
% 1.53/1.75 tff(2787,plain,
% 1.53/1.75 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[727])).
% 1.53/1.75 tff(2788,plain,
% 1.53/1.75 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2787])).
% 1.53/1.75 tff(2789,plain,
% 1.53/1.75 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2788, 2786])).
% 1.53/1.75 tff(2790,plain,
% 1.53/1.75 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2789, 2193])).
% 1.53/1.75 tff(2791,plain,
% 1.53/1.75 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2790])).
% 1.53/1.75 tff(2792,plain,
% 1.53/1.75 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2791])).
% 1.53/1.75 tff(2793,plain,
% 1.53/1.75 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[729])).
% 1.53/1.75 tff(2794,plain,
% 1.53/1.75 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2793, 987])).
% 1.53/1.75 tff(2795,plain,
% 1.53/1.75 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2794])).
% 1.53/1.75 tff(2796,plain,
% 1.53/1.75 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2795])).
% 1.53/1.75 tff(2797,plain,
% 1.53/1.75 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[996, 2796])).
% 1.53/1.75 tff(2798,plain,
% 1.53/1.75 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2746, 2797])).
% 1.53/1.75 tff(2799,plain,
% 1.53/1.75 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2798, 2792])).
% 1.53/1.75 tff(2800,plain,
% 1.53/1.75 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2788])).
% 1.53/1.75 tff(2801,plain,
% 1.53/1.75 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2800])).
% 1.53/1.75 tff(2802,plain,
% 1.53/1.75 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2801])).
% 1.53/1.75 tff(2803,plain,
% 1.53/1.75 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[954, 945, 2])).
% 1.53/1.75 tff(2804,plain,
% 1.53/1.75 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[943, 2803])).
% 1.53/1.75 tff(2805,plain,
% 1.53/1.75 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1139, 1131, 2])).
% 1.53/1.75 tff(2806,plain,
% 1.53/1.75 (b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[801, 2805, 634])).
% 1.53/1.75 tff(2807,plain,
% 1.53/1.75 (r(s(s(s(s(s(elem!1))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2787])).
% 1.53/1.75 tff(2808,plain,
% 1.53/1.75 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2807])).
% 1.53/1.75 tff(2809,plain,
% 1.53/1.75 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2808])).
% 1.53/1.75 tff(2810,plain,
% 1.53/1.75 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2787])).
% 1.53/1.75 tff(2811,plain,
% 1.53/1.75 (r(s(s(s(s(s(z))))), s(z))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[945, 2810])).
% 1.53/1.75 tff(2812,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(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2813,plain,
% 1.53/1.75 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2814,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(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(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(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2813])).
% 1.53/1.75 tff(2815,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(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(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(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2814, 2812])).
% 1.53/1.75 tff(2816,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(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2817,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(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2816, 2815])).
% 1.53/1.75 tff(2818,plain,
% 1.53/1.75 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2817, 65, 230, 2, 2811])).
% 1.53/1.75 tff(2819,plain,
% 1.53/1.75 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2818, 2809])).
% 1.53/1.75 tff(2820,plain,
% 1.53/1.75 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[923, 2819])).
% 1.53/1.75 tff(2821,plain,
% 1.53/1.75 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2439, 2820, 825, 2806, 2804])).
% 1.53/1.75 tff(2822,plain,
% 1.53/1.75 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2821, 2802])).
% 1.53/1.75 tff(2823,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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2824,plain,
% 1.53/1.75 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2825,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(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2824])).
% 1.53/1.75 tff(2826,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(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2825, 2823])).
% 1.53/1.75 tff(2827,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(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2828,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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.53/1.75 tff(2829,plain,
% 1.53/1.75 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2828, 65, 787, 1131, 2811])).
% 1.53/1.75 tff(2830,plain,
% 1.53/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2831,plain,
% 1.53/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2832,plain,
% 1.53/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2831, 2830])).
% 1.53/1.75 tff(2833,plain,
% 1.53/1.75 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2832, 47, 2829])).
% 1.53/1.75 tff(2834,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2833, 2822, 2799])).
% 1.53/1.75 tff(2835,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2836,plain,
% 1.53/1.75 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2835, 2728, 2669, 2701, 2764, 2785, 2])).
% 1.53/1.75 tff(2837,plain,
% 1.53/1.75 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[968, 2836])).
% 1.53/1.75 tff(2838,plain,
% 1.53/1.75 (~b(z, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2039, 600, 599, 121, 152])).
% 1.53/1.75 tff(2839,plain,
% 1.53/1.75 (r(z, s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[295, 2838])).
% 1.53/1.75 tff(2840,plain,
% 1.53/1.75 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[751, 298, 121, 152, 600, 599])).
% 1.53/1.75 tff(2841,plain,
% 1.53/1.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2727, 2840, 120, 2839, 340])).
% 1.53/1.75 tff(2842,plain,
% 1.53/1.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[690, 2841, 679])).
% 1.53/1.75 tff(2843,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2844,plain,
% 1.53/1.75 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), 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(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2845,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2844])).
% 1.53/1.75 tff(2846,plain,
% 1.53/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2845, 2843])).
% 1.53/1.75 tff(2847,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2848,plain,
% 1.53/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 1.53/1.75 tff(2849,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2848, 162, 121, 444, 298, 600, 825, 2842])).
% 1.53/1.75 tff(2850,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2851,plain,
% 1.53/1.75 (~b(s(s(s(z))), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2850, 2679, 558, 2625, 2669, 2528, 340, 2541, 494])).
% 1.53/1.75 tff(2852,plain,
% 1.53/1.75 (r(s(s(s(z))), z)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[381, 2851])).
% 1.53/1.75 tff(2853,plain,
% 1.53/1.75 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[979, 895, 121, 152, 970])).
% 1.53/1.75 tff(2854,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[983, 47, 2853, 877, 865])).
% 1.53/1.75 tff(2855,plain,((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2856,plain,
% 1.53/1.75 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2855, 2837, 2541, 558, 2852])).
% 1.53/1.75 tff(2857,plain,
% 1.53/1.75 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1001, 2856])).
% 1.53/1.75 tff(2858,plain,
% 1.53/1.75 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1037, 2857, 494, 2625, 2837])).
% 1.53/1.75 tff(2859,plain,
% 1.53/1.75 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1050, 2858])).
% 1.53/1.75 tff(2860,assumption,(r(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.53/1.75 tff(2861,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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), 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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2862,plain,
% 1.53/1.75 (((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(2863,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(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2862])).
% 1.53/1.75 tff(2864,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(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.53/1.75 inference(transitivity,[status(thm)],[2863, 2861])).
% 1.53/1.75 tff(2865,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(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(2866,plain,
% 1.53/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 1.53/1.75 tff(2867,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2866, 65, 123, 1004, 2860])).
% 1.53/1.75 tff(2868,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(2869,plain,
% 1.53/1.75 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[2868, 2859, 2749])).
% 1.53/1.75 tff(2870,plain,
% 1.53/1.75 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1789, 2869, 2747])).
% 1.53/1.75 tff(2871,plain,
% 1.53/1.75 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2870, 2733])).
% 1.53/1.75 tff(2872,plain,
% 1.53/1.75 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[2871, 2732])).
% 1.53/1.75 tff(2873,plain,
% 1.53/1.75 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[2730])).
% 1.53/1.75 tff(2874,plain,
% 1.53/1.75 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.53/1.75 inference(symmetry,[status(thm)],[2873])).
% 1.53/1.75 tff(2875,plain,
% 1.53/1.75 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2751])).
% 1.53/1.76 tff(2876,plain,
% 1.53/1.76 (s(elem!1) = s(z)),
% 1.53/1.76 inference(transitivity,[status(thm)],[325, 2875, 15])).
% 1.53/1.76 tff(2877,plain,
% 1.53/1.76 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2876])).
% 1.53/1.76 tff(2878,plain,
% 1.53/1.76 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2877])).
% 1.53/1.76 tff(2879,plain,
% 1.53/1.76 (z = elem!1),
% 1.53/1.76 inference(transitivity,[status(thm)],[1182, 2878, 1170])).
% 1.53/1.76 tff(2880,plain,
% 1.53/1.76 (elem!1 = z),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1208, 2879])).
% 1.53/1.76 tff(2881,plain,
% 1.53/1.76 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.53/1.76 inference(commutativity,[status(thm)],[])).
% 1.53/1.76 tff(2882,plain,
% 1.53/1.76 (elem!1 = z),
% 1.53/1.76 inference(transitivity,[status(thm)],[1171, 2877, 13])).
% 1.53/1.76 tff(2883,plain,
% 1.53/1.76 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(z))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2882, 2729])).
% 1.53/1.76 tff(2884,plain,
% 1.53/1.76 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.53/1.76 inference(transitivity,[status(thm)],[2883, 2881])).
% 1.53/1.76 tff(2885,plain,
% 1.53/1.76 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2884])).
% 1.53/1.76 tff(2886,plain,
% 1.53/1.76 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2885])).
% 1.53/1.76 tff(2887,plain,
% 1.53/1.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2888,plain,
% 1.53/1.76 (~(s(s(s(s(s(z))))) = z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2887, 33])).
% 1.53/1.76 tff(2889,plain,
% 1.53/1.76 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2888, 2886])).
% 1.53/1.76 tff(2890,plain,
% 1.53/1.76 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2882, 2735])).
% 1.53/1.76 tff(2891,plain,
% 1.53/1.76 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2890])).
% 1.53/1.76 tff(2892,plain,
% 1.53/1.76 (r(elem!1, s(s(s(elem!1))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2627, 2891])).
% 1.53/1.76 tff(2893,plain,
% 1.53/1.76 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2735])).
% 1.53/1.76 tff(2894,plain,
% 1.53/1.76 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2893])).
% 1.53/1.76 tff(2895,plain,
% 1.53/1.76 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2730])).
% 1.53/1.76 tff(2896,plain,
% 1.53/1.76 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2895, 2894])).
% 1.53/1.76 tff(2897,plain,
% 1.53/1.76 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2896])).
% 1.53/1.76 tff(2898,plain,
% 1.53/1.76 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2729])).
% 1.53/1.76 tff(2899,plain,
% 1.53/1.76 (b(s(s(s(s(s(z))))), s(z))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2837, 2898])).
% 1.53/1.76 tff(2900,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2730])).
% 1.53/1.76 tff(2901,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.76 inference(symmetry,[status(thm)],[2900])).
% 1.53/1.76 tff(2902,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2857, 2901])).
% 1.53/1.76 tff(2903,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.53/1.76 tff(2904,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.53/1.76 tff(2905,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2906,plain,
% 1.53/1.76 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2907,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2906])).
% 1.53/1.76 tff(2908,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2907, 2905])).
% 1.53/1.76 tff(2909,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2910,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2909, 2908])).
% 1.53/1.76 tff(2911,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2910, 162, 600, 599, 1870, 2904, 2903])).
% 1.53/1.76 tff(2912,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2913,plain,
% 1.53/1.76 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2912, 2625, 494, 2902, 2899])).
% 1.53/1.76 tff(2914,plain,
% 1.53/1.76 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2913, 2897])).
% 1.53/1.76 tff(2915,plain,
% 1.53/1.76 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1731, 2914, 2740])).
% 1.53/1.76 tff(2916,plain,
% 1.53/1.76 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1726, 2915, 2892])).
% 1.53/1.76 tff(2917,plain,
% 1.53/1.76 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1813, 2916, 2889])).
% 1.53/1.76 tff(2918,plain,
% 1.53/1.76 (b(z, s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1821, 2917, 2880])).
% 1.53/1.76 tff(2919,plain,
% 1.53/1.76 (b(z, s(s(s(s(s(z))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2918, 2874])).
% 1.53/1.76 tff(2920,plain,
% 1.53/1.76 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[979, 2918, 558, 2541, 2837])).
% 1.53/1.76 tff(2921,plain,
% 1.53/1.76 (r(s(s(s(s(s(elem!1))))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[894, 2920])).
% 1.53/1.76 tff(2922,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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2923,plain,
% 1.53/1.76 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2924,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(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2923])).
% 1.53/1.76 tff(2925,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(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2924, 2922])).
% 1.53/1.76 tff(2926,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(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2927,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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.53/1.76 tff(2928,plain,
% 1.53/1.76 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2927, 65, 230, 878])).
% 1.53/1.76 tff(2929,plain,
% 1.53/1.76 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[923, 2928])).
% 1.53/1.76 tff(2930,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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), 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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2931,plain,
% 1.53/1.76 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2932,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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), 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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2931])).
% 1.53/1.76 tff(2933,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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), 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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2932, 2930])).
% 1.53/1.76 tff(2934,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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2935,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(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 1.53/1.76 tff(2936,plain,
% 1.53/1.76 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2935, 65, 230, 878])).
% 1.53/1.76 tff(2937,plain,
% 1.53/1.76 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[943, 2936])).
% 1.53/1.76 tff(2938,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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2939,plain,
% 1.53/1.76 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2940,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(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2939])).
% 1.53/1.76 tff(2941,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(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2940, 2938])).
% 1.53/1.76 tff(2942,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(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2943,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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.53/1.76 tff(2944,plain,
% 1.53/1.76 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2943, 65, 299, 866, 878])).
% 1.53/1.76 tff(2945,plain,
% 1.53/1.76 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2375, 47, 995, 2944])).
% 1.53/1.76 tff(2946,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(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(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(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(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2947,plain,
% 1.53/1.76 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(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(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2948,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(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(s(s(s(elem!1)))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2947])).
% 1.53/1.76 tff(2949,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(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(s(s(s(elem!1))))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2948, 2946])).
% 1.53/1.76 tff(2950,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2951,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 1.53/1.76 tff(2952,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2951, 162, 444, 2945, 2937, 1003, 2929])).
% 1.53/1.76 tff(2953,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2954,plain,
% 1.53/1.76 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2953, 2921, 2679, 2857, 2852, 2785])).
% 1.53/1.76 tff(2955,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[338, 2954])).
% 1.53/1.76 tff(2956,plain,
% 1.53/1.76 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1336, 2955, 2880])).
% 1.53/1.76 tff(2957,plain,
% 1.53/1.76 (~r(s(s(s(s(z)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2715, 65, 2627, 2701])).
% 1.53/1.76 tff(2958,plain,
% 1.53/1.76 (b(s(s(s(s(z)))), z)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1089, 2957])).
% 1.53/1.76 tff(2959,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2960,plain,
% 1.53/1.76 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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)))))) | (~b(s(s(z)), s(s(s(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)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(2961,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[2960])).
% 1.53/1.76 tff(2962,plain,
% 1.53/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.53/1.76 inference(transitivity,[status(thm)],[2961, 2959])).
% 1.53/1.76 tff(2963,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(2964,plain,
% 1.53/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 1.53/1.76 tff(2965,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2964, 162, 2679, 2958, 2956, 2766, 2919, 2872])).
% 1.53/1.76 tff(2966,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(2967,plain,
% 1.53/1.76 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[2966, 193, 384, 2])).
% 1.53/1.76 tff(2968,plain,
% 1.53/1.76 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[360, 2967])).
% 1.53/1.77 tff(2969,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2970,plain,
% 1.53/1.77 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), 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(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2971,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2970])).
% 1.53/1.77 tff(2972,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2971, 2969])).
% 1.53/1.77 tff(2973,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2974,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2973, 2972])).
% 1.53/1.77 tff(2975,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2974, 162, 121, 444, 363, 526, 298, 600])).
% 1.53/1.77 tff(2976,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2977,plain,
% 1.53/1.77 (~b(s(s(s(z))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2976, 444, 526, 121, 600, 363])).
% 1.53/1.77 tff(2978,plain,
% 1.53/1.77 (r(s(s(s(z))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[381, 2977])).
% 1.53/1.77 tff(2979,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2980,plain,
% 1.53/1.77 (((~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(s(s(elem!1)))), 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2981,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2980])).
% 1.53/1.77 tff(2982,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2981, 2979])).
% 1.53/1.77 tff(2983,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2984,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2983, 2982])).
% 1.53/1.77 tff(2985,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2984, 162, 416, 444, 363, 445, 526])).
% 1.53/1.77 tff(2986,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2987,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2986, 444, 416, 363, 526])).
% 1.53/1.77 tff(2988,plain,
% 1.53/1.77 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[459, 2987])).
% 1.53/1.77 tff(2989,plain,
% 1.53/1.77 (~r(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2028, 2988, 2978])).
% 1.53/1.77 tff(2990,plain,
% 1.53/1.77 (b(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[245, 2989])).
% 1.53/1.77 tff(2991,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2992,plain,
% 1.53/1.77 (((~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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)))))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(2993,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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))))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[2992])).
% 1.53/1.77 tff(2994,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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)))))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[2993, 2991])).
% 1.53/1.77 tff(2995,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(2996,plain,
% 1.53/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[2995, 2994])).
% 1.53/1.77 tff(2997,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2996, 162, 416, 120, 2990, 444, 363, 526])).
% 1.53/1.77 tff(2998,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(2999,plain,
% 1.53/1.77 (~b(s(s(z)), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2998, 120, 416, 363, 526, 121, 600])).
% 1.53/1.77 tff(3000,plain,
% 1.53/1.77 (r(s(s(z)), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[442, 2999])).
% 1.53/1.77 tff(3001,plain,
% 1.53/1.77 (~r(s(z), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2539, 120, 416, 526, 384])).
% 1.53/1.77 tff(3002,plain,
% 1.53/1.77 (b(s(z), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[175, 3001])).
% 1.53/1.77 tff(3003,plain,
% 1.53/1.77 (~b(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2039, 3002, 599, 121, 600])).
% 1.53/1.77 tff(3004,plain,
% 1.53/1.77 (r(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[295, 3003])).
% 1.53/1.77 tff(3005,plain,
% 1.53/1.77 (~r(z, s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[833, 3000, 3004])).
% 1.53/1.77 tff(3006,plain,
% 1.53/1.77 (b(z, s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[524, 3005])).
% 1.53/1.77 tff(3007,plain,
% 1.53/1.77 (~b(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[546, 3006, 416, 526, 120])).
% 1.53/1.77 tff(3008,plain,
% 1.53/1.77 (r(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[245, 3007])).
% 1.53/1.77 tff(3009,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2320, 65, 3004, 3008, 3000])).
% 1.53/1.77 tff(3010,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(3011,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3010, 2968, 514, 405, 558, 2528, 494, 384])).
% 1.53/1.77 tff(3012,plain,
% 1.53/1.77 (r(s(s(s(z))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[595, 3011])).
% 1.53/1.77 tff(3013,plain,
% 1.53/1.77 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2517, 3012, 193])).
% 1.53/1.77 tff(3014,plain,
% 1.53/1.77 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[590, 3012, 2968, 405, 2, 384])).
% 1.53/1.77 tff(3015,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[338, 3014, 3013])).
% 1.53/1.77 tff(3016,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(3017,plain,
% 1.53/1.77 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3016, 2, 384])).
% 1.53/1.77 tff(3018,plain,
% 1.53/1.77 (b(s(z), s(s(s(s(elem!1)))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[191, 3017])).
% 1.53/1.77 tff(3019,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.53/1.77 tff(3020,plain,
% 1.53/1.77 (r(z, s(s(z)))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[524, 3019])).
% 1.53/1.77 tff(3021,plain,
% 1.53/1.77 (~r(s(z), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[393, 3020, 384])).
% 1.53/1.77 tff(3022,plain,
% 1.53/1.77 (b(s(z), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[175, 3021])).
% 1.53/1.77 tff(3023,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(z, s(z))) | (~r(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(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3024,plain,
% 1.53/1.77 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3025,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(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), 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(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[3024])).
% 1.53/1.77 tff(3026,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(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), 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(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[3025, 3023])).
% 1.53/1.77 tff(3027,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(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(3028,plain,
% 1.53/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 1.53/1.77 tff(3029,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3028, 65, 97, 384, 55])).
% 1.53/1.77 tff(3030,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(3031,plain,
% 1.53/1.77 (~r(z, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3030, 3020, 384])).
% 1.53/1.77 tff(3032,plain,
% 1.53/1.77 (b(z, s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[117, 3031])).
% 1.53/1.77 tff(3033,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2549, 385, 123])).
% 1.53/1.77 tff(3034,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[360, 3033])).
% 1.53/1.77 tff(3035,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(elem!1)))), s(z))) | (~r(s(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)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3036,plain,
% 1.53/1.77 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(3037,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(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), 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(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[3036])).
% 1.53/1.77 tff(3038,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(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), 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(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.53/1.77 inference(transitivity,[status(thm)],[3037, 3035])).
% 1.53/1.77 tff(3039,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(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(3040,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(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 1.53/1.77 tff(3041,plain,
% 1.53/1.77 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[3040, 65, 54, 384])).
% 1.53/1.77 tff(3042,plain,
% 1.53/1.77 (b(s(s(s(s(elem!1)))), s(z))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[149, 3041])).
% 1.53/1.77 tff(3043,plain,
% 1.53/1.77 (~r(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[554, 65, 97, 2])).
% 1.53/1.77 tff(3044,plain,
% 1.53/1.77 (b(s(s(z)), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[245, 3043])).
% 1.53/1.77 tff(3045,plain,
% 1.53/1.77 (~r(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[2611, 385, 97])).
% 1.53/1.77 tff(3046,plain,
% 1.53/1.77 (b(z, s(s(s(z))))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[295, 3045])).
% 1.53/1.77 tff(3047,plain,
% 1.53/1.77 (~r(s(s(s(z))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1377, 385, 97])).
% 1.53/1.77 tff(3048,plain,
% 1.53/1.77 (b(s(s(s(z))), z)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[381, 3047])).
% 1.53/1.77 tff(3049,plain,
% 1.53/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3050,plain,
% 1.53/1.78 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3051,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3050])).
% 1.53/1.78 tff(3052,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3051, 3049])).
% 1.53/1.78 tff(3053,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3054,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 1.53/1.78 tff(3055,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3054, 162, 538, 537, 445, 298, 297])).
% 1.53/1.78 tff(3056,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3057,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3056, 3048, 578, 537, 3046, 538])).
% 1.53/1.78 tff(3058,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3059,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3058, 525, 3044, 97, 384])).
% 1.53/1.78 tff(3060,plain,
% 1.53/1.78 (b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[595, 3059])).
% 1.53/1.78 tff(3061,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3058, 537, 538, 97, 384])).
% 1.53/1.78 tff(3062,plain,
% 1.53/1.78 (b(s(s(s(z))), s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[595, 3061])).
% 1.53/1.78 tff(3063,plain,
% 1.53/1.78 (~b(s(s(s(z))), s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1465, 443, 537, 538, 297])).
% 1.53/1.78 tff(3064,plain,
% 1.53/1.78 (r(s(s(s(z))), s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[459, 3063])).
% 1.53/1.78 tff(3065,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[466, 65, 384, 395, 3064])).
% 1.53/1.78 tff(3066,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3067,plain,
% 1.53/1.78 (~r(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3066, 297, 537, 538, 384])).
% 1.53/1.78 tff(3068,plain,
% 1.53/1.78 (b(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[493, 3067])).
% 1.53/1.78 tff(3069,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[307, 299, 54])).
% 1.53/1.78 tff(3070,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[459, 3069])).
% 1.53/1.78 tff(3071,plain,
% 1.53/1.78 (~b(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3056, 3070, 537, 297, 538])).
% 1.53/1.78 tff(3072,plain,
% 1.53/1.78 (r(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[381, 3071])).
% 1.53/1.78 tff(3073,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))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3074,plain,
% 1.53/1.78 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3075,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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3074])).
% 1.53/1.78 tff(3076,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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3075, 3073])).
% 1.53/1.78 tff(3077,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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3078,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3077, 3076])).
% 1.53/1.78 tff(3079,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3078, 65, 97, 495, 299, 3072])).
% 1.53/1.78 tff(3080,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3081,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3080, 297, 495, 537, 97, 538, 54])).
% 1.53/1.78 tff(3082,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[338, 3081])).
% 1.53/1.78 tff(3083,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[608, 3082, 3042, 3068, 3062])).
% 1.53/1.78 tff(3084,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[360, 3083])).
% 1.53/1.78 tff(3085,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[348, 3084, 54])).
% 1.53/1.78 tff(3086,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[459, 3085])).
% 1.53/1.78 tff(3087,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(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3088,plain,
% 1.53/1.78 (((~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(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3089,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(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(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3088])).
% 1.53/1.78 tff(3090,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(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(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3089, 3087])).
% 1.53/1.78 tff(3091,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(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)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3092,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3091, 3090])).
% 1.53/1.78 tff(3093,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3092, 65, 54, 417, 340])).
% 1.53/1.78 tff(3094,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3095,plain,
% 1.53/1.78 (~r(s(s(z)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3094, 3084, 54])).
% 1.53/1.78 tff(3096,plain,
% 1.53/1.78 (b(s(s(z)), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[442, 3095])).
% 1.53/1.78 tff(3097,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1465, 3096, 3086, 537, 538, 297])).
% 1.53/1.78 tff(3098,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3099,plain,
% 1.53/1.78 (~b(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3098, 525, 3044, 54, 495, 97, 384])).
% 1.53/1.78 tff(3100,plain,
% 1.53/1.78 (r(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[295, 3099])).
% 1.53/1.78 tff(3101,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1644, 65, 97, 1, 395])).
% 1.53/1.78 tff(3102,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3103,plain,
% 1.53/1.78 (~r(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3102, 3100, 97])).
% 1.53/1.78 tff(3104,plain,
% 1.53/1.78 (b(s(z), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[493, 3103])).
% 1.53/1.78 tff(3105,plain,
% 1.53/1.78 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[2507, 3100, 495])).
% 1.53/1.78 tff(3106,plain,
% 1.53/1.78 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[338, 3105])).
% 1.53/1.78 tff(3107,plain,
% 1.53/1.78 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[566, 3100, 495])).
% 1.53/1.78 tff(3108,plain,
% 1.53/1.78 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[360, 3107])).
% 1.53/1.78 tff(3109,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[608, 3108, 3106, 3042, 3104, 3060])).
% 1.53/1.78 tff(3110,plain,((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3111,plain,
% 1.53/1.78 (~r(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3110, 495, 54, 384, 2])).
% 1.53/1.78 tff(3112,plain,
% 1.53/1.78 (b(z, s(z))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[117, 3111])).
% 1.53/1.78 tff(3113,plain,
% 1.53/1.78 (~r(s(z), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[393, 55, 384])).
% 1.53/1.78 tff(3114,plain,
% 1.53/1.78 (b(s(z), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[175, 3113])).
% 1.53/1.78 tff(3115,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3116,plain,
% 1.53/1.78 (((~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)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3117,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3116])).
% 1.53/1.78 tff(3118,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3117, 3115])).
% 1.53/1.78 tff(3119,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3120,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3119, 3118])).
% 1.53/1.78 tff(3121,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3120, 162, 152, 121, 177, 151, 122])).
% 1.53/1.78 tff(3122,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3123,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3122, 3114, 177, 3042, 121])).
% 1.53/1.78 tff(3124,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[95, 3123])).
% 1.53/1.78 tff(3125,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[90, 65, 54, 3124, 55])).
% 1.53/1.78 tff(3126,plain,((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3127,plain,
% 1.53/1.78 (~r(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3126, 3112, 3018, 54, 384])).
% 1.53/1.78 tff(3128,plain,
% 1.53/1.78 (b(z, s(s(z)))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[524, 3127])).
% 1.53/1.78 tff(3129,plain,
% 1.53/1.78 (~r(s(z), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[238, 230, 2])).
% 1.53/1.78 tff(3130,plain,
% 1.53/1.78 (b(s(z), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[175, 3129])).
% 1.53/1.78 tff(3131,plain,
% 1.53/1.78 (~b(s(s(s(s(elem!1)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3122, 3130, 177, 151, 121])).
% 1.53/1.78 tff(3132,plain,
% 1.53/1.78 (r(s(s(s(s(elem!1)))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[95, 3131])).
% 1.53/1.78 tff(3133,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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3134,plain,
% 1.53/1.78 (((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3135,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(z)), z)) | (~r(s(s(s(s(elem!1)))), 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(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3134])).
% 1.53/1.78 tff(3136,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(z)), z)) | (~r(s(s(s(s(elem!1)))), 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(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3135, 3133])).
% 1.53/1.78 tff(3137,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(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3138,plain,
% 1.53/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3137, 3136])).
% 1.53/1.78 tff(3139,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3138, 65, 54, 3132, 230])).
% 1.53/1.78 tff(3140,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3141,plain,
% 1.53/1.78 (~r(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3140, 3112, 3018, 3042, 54, 2])).
% 1.53/1.78 tff(3142,plain,
% 1.53/1.78 (b(s(s(z)), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[245, 3141])).
% 1.53/1.78 tff(3143,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3144,plain,
% 1.53/1.78 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(rewrite,[status(thm)],[])).
% 1.53/1.78 tff(3145,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.53/1.78 inference(monotonicity,[status(thm)],[3144])).
% 1.53/1.78 tff(3146,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.53/1.78 inference(transitivity,[status(thm)],[3145, 3143])).
% 1.53/1.78 tff(3147,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.53/1.78 inference(quant_inst,[status(thm)],[])).
% 1.53/1.78 tff(3148,plain,
% 1.53/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.53/1.78 inference(modus_ponens,[status(thm)],[3147, 3146])).
% 1.53/1.78 tff(3149,plain,
% 1.53/1.78 ($false),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3148, 162, 538, 537, 444, 445, 298])).
% 1.53/1.78 tff(3150,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.78 tff(3151,plain,
% 1.53/1.78 (~b(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[3150, 578, 3142, 588, 3128])).
% 1.53/1.78 tff(3152,plain,
% 1.53/1.78 (r(s(s(s(z))), z)),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[381, 3151])).
% 1.53/1.78 tff(3153,plain,
% 1.53/1.78 (~b(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1465, 445, 537, 538, 444])).
% 1.53/1.78 tff(3154,plain,
% 1.53/1.78 (r(z, s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[295, 3153])).
% 1.53/1.78 tff(3155,plain,
% 1.53/1.78 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[1098, 825, 495, 3154, 538, 537])).
% 1.53/1.78 tff(3156,plain,
% 1.53/1.78 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.53/1.78 inference(unit_resolution,[status(thm)],[690, 3155, 679])).
% 1.53/1.78 tff(3157,plain,
% 1.53/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3158,plain,
% 1.53/1.79 (((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3159,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3158])).
% 1.53/1.79 tff(3160,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3159, 3157])).
% 1.53/1.79 tff(3161,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3162,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 1.53/1.79 tff(3163,plain,
% 1.53/1.79 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3162, 162, 444, 445, 825, 3156])).
% 1.53/1.79 tff(3164,plain,
% 1.53/1.79 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[675, 3163, 664])).
% 1.53/1.79 tff(3165,plain,
% 1.53/1.79 (~b(s(s(s(z))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3150, 445, 538, 444, 537])).
% 1.53/1.79 tff(3166,plain,
% 1.53/1.79 (r(s(s(s(z))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[381, 3165])).
% 1.53/1.79 tff(3167,plain,
% 1.53/1.79 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2685, 162, 444, 445, 825, 3156])).
% 1.53/1.79 tff(3168,plain,
% 1.53/1.79 (r(s(s(z)), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[801, 3167, 634])).
% 1.53/1.79 tff(3169,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1139, 3168, 2])).
% 1.53/1.79 tff(3170,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[775, 3169, 642])).
% 1.53/1.79 tff(3171,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2697, 65, 2, 788, 645])).
% 1.53/1.79 tff(3172,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(3173,plain,
% 1.53/1.79 (~r(s(z), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3172, 3168, 2])).
% 1.53/1.79 tff(3174,plain,
% 1.53/1.79 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[658, 3173, 643])).
% 1.53/1.79 tff(3175,plain,
% 1.53/1.79 (~b(z, s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2657, 3174, 121, 152, 3170])).
% 1.53/1.79 tff(3176,plain,
% 1.53/1.79 (r(z, s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[823, 3175])).
% 1.53/1.79 tff(3177,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))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3178,plain,
% 1.53/1.79 (((~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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3179,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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3178])).
% 1.53/1.79 tff(3180,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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3179, 3177])).
% 1.53/1.79 tff(3181,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(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)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3182,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 1.53/1.79 tff(3183,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3182, 65, 3176, 3166, 3164])).
% 1.53/1.79 tff(3184,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(3185,plain,
% 1.53/1.79 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3184, 152, 3112, 2, 588, 578, 495, 3142, 3128])).
% 1.53/1.79 tff(3186,plain,
% 1.53/1.79 (r(s(s(s(s(z)))), s(s(z)))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[709, 3185, 635])).
% 1.53/1.79 tff(3187,plain,
% 1.53/1.79 (~r(s(z), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[653, 3186, 384])).
% 1.53/1.79 tff(3188,plain,
% 1.53/1.79 (b(s(z), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[658, 3187, 643])).
% 1.53/1.79 tff(3189,plain,
% 1.53/1.79 (~r(s(s(s(s(z)))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1594, 65, 384, 3186])).
% 1.53/1.79 tff(3190,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), s(z))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[775, 3189, 642])).
% 1.53/1.79 tff(3191,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3192,plain,
% 1.53/1.79 (((~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(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3193,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3192])).
% 1.53/1.79 tff(3194,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3193, 3191])).
% 1.53/1.79 tff(3195,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3196,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 1.53/1.79 tff(3197,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3196, 162, 152, 121, 1076, 694, 1437])).
% 1.53/1.79 tff(3198,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(3199,plain,
% 1.53/1.79 (~b(s(s(s(s(z)))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3198, 3190, 3112, 152, 3188])).
% 1.53/1.79 tff(3200,plain,
% 1.53/1.79 (r(s(s(s(s(z)))), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1089, 3199])).
% 1.53/1.79 tff(3201,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 1.53/1.79 tff(3202,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(elem!1)))), 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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3203,plain,
% 1.53/1.79 (((~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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~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(s(s(z)))))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3204,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(z)))) | (~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(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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3203])).
% 1.53/1.79 tff(3205,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(z)))) | (~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(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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3204, 3202])).
% 1.53/1.79 tff(3206,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(z)))) | (~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(s(s(z)))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3207,plain,
% 1.53/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3206, 3205])).
% 1.53/1.79 tff(3208,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3207, 65, 54, 644, 3201])).
% 1.53/1.79 tff(3209,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(3210,plain,
% 1.53/1.79 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3209, 3186, 54])).
% 1.53/1.79 tff(3211,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 1.53/1.79 tff(3212,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3213,plain,
% 1.53/1.79 (((~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)))))) | (~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)))))) | (~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(s(z)))), s(z))))),
% 1.53/1.79 inference(rewrite,[status(thm)],[])).
% 1.53/1.79 tff(3214,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3213])).
% 1.53/1.79 tff(3215,plain,
% 1.53/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(z))))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3214, 3212])).
% 1.53/1.79 tff(3216,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~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)))))))),
% 1.53/1.79 inference(quant_inst,[status(thm)],[])).
% 1.53/1.79 tff(3217,plain,
% 1.53/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3216, 3215])).
% 1.53/1.79 tff(3218,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3217, 162, 177, 151, 694, 1437, 3211])).
% 1.53/1.79 tff(3219,plain,((~b(s(s(s(s(elem!1)))), s(s(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(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(3220,plain,
% 1.53/1.79 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3219, 3190, 3042, 3018, 3188])).
% 1.53/1.79 tff(3221,plain,
% 1.53/1.79 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[763, 47, 3220, 3210])).
% 1.53/1.79 tff(3222,plain,
% 1.53/1.79 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3221])).
% 1.53/1.79 tff(3223,plain,
% 1.53/1.79 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[20, 3222, 630])).
% 1.53/1.79 tff(3224,plain,
% 1.53/1.79 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3223])).
% 1.53/1.79 tff(3225,plain,
% 1.53/1.79 (s(s(elem!1)) = s(s(z))),
% 1.53/1.79 inference(transitivity,[status(thm)],[25, 3224, 312])).
% 1.53/1.79 tff(3226,plain,
% 1.53/1.79 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3225, 3221])).
% 1.53/1.79 tff(3227,plain,
% 1.53/1.79 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3226])).
% 1.53/1.79 tff(3228,plain,
% 1.53/1.79 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3227])).
% 1.53/1.79 tff(3229,plain,
% 1.53/1.79 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[634, 3228])).
% 1.53/1.79 tff(3230,plain,
% 1.53/1.79 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3221])).
% 1.53/1.79 tff(3231,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.79 inference(symmetry,[status(thm)],[3230])).
% 1.53/1.79 tff(3232,plain,
% 1.53/1.79 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3225])).
% 1.53/1.79 tff(3233,plain,
% 1.53/1.79 (s(elem!1) = s(z)),
% 1.53/1.79 inference(transitivity,[status(thm)],[325, 3232, 15])).
% 1.53/1.79 tff(3234,plain,
% 1.53/1.79 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3233])).
% 1.53/1.79 tff(3235,plain,
% 1.53/1.79 (elem!1 = z),
% 1.53/1.79 inference(transitivity,[status(thm)],[1171, 3234, 13])).
% 1.53/1.79 tff(3236,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3235])).
% 1.53/1.79 tff(3237,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.53/1.79 inference(symmetry,[status(thm)],[3236])).
% 1.53/1.79 tff(3238,plain,
% 1.53/1.79 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.79 inference(transitivity,[status(thm)],[3237, 3231])).
% 1.53/1.79 tff(3239,plain,
% 1.53/1.79 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3238])).
% 1.53/1.79 tff(3240,plain,
% 1.53/1.79 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3199, 3239])).
% 1.53/1.79 tff(3241,plain,
% 1.53/1.79 ((elem!1 = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3221])).
% 1.53/1.79 tff(3242,plain,
% 1.53/1.79 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3241])).
% 1.53/1.79 tff(3243,plain,
% 1.53/1.79 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3235])).
% 1.53/1.79 tff(3244,plain,
% 1.53/1.79 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.53/1.79 inference(transitivity,[status(thm)],[3243, 813])).
% 1.53/1.79 tff(3245,plain,
% 1.53/1.79 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3244])).
% 1.53/1.79 tff(3246,plain,
% 1.53/1.79 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.53/1.79 inference(transitivity,[status(thm)],[3245, 3242, 1163])).
% 1.53/1.79 tff(3247,plain,
% 1.53/1.79 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3246])).
% 1.53/1.79 tff(3248,plain,
% 1.53/1.79 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[817, 3247])).
% 1.53/1.79 tff(3249,plain,
% 1.53/1.79 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3225])).
% 1.53/1.79 tff(3250,plain,
% 1.53/1.79 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3249])).
% 1.53/1.79 tff(3251,plain,
% 1.53/1.79 (r(s(z), s(s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[384, 3250])).
% 1.53/1.79 tff(3252,plain,
% 1.53/1.79 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3234])).
% 1.53/1.79 tff(3253,plain,
% 1.53/1.79 (z = elem!1),
% 1.53/1.79 inference(transitivity,[status(thm)],[1182, 3252, 1170])).
% 1.53/1.79 tff(3254,plain,
% 1.53/1.79 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3253])).
% 1.53/1.79 tff(3255,plain,
% 1.53/1.79 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3254, 1179])).
% 1.53/1.79 tff(3256,plain,
% 1.53/1.79 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.53/1.79 inference(transitivity,[status(thm)],[3255, 1180])).
% 1.53/1.79 tff(3257,plain,
% 1.53/1.79 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3256])).
% 1.53/1.79 tff(3258,plain,
% 1.53/1.79 (~(s(z) = elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[111, 3257])).
% 1.53/1.79 tff(3259,plain,
% 1.53/1.79 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3225])).
% 1.53/1.79 tff(3260,plain,
% 1.53/1.79 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3259])).
% 1.53/1.79 tff(3261,plain,
% 1.53/1.79 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3235])).
% 1.53/1.79 tff(3262,plain,
% 1.53/1.79 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.53/1.79 inference(symmetry,[status(thm)],[3261])).
% 1.53/1.79 tff(3263,plain,
% 1.53/1.79 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(transitivity,[status(thm)],[3262, 3260])).
% 1.53/1.79 tff(3264,plain,
% 1.53/1.79 (b(elem!1, s(s(elem!1)))),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3128, 3263])).
% 1.53/1.79 tff(3265,plain,
% 1.53/1.79 (~b(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1465, 578, 3128, 3142, 588])).
% 1.53/1.79 tff(3266,plain,
% 1.53/1.79 (r(z, s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[295, 3265])).
% 1.53/1.79 tff(3267,plain,
% 1.53/1.79 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[2507, 3266, 495])).
% 1.53/1.79 tff(3268,plain,
% 1.53/1.79 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[338, 3267])).
% 1.53/1.79 tff(3269,plain,
% 1.53/1.79 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[566, 3266, 495])).
% 1.53/1.79 tff(3270,plain,
% 1.53/1.79 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[360, 3269])).
% 1.53/1.79 tff(3271,plain,
% 1.53/1.79 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.53/1.79 inference(monotonicity,[status(thm)],[3235])).
% 1.53/1.79 tff(3272,plain,
% 1.53/1.79 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.53/1.79 inference(symmetry,[status(thm)],[3271])).
% 1.53/1.79 tff(3273,plain,
% 1.53/1.79 (r(s(s(s(z))), elem!1)),
% 1.53/1.79 inference(modus_ponens,[status(thm)],[3152, 3272])).
% 1.53/1.79 tff(3274,plain,
% 1.53/1.79 (elem!1 = z),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1208, 3253])).
% 1.53/1.79 tff(3275,plain,
% 1.53/1.79 ($false),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[1990, 3274, 3273, 385, 3152, 495, 3270, 3268, 3264, 3258, 3251, 3248, 3240, 3229, 3200])).
% 1.53/1.79 tff(3276,plain,((~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.79 tff(3277,plain,
% 1.53/1.79 (~b(s(z), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[3276, 385, 495, 384, 54, 2])).
% 1.53/1.79 tff(3278,plain,
% 1.53/1.79 (r(s(z), z)),
% 1.53/1.79 inference(unit_resolution,[status(thm)],[175, 3277])).
% 1.53/1.80 tff(3279,plain,
% 1.53/1.80 ($false),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[1389, 65, 3278, 385, 3152])).
% 1.53/1.80 tff(3280,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.80 tff(3281,plain,
% 1.53/1.80 (~r(s(s(s(z))), s(z))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3280, 495, 384, 54, 2])).
% 1.53/1.80 tff(3282,plain,
% 1.53/1.80 (b(s(s(s(z))), s(z))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[595, 3281])).
% 1.53/1.80 tff(3283,plain,
% 1.53/1.80 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[348, 273, 54])).
% 1.53/1.80 tff(3284,plain,
% 1.53/1.80 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[360, 3283])).
% 1.53/1.80 tff(3285,plain,
% 1.53/1.80 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[307, 273, 54])).
% 1.53/1.80 tff(3286,plain,
% 1.53/1.80 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[338, 3285])).
% 1.53/1.80 tff(3287,plain,
% 1.53/1.80 ($false),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[608, 3286, 3284, 151, 600, 599])).
% 1.53/1.80 tff(3288,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.80 tff(3289,plain,
% 1.53/1.80 (~r(s(s(s(z))), s(s(z)))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3288, 599, 600, 151, 54])).
% 1.53/1.80 tff(3290,plain,
% 1.53/1.80 (b(s(s(s(z))), s(s(z)))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[459, 3289])).
% 1.53/1.80 tff(3291,plain,
% 1.53/1.80 (~b(s(s(s(z))), z)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3056, 297, 537, 538, 3290])).
% 1.53/1.80 tff(3292,plain,
% 1.53/1.80 (r(s(s(s(z))), z)),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[381, 3291])).
% 1.53/1.80 tff(3293,plain,
% 1.53/1.80 (~b(s(s(z)), s(s(s(z))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[1465, 297, 537, 538, 3290])).
% 1.53/1.80 tff(3294,plain,
% 1.53/1.80 (r(s(s(z)), s(s(s(z))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[442, 3293])).
% 1.53/1.80 tff(3295,plain,
% 1.53/1.80 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[3094, 3294, 54])).
% 1.53/1.80 tff(3296,plain,
% 1.53/1.80 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[360, 3295])).
% 1.53/1.80 tff(3297,plain,
% 1.53/1.80 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[608, 3296, 151, 600, 599])).
% 1.53/1.80 tff(3298,plain,
% 1.53/1.80 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.53/1.80 inference(unit_resolution,[status(thm)],[338, 3297])).
% 1.53/1.80 tff(3299,plain,
% 1.53/1.80 (((~![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))), 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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(3300,plain,
% 1.53/1.80 (((~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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.53/1.80 inference(rewrite,[status(thm)],[])).
% 1.53/1.80 tff(3301,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))))),
% 1.53/1.80 inference(monotonicity,[status(thm)],[3300])).
% 1.53/1.80 tff(3302,plain,
% 1.53/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3301, 3299])).
% 1.63/1.80 tff(3303,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(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)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3304,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 1.63/1.80 tff(3305,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3304, 65, 495, 3298, 3292])).
% 1.63/1.80 tff(3306,plain,((~b(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3307,plain,
% 1.63/1.80 (~b(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3306, 599, 151, 600, 495, 54, 537, 538])).
% 1.63/1.80 tff(3308,plain,
% 1.63/1.80 (r(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[295, 3307])).
% 1.63/1.80 tff(3309,plain,
% 1.63/1.80 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2507, 3308, 495])).
% 1.63/1.80 tff(3310,plain,
% 1.63/1.80 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[338, 3309])).
% 1.63/1.80 tff(3311,plain,
% 1.63/1.80 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[566, 3308, 495])).
% 1.63/1.80 tff(3312,plain,
% 1.63/1.80 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[360, 3311])).
% 1.63/1.80 tff(3313,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[608, 3312, 3310, 151, 600, 599])).
% 1.63/1.80 tff(3314,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3315,plain,
% 1.63/1.80 (~b(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3314, 3282, 3042, 495, 54, 3128, 3142])).
% 1.63/1.80 tff(3316,plain,
% 1.63/1.80 (r(s(z), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[493, 3315])).
% 1.63/1.80 tff(3317,plain,
% 1.63/1.80 (~b(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3066, 3316, 3128, 3142, 384])).
% 1.63/1.80 tff(3318,plain,
% 1.63/1.80 (r(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[295, 3317])).
% 1.63/1.80 tff(3319,plain,
% 1.63/1.80 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2507, 3318, 495])).
% 1.63/1.80 tff(3320,plain,
% 1.63/1.80 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[338, 3319])).
% 1.63/1.80 tff(3321,plain,
% 1.63/1.80 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[566, 3318, 495])).
% 1.63/1.80 tff(3322,plain,
% 1.63/1.80 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[360, 3321])).
% 1.63/1.80 tff(3323,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3324,plain,
% 1.63/1.80 (((~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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(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(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3325,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3324])).
% 1.63/1.80 tff(3326,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3325, 3323])).
% 1.63/1.80 tff(3327,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3328,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 1.63/1.80 tff(3329,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3328, 162, 3018, 3042, 3322, 3320, 3282])).
% 1.63/1.80 tff(3330,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3331,plain,
% 1.63/1.80 (~r(z, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3330, 54, 384, 2])).
% 1.63/1.80 tff(3332,plain,
% 1.63/1.80 (b(z, s(s(s(s(elem!1)))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[83, 3331])).
% 1.63/1.80 tff(3333,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3334,plain,
% 1.63/1.80 (((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3335,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3334])).
% 1.63/1.80 tff(3336,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3335, 3333])).
% 1.63/1.80 tff(3337,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3338,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3337, 3336])).
% 1.63/1.80 tff(3339,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3338, 162, 152, 177, 151, 122, 120])).
% 1.63/1.80 tff(3340,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3341,plain,
% 1.63/1.80 (~b(s(s(s(s(elem!1)))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3340, 3130, 177, 120, 151])).
% 1.63/1.80 tff(3342,plain,
% 1.63/1.80 (r(s(s(s(s(elem!1)))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[95, 3341])).
% 1.63/1.80 tff(3343,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3138, 65, 54, 3342, 230])).
% 1.63/1.80 tff(3344,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3345,plain,
% 1.63/1.80 (~r(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3344, 54, 3018, 3332, 3042, 2])).
% 1.63/1.80 tff(3346,plain,
% 1.63/1.80 (b(s(s(z)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[245, 3345])).
% 1.63/1.80 tff(3347,plain,
% 1.63/1.80 (~r(z, s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3030, 55, 384])).
% 1.63/1.80 tff(3348,plain,
% 1.63/1.80 (~b(z, s(z))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3126, 55, 177, 54, 384])).
% 1.63/1.80 tff(3349,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[117, 3348, 3347])).
% 1.63/1.80 tff(3350,plain,((~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3351,plain,
% 1.63/1.80 (~r(z, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3350, 54, 3018, 384])).
% 1.63/1.80 tff(3352,plain,
% 1.63/1.80 (b(z, s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[524, 3351])).
% 1.63/1.80 tff(3353,plain,
% 1.63/1.80 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[348, 340, 54])).
% 1.63/1.80 tff(3354,plain,
% 1.63/1.80 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[459, 3353])).
% 1.63/1.80 tff(3355,plain,
% 1.63/1.80 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3094, 340, 54])).
% 1.63/1.80 tff(3356,plain,
% 1.63/1.80 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[442, 3355])).
% 1.63/1.80 tff(3357,plain,
% 1.63/1.80 (~b(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1465, 3356, 3352, 3346, 3354])).
% 1.63/1.80 tff(3358,plain,
% 1.63/1.80 (r(z, s(s(s(z))))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[295, 3357])).
% 1.63/1.80 tff(3359,plain,
% 1.63/1.80 (~r(s(s(s(s(elem!1)))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2601, 3358, 340])).
% 1.63/1.80 tff(3360,plain,
% 1.63/1.80 (b(s(s(s(s(elem!1)))), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[95, 3359])).
% 1.63/1.80 tff(3361,plain,
% 1.63/1.80 (~b(s(z), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3340, 3360, 3018, 3332, 3042])).
% 1.63/1.80 tff(3362,plain,
% 1.63/1.80 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[729])).
% 1.63/1.80 tff(3363,plain,
% 1.63/1.80 (s(s(elem!1)) = s(s(z))),
% 1.63/1.80 inference(transitivity,[status(thm)],[25, 3362, 312])).
% 1.63/1.80 tff(3364,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3363])).
% 1.63/1.80 tff(3365,plain,
% 1.63/1.80 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.63/1.80 inference(symmetry,[status(thm)],[3364])).
% 1.63/1.80 tff(3366,plain,
% 1.63/1.80 (r(s(s(elem!1)), s(z))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[2, 3365])).
% 1.63/1.80 tff(3367,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.63/1.80 tff(3368,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(elem!1)))) | (~r(s(s(elem!1)), 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(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3369,plain,
% 1.63/1.80 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3370,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(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3369])).
% 1.63/1.80 tff(3371,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(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3370, 3368])).
% 1.63/1.80 tff(3372,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(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3373,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(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.63/1.80 tff(3374,plain,
% 1.63/1.80 (~r(z, s(s(elem!1)))),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3373, 65, 3367, 97])).
% 1.63/1.80 tff(3375,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.63/1.80 tff(3376,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(elem!1)), s(z))) | (~r(s(s(elem!1)), 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(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3377,plain,
% 1.63/1.80 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3378,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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(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(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z)))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3377])).
% 1.63/1.80 tff(3379,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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(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(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3378, 3376])).
% 1.63/1.80 tff(3380,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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(3381,plain,
% 1.63/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z)))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[3380, 3379])).
% 1.63/1.80 tff(3382,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3381, 65, 3367, 97, 3375])).
% 1.63/1.80 tff(3383,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(3384,plain,
% 1.63/1.80 (~r(s(s(elem!1)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3383, 3367, 97])).
% 1.63/1.80 tff(3385,plain,
% 1.63/1.80 (b(s(s(elem!1)), z)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2783, 3384])).
% 1.63/1.80 tff(3386,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3387,plain,
% 1.63/1.80 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(3388,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[3387])).
% 1.63/1.80 tff(3389,plain,
% 1.63/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[3388, 3386])).
% 1.63/1.80 tff(3390,plain,
% 1.63/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3391,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 1.63/1.81 tff(3392,plain,
% 1.63/1.81 (~b(z, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3391, 162, 3385, 1147, 122, 120])).
% 1.63/1.81 tff(3393,plain,
% 1.63/1.81 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.63/1.81 inference(commutativity,[status(thm)],[])).
% 1.63/1.81 tff(3394,plain,
% 1.63/1.81 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3393])).
% 1.63/1.81 tff(3395,plain,
% 1.63/1.81 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3394])).
% 1.63/1.81 tff(3396,plain,
% 1.63/1.81 (~(z = s(s(elem!1)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[35, 3395])).
% 1.63/1.81 tff(3397,plain,
% 1.63/1.81 (((~![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))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3398,plain,
% 1.63/1.81 ((~![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))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3399,plain,
% 1.63/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 1.63/1.81 tff(3400,plain,
% 1.63/1.81 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3399, 47])).
% 1.63/1.81 tff(3401,plain,
% 1.63/1.81 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3400, 3396])).
% 1.63/1.81 tff(3402,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3401, 3392, 3374])).
% 1.63/1.81 tff(3403,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3404,plain,
% 1.63/1.81 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3403, 3366, 97, 120, 122])).
% 1.63/1.81 tff(3405,plain,
% 1.63/1.81 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3363])).
% 1.63/1.81 tff(3406,plain,
% 1.63/1.81 (s(elem!1) = s(z)),
% 1.63/1.81 inference(transitivity,[status(thm)],[325, 3405, 15])).
% 1.63/1.81 tff(3407,plain,
% 1.63/1.81 (r(s(elem!1), z) <=> r(s(z), z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3406])).
% 1.63/1.81 tff(3408,plain,
% 1.63/1.81 (r(s(z), z) <=> r(s(elem!1), z)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3407])).
% 1.63/1.81 tff(3409,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.63/1.81 tff(3410,plain,
% 1.63/1.81 (r(s(z), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[175, 3409])).
% 1.63/1.81 tff(3411,plain,
% 1.63/1.81 (r(s(elem!1), z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3410, 3408])).
% 1.63/1.81 tff(3412,plain,
% 1.63/1.81 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3363])).
% 1.63/1.81 tff(3413,plain,
% 1.63/1.81 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3412])).
% 1.63/1.81 tff(3414,plain,
% 1.63/1.81 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3406])).
% 1.63/1.81 tff(3415,plain,
% 1.63/1.81 (elem!1 = z),
% 1.63/1.81 inference(transitivity,[status(thm)],[1171, 3414, 13])).
% 1.63/1.81 tff(3416,plain,
% 1.63/1.81 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3415])).
% 1.63/1.81 tff(3417,plain,
% 1.63/1.81 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3416])).
% 1.63/1.81 tff(3418,plain,
% 1.63/1.81 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.63/1.81 inference(transitivity,[status(thm)],[3417, 3413])).
% 1.63/1.81 tff(3419,plain,
% 1.63/1.81 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3418])).
% 1.63/1.81 tff(3420,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.63/1.81 tff(3421,plain,
% 1.63/1.81 (~r(s(s(elem!1)), elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3420, 3419])).
% 1.63/1.81 tff(3422,plain,
% 1.63/1.81 (b(elem!1, z) <=> b(z, z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3415])).
% 1.63/1.81 tff(3423,plain,
% 1.63/1.81 (b(z, z) <=> b(elem!1, z)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3422])).
% 1.63/1.81 tff(3424,plain,
% 1.63/1.81 ((~b(z, z)) <=> (~b(elem!1, z))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3423])).
% 1.63/1.81 tff(3425,plain,
% 1.63/1.81 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.63/1.81 inference(bind,[status(th)],[])).
% 1.63/1.81 tff(3426,plain,
% 1.63/1.81 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.63/1.81 inference(quant_intro,[status(thm)],[3425])).
% 1.63/1.81 tff(3427,plain,
% 1.63/1.81 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3428,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.63/1.81 tff(3429,plain,
% 1.63/1.81 (![X: $i] : (~b(X, X))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3428, 3427])).
% 1.63/1.81 tff(3430,plain,(
% 1.63/1.81 ![X: $i] : (~b(X, X))),
% 1.63/1.81 inference(skolemize,[status(sab)],[3429])).
% 1.63/1.81 tff(3431,plain,
% 1.63/1.81 (![X: $i] : (~b(X, X))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3430, 3426])).
% 1.63/1.81 tff(3432,plain,
% 1.63/1.81 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3433,plain,
% 1.63/1.81 (~b(z, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3432, 3431])).
% 1.63/1.81 tff(3434,plain,
% 1.63/1.81 (~b(elem!1, z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3433, 3424])).
% 1.63/1.81 tff(3435,plain,
% 1.63/1.81 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3406])).
% 1.63/1.81 tff(3436,plain,
% 1.63/1.81 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3435])).
% 1.63/1.81 tff(3437,plain,
% 1.63/1.81 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3415])).
% 1.63/1.81 tff(3438,plain,
% 1.63/1.81 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3437])).
% 1.63/1.81 tff(3439,plain,
% 1.63/1.81 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 1.63/1.81 inference(transitivity,[status(thm)],[3438, 3436])).
% 1.63/1.81 tff(3440,plain,
% 1.63/1.81 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3439])).
% 1.63/1.81 tff(3441,plain,
% 1.63/1.81 (~b(s(elem!1), elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3409, 3440])).
% 1.63/1.81 tff(3442,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.63/1.81 tff(3443,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.63/1.81 tff(3444,plain,
% 1.63/1.81 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.63/1.81 inference(commutativity,[status(thm)],[])).
% 1.63/1.81 tff(3445,plain,
% 1.63/1.81 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3444])).
% 1.63/1.81 tff(3446,plain,
% 1.63/1.81 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3445])).
% 1.63/1.81 tff(3447,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.63/1.81 tff(3448,plain,
% 1.63/1.81 (s(s(s(s(elem!1)))) = elem!1),
% 1.63/1.81 inference(symmetry,[status(thm)],[3447])).
% 1.63/1.81 tff(3449,plain,
% 1.63/1.81 (b(s(s(s(s(elem!1)))), z) <=> b(elem!1, z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3448])).
% 1.63/1.81 tff(3450,plain,
% 1.63/1.81 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3449])).
% 1.63/1.81 tff(3451,plain,
% 1.63/1.81 ((~b(elem!1, z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3450])).
% 1.63/1.81 tff(3452,plain,
% 1.63/1.81 (~b(s(s(s(s(elem!1)))), z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3442, 3451])).
% 1.63/1.81 tff(3453,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[122, 3452])).
% 1.63/1.81 tff(3454,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3455,plain,
% 1.63/1.81 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3454, 122, 3442])).
% 1.63/1.81 tff(3456,plain,
% 1.63/1.81 (~(elem!1 = s(s(elem!1)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1555, 3455])).
% 1.63/1.81 tff(3457,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.63/1.81 tff(3458,plain,
% 1.63/1.81 (s(elem!1) = elem!1),
% 1.63/1.81 inference(symmetry,[status(thm)],[3457])).
% 1.63/1.81 tff(3459,plain,
% 1.63/1.81 (s(s(elem!1)) = s(elem!1)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3458])).
% 1.63/1.81 tff(3460,plain,
% 1.63/1.81 (s(elem!1) = s(s(elem!1))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3459])).
% 1.63/1.81 tff(3461,plain,
% 1.63/1.81 (elem!1 = s(s(elem!1))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3457, 3460])).
% 1.63/1.81 tff(3462,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1559, 3461])).
% 1.63/1.81 tff(3463,plain,((~(elem!1 = s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3464,plain,
% 1.63/1.81 (~(elem!1 = s(elem!1))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3463, 3456])).
% 1.63/1.81 tff(3465,plain,
% 1.63/1.81 (~(s(elem!1) = elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3464, 3446])).
% 1.63/1.81 tff(3466,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.63/1.81 tff(3467,plain,
% 1.63/1.81 (((~![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))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3468,plain,
% 1.63/1.81 ((~![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))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3469,plain,
% 1.63/1.81 ((~![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)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3468, 3467])).
% 1.63/1.81 tff(3470,plain,
% 1.63/1.81 ((s(elem!1) = elem!1) | r(s(elem!1), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3469, 47, 3466])).
% 1.63/1.81 tff(3471,plain,
% 1.63/1.81 (r(s(elem!1), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3470, 3465])).
% 1.63/1.81 tff(3472,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.63/1.81 tff(3473,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.63/1.81 tff(3474,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(elem!1, z)) | (~r(s(elem!1), 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(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3475,plain,
% 1.63/1.81 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3476,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(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~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(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3475])).
% 1.63/1.81 tff(3477,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(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~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(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3476, 3474])).
% 1.63/1.81 tff(3478,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(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3479,plain,
% 1.63/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3478, 3477])).
% 1.63/1.81 tff(3480,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3479, 65, 3473, 3443, 3472])).
% 1.63/1.81 tff(3481,plain,((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3482,plain,
% 1.63/1.81 (~r(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3481, 3471, 3443])).
% 1.63/1.81 tff(3483,plain,
% 1.63/1.81 (((~![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))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3484,plain,
% 1.63/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3485,plain,
% 1.63/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3484, 3483])).
% 1.63/1.81 tff(3486,plain,
% 1.63/1.81 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3485, 47])).
% 1.63/1.81 tff(3487,plain,
% 1.63/1.81 (elem!1 = z),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3486, 3482, 3442])).
% 1.63/1.81 tff(3488,plain,
% 1.63/1.81 (s(elem!1) = s(z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3487])).
% 1.63/1.81 tff(3489,plain,
% 1.63/1.81 (s(s(elem!1)) = s(s(z))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3488])).
% 1.63/1.81 tff(3490,plain,
% 1.63/1.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3489])).
% 1.63/1.81 tff(3491,plain,
% 1.63/1.81 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3490])).
% 1.63/1.81 tff(3492,plain,
% 1.63/1.81 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3491])).
% 1.63/1.81 tff(3493,plain,
% 1.63/1.81 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3492])).
% 1.63/1.81 tff(3494,plain,
% 1.63/1.81 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3493])).
% 1.63/1.81 tff(3495,plain,
% 1.63/1.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3490])).
% 1.63/1.81 tff(3496,plain,
% 1.63/1.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3495, 3494])).
% 1.63/1.81 tff(3497,plain,
% 1.63/1.81 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1540, 3455])).
% 1.63/1.81 tff(3498,plain,
% 1.63/1.81 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1259, 3497])).
% 1.63/1.81 tff(3499,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3492])).
% 1.63/1.81 tff(3500,plain,
% 1.63/1.81 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3499])).
% 1.63/1.81 tff(3501,plain,
% 1.63/1.81 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3492])).
% 1.63/1.81 tff(3502,plain,
% 1.63/1.81 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3501])).
% 1.63/1.81 tff(3503,plain,
% 1.63/1.81 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3492])).
% 1.63/1.81 tff(3504,plain,
% 1.63/1.81 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3503])).
% 1.63/1.81 tff(3505,plain,
% 1.63/1.81 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3487])).
% 1.63/1.81 tff(3506,plain,
% 1.63/1.81 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1493, 3497, 1489])).
% 1.63/1.81 tff(3507,plain,
% 1.63/1.81 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3487])).
% 1.63/1.81 tff(3508,plain,
% 1.63/1.81 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3507])).
% 1.63/1.81 tff(3509,plain,
% 1.63/1.81 (r(s(elem!1), z) <=> r(s(z), z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3488])).
% 1.63/1.81 tff(3510,plain,
% 1.63/1.81 (r(s(elem!1), z) <=> r(s(z), elem!1)),
% 1.63/1.81 inference(transitivity,[status(thm)],[3509, 3508])).
% 1.63/1.81 tff(3511,plain,
% 1.63/1.81 (r(s(z), elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3443, 3510])).
% 1.63/1.81 tff(3512,plain,
% 1.63/1.81 (~(s(s(elem!1)) = elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1561, 3456])).
% 1.63/1.81 tff(3513,plain,
% 1.63/1.81 (b(s(s(elem!1)), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1569, 3512, 1563])).
% 1.63/1.81 tff(3514,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.63/1.81 tff(3515,plain,
% 1.63/1.81 (~(s(elem!1) = elem!1)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3514, 3446])).
% 1.63/1.81 tff(3516,plain,
% 1.63/1.81 (r(s(elem!1), elem!1)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3470, 3515])).
% 1.63/1.81 tff(3517,plain,
% 1.63/1.81 (~(elem!1 = z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1607, 1604, 1600])).
% 1.63/1.81 tff(3518,plain,
% 1.63/1.81 (r(elem!1, z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3486, 3517, 3442])).
% 1.63/1.81 tff(3519,plain,
% 1.63/1.81 ($false),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3479, 65, 3518, 3443, 3516])).
% 1.63/1.81 tff(3520,plain,(b(s(s(elem!1)), z) | (~r(s(elem!1), z)) | b(elem!1, z) | (~b(s(s(elem!1)), elem!1)) | b(s(elem!1), elem!1) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.81 tff(3521,plain,
% 1.63/1.81 (b(s(s(elem!1)), z)),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3520, 3513, 3442, 3443, 3466, 3464])).
% 1.63/1.81 tff(3522,plain,
% 1.63/1.81 (r(s(z), z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3443, 3509])).
% 1.63/1.81 tff(3523,plain,
% 1.63/1.81 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.81 tff(3524,plain,
% 1.63/1.81 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3523])).
% 1.63/1.81 tff(3525,plain,
% 1.63/1.81 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(commutativity,[status(thm)],[])).
% 1.63/1.81 tff(3526,plain,
% 1.63/1.81 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1214])).
% 1.63/1.81 tff(3527,plain,
% 1.63/1.81 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3526, 3525])).
% 1.63/1.81 tff(3528,plain,
% 1.63/1.81 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3527])).
% 1.63/1.81 tff(3529,plain,
% 1.63/1.81 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1275, 3528])).
% 1.63/1.81 tff(3530,plain,
% 1.63/1.81 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1331])).
% 1.63/1.81 tff(3531,plain,
% 1.63/1.81 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1211])).
% 1.63/1.81 tff(3532,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.81 tff(3533,plain,
% 1.63/1.81 (r(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3532, 3531])).
% 1.63/1.81 tff(3534,plain,
% 1.63/1.81 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1495, 1954])).
% 1.63/1.81 tff(3535,plain,
% 1.63/1.81 (r(s(s(z)), s(s(s(s(z)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3534, 1953])).
% 1.63/1.81 tff(3536,plain,
% 1.63/1.81 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.81 tff(3537,plain,
% 1.63/1.81 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 1.63/1.81 inference(symmetry,[status(thm)],[3536])).
% 1.63/1.81 tff(3538,plain,
% 1.63/1.81 (b(s(s(s(s(z)))), z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[122, 3537])).
% 1.63/1.81 tff(3539,plain,
% 1.63/1.81 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1485])).
% 1.63/1.81 tff(3540,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.81 tff(3541,plain,
% 1.63/1.81 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3540])).
% 1.63/1.81 tff(3542,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), s(z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[123, 3541])).
% 1.63/1.81 tff(3543,plain,
% 1.63/1.81 (~r(s(s(z)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1139, 3542, 788])).
% 1.63/1.81 tff(3544,plain,
% 1.63/1.81 (b(s(s(z)), s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[271, 3543])).
% 1.63/1.81 tff(3545,plain,
% 1.63/1.81 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.81 tff(3546,plain,
% 1.63/1.81 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3545])).
% 1.63/1.81 tff(3547,plain,
% 1.63/1.81 (r(z, s(s(s(s(z)))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[495, 3546])).
% 1.63/1.81 tff(3548,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(z, s(s(z)))) | (~r(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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3549,plain,
% 1.63/1.81 (((~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3550,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(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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3549])).
% 1.63/1.81 tff(3551,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(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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3550, 3548])).
% 1.63/1.81 tff(3552,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(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3553,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(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 1.63/1.81 tff(3554,plain,
% 1.63/1.81 ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3553, 65])).
% 1.63/1.81 tff(3555,plain,
% 1.63/1.81 (~r(z, s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3554, 788, 3547])).
% 1.63/1.81 tff(3556,plain,
% 1.63/1.81 (b(z, s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[524, 3555])).
% 1.63/1.81 tff(3557,plain,
% 1.63/1.81 (b(s(s(z)), z)),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[1148, 1599])).
% 1.63/1.81 tff(3558,plain,
% 1.63/1.81 (~r(z, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[1431, 123, 495])).
% 1.63/1.81 tff(3559,plain,
% 1.63/1.81 (b(z, s(z))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[117, 3558])).
% 1.63/1.81 tff(3560,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3561,plain,
% 1.63/1.81 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(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(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3562,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[3561])).
% 1.63/1.81 tff(3563,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.81 inference(transitivity,[status(thm)],[3562, 3560])).
% 1.63/1.81 tff(3564,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.81 inference(quant_inst,[status(thm)],[])).
% 1.63/1.81 tff(3565,plain,
% 1.63/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3564, 3563])).
% 1.63/1.81 tff(3566,plain,
% 1.63/1.81 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[3565, 162, 3559, 3557, 3556, 3544, 1076])).
% 1.63/1.81 tff(3567,plain,
% 1.63/1.81 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3566, 3539])).
% 1.63/1.81 tff(3568,plain,
% 1.63/1.81 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.81 inference(unit_resolution,[status(thm)],[52, 3567])).
% 1.63/1.81 tff(3569,plain,
% 1.63/1.81 (r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3568, 1345])).
% 1.63/1.81 tff(3570,plain,
% 1.63/1.81 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1762])).
% 1.63/1.81 tff(3571,plain,
% 1.63/1.81 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.63/1.81 inference(symmetry,[status(thm)],[3570])).
% 1.63/1.81 tff(3572,plain,
% 1.63/1.81 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.63/1.81 inference(symmetry,[status(thm)],[1327])).
% 1.63/1.81 tff(3573,plain,
% 1.63/1.81 (b(z, s(s(elem!1)))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3556, 3572])).
% 1.63/1.81 tff(3574,plain,
% 1.63/1.81 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(monotonicity,[status(thm)],[1762])).
% 1.63/1.81 tff(3575,plain,
% 1.63/1.81 (b(s(s(elem!1)), s(z))),
% 1.63/1.81 inference(modus_ponens,[status(thm)],[3544, 3574])).
% 1.63/1.81 tff(3576,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.63/1.81 tff(3577,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.63/1.81 tff(3578,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3579,plain,
% 1.63/1.81 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.63/1.81 inference(rewrite,[status(thm)],[])).
% 1.63/1.81 tff(3580,plain,
% 1.63/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3579])).
% 1.63/1.82 tff(3581,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3580, 3578])).
% 1.63/1.82 tff(3582,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3583,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3582, 3581])).
% 1.63/1.82 tff(3584,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3583, 162, 3577, 1149, 3576, 121, 1148])).
% 1.63/1.82 tff(3585,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3586,plain,
% 1.63/1.82 (~b(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3585, 3575, 1148, 3573, 3559])).
% 1.63/1.82 tff(3587,plain,
% 1.63/1.82 (((~![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))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3588,plain,
% 1.63/1.82 ((~![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))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3589,plain,
% 1.63/1.82 ((~![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)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3588, 3587])).
% 1.63/1.82 tff(3590,plain,
% 1.63/1.82 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3589, 47])).
% 1.63/1.82 tff(3591,plain,
% 1.63/1.82 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3590, 330])).
% 1.63/1.82 tff(3592,plain,
% 1.63/1.82 (r(s(z), s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3591, 3586])).
% 1.63/1.82 tff(3593,plain,
% 1.63/1.82 (r(s(z), s(s(z)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3592, 3571])).
% 1.63/1.82 tff(3594,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(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(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(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3595,plain,
% 1.63/1.82 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3596,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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3595])).
% 1.63/1.82 tff(3597,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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3596, 3594])).
% 1.63/1.82 tff(3598,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(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3599,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3598, 3597])).
% 1.63/1.82 tff(3600,plain,
% 1.63/1.82 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3599, 65, 194, 3593, 3542])).
% 1.63/1.82 tff(3601,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3600, 3569])).
% 1.63/1.82 tff(3602,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~(elem!1 = z)) | (~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3603,plain,
% 1.63/1.82 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3602, 3538, 194, 1148, 1211, 3535, 3533])).
% 1.63/1.82 tff(3604,plain,
% 1.63/1.82 (b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[149, 3603])).
% 1.63/1.82 tff(3605,plain,
% 1.63/1.82 (b(s(s(s(s(z)))), s(z))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3604, 1423])).
% 1.63/1.82 tff(3606,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(z), elem!1)) | (~r(s(z), s(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(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3607,plain,
% 1.63/1.82 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3608,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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(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(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3607])).
% 1.63/1.82 tff(3609,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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(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(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3608, 3606])).
% 1.63/1.82 tff(3610,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(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3611,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3610, 3609])).
% 1.63/1.82 tff(3612,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3611, 65, 1655, 3532, 193])).
% 1.63/1.82 tff(3613,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3614,plain,
% 1.63/1.82 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3613, 3532, 1655])).
% 1.63/1.82 tff(3615,plain,
% 1.63/1.82 (b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[191, 3614])).
% 1.63/1.82 tff(3616,plain,
% 1.63/1.82 (b(s(z), s(s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3615, 1418])).
% 1.63/1.82 tff(3617,plain,
% 1.63/1.82 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = z)),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1211])).
% 1.63/1.82 tff(3618,plain,
% 1.63/1.82 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.63/1.82 inference(symmetry,[status(thm)],[3617])).
% 1.63/1.82 tff(3619,plain,
% 1.63/1.82 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3618])).
% 1.63/1.82 tff(3620,plain,
% 1.63/1.82 (~(s(s(s(z))) = elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[286, 3619])).
% 1.63/1.82 tff(3621,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.63/1.82 tff(3622,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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3623,plain,
% 1.63/1.82 (((~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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3624,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(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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3623])).
% 1.63/1.82 tff(3625,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(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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3624, 3622])).
% 1.63/1.82 tff(3626,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(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)))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3627,plain,
% 1.63/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3626, 3625])).
% 1.63/1.82 tff(3628,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3627, 65, 3532, 1495, 3621])).
% 1.63/1.82 tff(3629,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3630,plain,
% 1.63/1.82 (~r(elem!1, s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3629, 3532, 1495])).
% 1.63/1.82 tff(3631,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.63/1.82 tff(3632,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.63/1.82 tff(3633,plain,
% 1.63/1.82 (((~![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))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3634,plain,
% 1.63/1.82 ((~![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))))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3635,plain,
% 1.63/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3634, 3633])).
% 1.63/1.82 tff(3636,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3635, 47, 3632, 1559, 3631])).
% 1.63/1.82 tff(3637,plain,(r(elem!1, s(s(elem!1))) | b(elem!1, s(s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3638,plain,
% 1.63/1.82 (b(elem!1, s(s(elem!1)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3637, 3630, 1559])).
% 1.63/1.82 tff(3639,plain,
% 1.63/1.82 (r(z, s(s(s(s(z)))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3533, 3546])).
% 1.63/1.82 tff(3640,plain,
% 1.63/1.82 (~r(z, s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3554, 3535, 3639])).
% 1.63/1.82 tff(3641,plain,
% 1.63/1.82 (b(z, s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[524, 3640])).
% 1.63/1.82 tff(3642,assumption,(~(s(s(s(z))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.82 tff(3643,plain,
% 1.63/1.82 (~r(z, s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3554, 788, 803])).
% 1.63/1.82 tff(3644,plain,
% 1.63/1.82 (b(z, s(s(z)))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[524, 3643])).
% 1.63/1.82 tff(3645,plain,
% 1.63/1.82 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1213])).
% 1.63/1.82 tff(3646,plain,
% 1.63/1.82 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.63/1.82 inference(symmetry,[status(thm)],[3645])).
% 1.63/1.82 tff(3647,plain,
% 1.63/1.82 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1211])).
% 1.63/1.82 tff(3648,plain,
% 1.63/1.82 ((~r(s(s(s(z))), z)) <=> (~r(s(s(s(z))), elem!1))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[1381])).
% 1.63/1.82 tff(3649,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3650,plain,
% 1.63/1.82 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3651,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.63/1.82 inference(monotonicity,[status(thm)],[3650])).
% 1.63/1.82 tff(3652,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.82 inference(transitivity,[status(thm)],[3651, 3649])).
% 1.63/1.82 tff(3653,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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)))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3654,plain,
% 1.63/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3653, 3652])).
% 1.63/1.82 tff(3655,plain,
% 1.63/1.82 ($false),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3654, 162, 537, 444, 383, 600, 1076, 825])).
% 1.63/1.82 tff(3656,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.82 tff(3657,plain,
% 1.63/1.82 (~b(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3656, 444, 537, 383, 1076, 825])).
% 1.63/1.82 tff(3658,plain,
% 1.63/1.82 (r(s(s(s(z))), s(z))),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[595, 3657])).
% 1.63/1.82 tff(3659,plain,
% 1.63/1.82 (~r(s(s(s(z))), z)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[1375, 65, 97, 3658])).
% 1.63/1.82 tff(3660,plain,
% 1.63/1.82 (~r(s(s(s(z))), elem!1)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3659, 3648])).
% 1.63/1.82 tff(3661,plain,
% 1.63/1.82 (((~![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))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3662,plain,
% 1.63/1.82 ((~![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))),
% 1.63/1.82 inference(quant_inst,[status(thm)],[])).
% 1.63/1.82 tff(3663,plain,
% 1.63/1.82 ((~![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)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3662, 3661])).
% 1.63/1.82 tff(3664,plain,
% 1.63/1.82 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3663, 47])).
% 1.63/1.82 tff(3665,plain,
% 1.63/1.82 (b(s(s(s(z))), elem!1)),
% 1.63/1.82 inference(unit_resolution,[status(thm)],[3664, 3660, 3620])).
% 1.63/1.82 tff(3666,plain,
% 1.63/1.82 (b(s(s(s(z))), z)),
% 1.63/1.82 inference(modus_ponens,[status(thm)],[3665, 3647])).
% 1.63/1.82 tff(3667,plain,
% 1.63/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3668,plain,
% 1.63/1.82 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.82 inference(rewrite,[status(thm)],[])).
% 1.63/1.82 tff(3669,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[3668])).
% 1.63/1.83 tff(3670,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[3669, 3667])).
% 1.63/1.83 tff(3671,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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)))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3672,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3671, 3670])).
% 1.63/1.83 tff(3673,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3672, 162, 538, 537, 444, 298, 1076, 825])).
% 1.63/1.83 tff(3674,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(3675,plain,
% 1.63/1.83 (~b(s(s(s(z))), z)),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3674, 444, 537, 538, 1076, 825])).
% 1.63/1.83 tff(3676,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3675, 3666])).
% 1.63/1.83 tff(3677,plain,((~b(s(s(z)), s(s(s(z))))) | (~(elem!1 = z)) | (~r(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(3678,plain,
% 1.63/1.83 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3677, 383, 97, 537, 1211, 1076, 825, 538])).
% 1.63/1.83 tff(3679,plain,
% 1.63/1.83 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[441, 3678, 437])).
% 1.63/1.83 tff(3680,plain,
% 1.63/1.83 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[299, 3524])).
% 1.63/1.83 tff(3681,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)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3682,plain,
% 1.63/1.83 (((~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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3683,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(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[3682])).
% 1.63/1.83 tff(3684,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(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[3683, 3681])).
% 1.63/1.83 tff(3685,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(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))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3686,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3685, 3684])).
% 1.63/1.83 tff(3687,plain,
% 1.63/1.83 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3686, 65, 417, 788])).
% 1.63/1.83 tff(3688,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3687, 3680])).
% 1.63/1.83 tff(3689,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~(elem!1 = z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(3690,plain,
% 1.63/1.83 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3689, 3679, 1211, 788])).
% 1.63/1.83 tff(3691,plain,
% 1.63/1.83 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[337, 3690, 3642])).
% 1.63/1.83 tff(3692,plain,
% 1.63/1.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3691, 1332])).
% 1.63/1.83 tff(3693,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3694,plain,
% 1.63/1.83 (((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(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)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3695,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[3694])).
% 1.63/1.83 tff(3696,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[3695, 3693])).
% 1.63/1.83 tff(3697,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3698,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3697, 3696])).
% 1.63/1.83 tff(3699,plain,
% 1.63/1.83 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3698, 162, 537, 694, 1076, 825])).
% 1.63/1.83 tff(3700,plain,
% 1.63/1.83 (~b(s(z), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3699, 3692])).
% 1.63/1.83 tff(3701,plain,
% 1.63/1.83 (r(s(z), s(s(s(z))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[493, 3700])).
% 1.63/1.83 tff(3702,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(z), s(s(s(z))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3703,plain,
% 1.63/1.83 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3704,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)), s(s(s(z))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[3703])).
% 1.63/1.83 tff(3705,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)), s(s(s(z))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[3704, 3702])).
% 1.63/1.83 tff(3706,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)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3707,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(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3706, 3705])).
% 1.63/1.83 tff(3708,plain,
% 1.63/1.83 (~r(s(z), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3707, 65, 3701, 3679, 788])).
% 1.63/1.83 tff(3709,plain,
% 1.63/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3710,plain,
% 1.63/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3711,plain,
% 1.63/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3710, 3709])).
% 1.63/1.83 tff(3712,plain,
% 1.63/1.83 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3711, 47])).
% 1.63/1.83 tff(3713,plain,
% 1.63/1.83 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3712, 265])).
% 1.63/1.83 tff(3714,plain,
% 1.63/1.83 (b(s(z), s(s(z)))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3713, 3708])).
% 1.63/1.83 tff(3715,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3716,plain,
% 1.63/1.83 (((~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(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), 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(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3717,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[3716])).
% 1.63/1.83 tff(3718,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[3717, 3715])).
% 1.63/1.83 tff(3719,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3720,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3719, 3718])).
% 1.63/1.83 tff(3721,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3720, 162, 383, 3714, 694, 825, 1437])).
% 1.63/1.83 tff(3722,plain,((~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))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(3723,plain,
% 1.63/1.83 (~b(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3722, 97, 825, 1437, 788, 3644, 1076, 1211, 3642, 694, 538])).
% 1.63/1.83 tff(3724,plain,
% 1.63/1.83 (r(s(s(z)), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[271, 3723])).
% 1.63/1.83 tff(3725,plain,
% 1.63/1.83 (r(s(s(elem!1)), s(z))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3724, 3646])).
% 1.63/1.83 tff(3726,plain,
% 1.63/1.83 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[1214])).
% 1.63/1.83 tff(3727,plain,
% 1.63/1.83 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.63/1.83 inference(symmetry,[status(thm)],[3726])).
% 1.63/1.83 tff(3728,plain,
% 1.63/1.83 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3689, 417, 1211, 788])).
% 1.63/1.83 tff(3729,plain,
% 1.63/1.83 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[337, 3728, 3642])).
% 1.63/1.83 tff(3730,plain,
% 1.63/1.83 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3729, 1332])).
% 1.63/1.83 tff(3731,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3732,plain,
% 1.63/1.83 (((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3733,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[3732])).
% 1.63/1.83 tff(3734,plain,
% 1.63/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[3733, 3731])).
% 1.63/1.83 tff(3735,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3736,plain,
% 1.63/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 1.63/1.83 tff(3737,plain,
% 1.63/1.83 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3736, 162, 537, 694, 1076, 825])).
% 1.63/1.83 tff(3738,plain,
% 1.63/1.83 (~b(s(s(s(z))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3737, 3730])).
% 1.63/1.83 tff(3739,plain,
% 1.63/1.83 (r(s(s(s(z))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[595, 3738])).
% 1.63/1.83 tff(3740,plain,
% 1.63/1.83 (r(s(s(s(elem!1))), s(z))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3739, 3727])).
% 1.63/1.83 tff(3741,plain,
% 1.63/1.83 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.83 inference(symmetry,[status(thm)],[2066])).
% 1.63/1.83 tff(3742,plain,
% 1.63/1.83 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[417, 3741])).
% 1.63/1.83 tff(3743,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.63/1.83 tff(3744,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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(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(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3745,plain,
% 1.63/1.83 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.63/1.83 inference(rewrite,[status(thm)],[])).
% 1.63/1.83 tff(3746,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(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.63/1.83 inference(monotonicity,[status(thm)],[3745])).
% 1.63/1.83 tff(3747,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(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.63/1.83 inference(transitivity,[status(thm)],[3746, 3744])).
% 1.63/1.83 tff(3748,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(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.83 inference(quant_inst,[status(thm)],[])).
% 1.63/1.83 tff(3749,plain,
% 1.63/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.63/1.83 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 1.63/1.83 tff(3750,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3749, 65, 3367, 2313, 3743])).
% 1.63/1.83 tff(3751,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.83 tff(3752,plain,
% 1.63/1.83 (~r(s(s(s(elem!1))), s(z))),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3751, 3742, 3367])).
% 1.63/1.83 tff(3753,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(unit_resolution,[status(thm)],[3752, 3740])).
% 1.63/1.83 tff(3754,plain,((~r(s(s(z)), s(s(s(z))))) | (~(elem!1 = z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(3755,plain,
% 1.63/1.84 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3754, 3725, 3644, 694, 1076, 825, 1211, 3642, 788])).
% 1.63/1.84 tff(3756,plain,
% 1.63/1.84 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[441, 3755, 437])).
% 1.63/1.84 tff(3757,plain,
% 1.63/1.84 (~b(s(s(s(z))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3674, 3756, 3644, 538, 1076, 825])).
% 1.63/1.84 tff(3758,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.63/1.84 tff(3759,plain,
% 1.63/1.84 (b(s(s(s(z))), z)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3758, 3647])).
% 1.63/1.84 tff(3760,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[376, 3759])).
% 1.63/1.84 tff(3761,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(3762,plain,
% 1.63/1.84 (~b(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3761, 3757, 1211])).
% 1.63/1.84 tff(3763,plain,
% 1.63/1.84 (r(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3664, 3762, 3620])).
% 1.63/1.84 tff(3764,plain,
% 1.63/1.84 (r(s(s(s(z))), z)),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3763, 1382])).
% 1.63/1.84 tff(3765,plain,
% 1.63/1.84 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1389, 65, 194])).
% 1.63/1.84 tff(3766,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3765, 3764])).
% 1.63/1.84 tff(3767,plain,
% 1.63/1.84 (b(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[595, 3766])).
% 1.63/1.84 tff(3768,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3736, 162, 537, 600, 694, 1076, 825, 693])).
% 1.63/1.84 tff(3769,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(3770,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3769, 3767, 3644, 694, 1076, 825])).
% 1.63/1.84 tff(3771,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3770, 3530])).
% 1.63/1.84 tff(3772,plain,
% 1.63/1.84 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[337, 3771, 3642])).
% 1.63/1.84 tff(3773,plain,
% 1.63/1.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3772, 3524])).
% 1.63/1.84 tff(3774,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(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3775,plain,
% 1.63/1.84 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3776,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(s(z)))))) | (~r(s(s(s(z))), s(s(s(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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[3775])).
% 1.63/1.84 tff(3777,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(s(z)))))) | (~r(s(s(s(z))), s(s(s(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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[3776, 3774])).
% 1.63/1.84 tff(3778,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(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(3779,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3778, 3777])).
% 1.63/1.84 tff(3780,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3779, 65, 97, 803, 3764])).
% 1.63/1.84 tff(3781,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3780, 3773])).
% 1.63/1.84 tff(3782,plain,((~r(z, s(z))) | (~(elem!1 = z)) | (~r(z, s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(3783,plain,
% 1.63/1.84 (~r(z, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3782, 825, 803, 3642, 694, 1076, 1211, 194, 538, 788, 1437])).
% 1.63/1.84 tff(3784,plain,
% 1.63/1.84 (b(z, s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[117, 3783])).
% 1.63/1.84 tff(3785,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3769, 600, 537, 694, 1076, 825])).
% 1.63/1.84 tff(3786,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3785, 3530])).
% 1.63/1.84 tff(3787,plain,
% 1.63/1.84 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[337, 3786, 3642])).
% 1.63/1.84 tff(3788,plain,
% 1.63/1.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3787, 3524])).
% 1.63/1.84 tff(3789,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3790,plain,
% 1.63/1.84 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, 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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3791,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[3790])).
% 1.63/1.84 tff(3792,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[3791, 3789])).
% 1.63/1.84 tff(3793,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(3794,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3793, 3792])).
% 1.63/1.84 tff(3795,plain,
% 1.63/1.84 (~b(z, s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3794, 162, 121, 538, 600, 1076, 825])).
% 1.63/1.84 tff(3796,plain,
% 1.63/1.84 (~b(z, s(s(s(elem!1))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3795, 2286])).
% 1.63/1.84 tff(3797,plain,
% 1.63/1.84 (r(z, s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[2296, 3796])).
% 1.63/1.84 tff(3798,plain,
% 1.63/1.84 (r(z, s(s(s(z))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3797, 2306])).
% 1.63/1.84 tff(3799,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(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(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3800,plain,
% 1.63/1.84 (((~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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3801,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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[3800])).
% 1.63/1.84 tff(3802,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(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(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[3801, 3799])).
% 1.63/1.84 tff(3803,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(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))))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(3804,plain,
% 1.63/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3803, 3802])).
% 1.63/1.84 tff(3805,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3804, 65, 3798, 803])).
% 1.63/1.84 tff(3806,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3805, 3788])).
% 1.63/1.84 tff(3807,plain,((~b(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~r(z, s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~b(z, 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(z)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(3808,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3807, 3784, 803, 3642, 1211, 538, 1076, 825, 3644, 694])).
% 1.63/1.84 tff(3809,plain,
% 1.63/1.84 (r(s(s(s(z))), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[595, 3808])).
% 1.63/1.84 tff(3810,plain,
% 1.63/1.84 (~r(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1392, 3809, 194, 1211])).
% 1.63/1.84 tff(3811,plain,
% 1.63/1.84 (b(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3664, 3810, 3620])).
% 1.63/1.84 tff(3812,plain,
% 1.63/1.84 (b(s(s(s(z))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3761, 3811, 1211])).
% 1.63/1.84 tff(3813,plain,
% 1.63/1.84 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3674, 3812, 3644, 538, 1076, 825])).
% 1.63/1.84 tff(3814,plain,
% 1.63/1.84 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[441, 3813, 437])).
% 1.63/1.84 tff(3815,plain,
% 1.63/1.84 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3689, 3814, 1211, 788])).
% 1.63/1.84 tff(3816,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[337, 3815, 3642])).
% 1.63/1.84 tff(3817,plain,
% 1.63/1.84 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3816, 1332])).
% 1.63/1.84 tff(3818,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.63/1.84 inference(symmetry,[status(thm)],[3574])).
% 1.63/1.84 tff(3819,plain,
% 1.63/1.84 (~r(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3754, 3814, 3644, 694, 1076, 825, 1211, 3642, 788])).
% 1.63/1.84 tff(3820,plain,
% 1.63/1.84 (((~![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)))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3821,plain,
% 1.63/1.84 ((~![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)))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(3822,plain,
% 1.63/1.84 ((~![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))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3821, 3820])).
% 1.63/1.84 tff(3823,plain,
% 1.63/1.84 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3822, 47])).
% 1.63/1.84 tff(3824,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3823, 331])).
% 1.63/1.84 tff(3825,plain,
% 1.63/1.84 (b(s(s(elem!1)), s(z))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3824, 3819])).
% 1.63/1.84 tff(3826,plain,
% 1.63/1.84 (b(s(s(z)), s(z))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3825, 3818])).
% 1.63/1.84 tff(3827,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3828,plain,
% 1.63/1.84 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, 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(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(rewrite,[status(thm)],[])).
% 1.63/1.84 tff(3829,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[3828])).
% 1.63/1.84 tff(3830,plain,
% 1.63/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[3829, 3827])).
% 1.63/1.84 tff(3831,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.84 inference(quant_inst,[status(thm)],[])).
% 1.63/1.84 tff(3832,plain,
% 1.63/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3831, 3830])).
% 1.63/1.84 tff(3833,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3832, 162, 3784, 3644, 3826, 3812, 1076, 3817])).
% 1.63/1.84 tff(3834,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(3835,plain,
% 1.63/1.84 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3834, 3538, 1211, 3529, 3616, 3535, 3557, 194, 3639, 3605])).
% 1.63/1.84 tff(3836,plain,
% 1.63/1.84 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3835, 3539])).
% 1.63/1.84 tff(3837,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[52, 3836])).
% 1.63/1.84 tff(3838,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3837, 1345])).
% 1.63/1.84 tff(3839,plain,
% 1.63/1.84 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.63/1.84 inference(symmetry,[status(thm)],[1476])).
% 1.63/1.84 tff(3840,plain,
% 1.63/1.84 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[2305])).
% 1.63/1.84 tff(3841,plain,
% 1.63/1.84 (~r(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1392, 385, 194, 1211])).
% 1.63/1.84 tff(3842,plain,
% 1.63/1.84 (b(s(s(s(z))), elem!1)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3664, 3841, 3620])).
% 1.63/1.84 tff(3843,plain,
% 1.63/1.84 (b(s(s(s(z))), z)),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3761, 3842, 1211])).
% 1.63/1.84 tff(3844,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.84 inference(transitivity,[status(thm)],[1293, 1339])).
% 1.63/1.84 tff(3845,plain,
% 1.63/1.84 (~b(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3150, 444, 537, 538, 298])).
% 1.63/1.84 tff(3846,plain,
% 1.63/1.84 (r(s(s(s(z))), s(s(z)))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[458, 3845, 436])).
% 1.63/1.84 tff(3847,plain,
% 1.63/1.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[685, 65, 3846, 644])).
% 1.63/1.84 tff(3848,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.84 inference(monotonicity,[status(thm)],[1216, 1270])).
% 1.63/1.84 tff(3849,plain,
% 1.63/1.84 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.84 inference(symmetry,[status(thm)],[3848])).
% 1.63/1.84 tff(3850,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.63/1.84 tff(3851,plain,
% 1.63/1.84 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.84 inference(modus_ponens,[status(thm)],[3850, 3849])).
% 1.63/1.84 tff(3852,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.63/1.84 tff(3853,plain,
% 1.63/1.84 ($false),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3852, 3851])).
% 1.63/1.84 tff(3854,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.84 tff(3855,plain,
% 1.63/1.84 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[3854, 3847, 1211])).
% 1.63/1.84 tff(3856,plain,
% 1.63/1.84 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.84 inference(unit_resolution,[status(thm)],[1304, 3855, 1275])).
% 1.63/1.85 tff(3857,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3856, 3844])).
% 1.63/1.85 tff(3858,plain,
% 1.63/1.85 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[3523])).
% 1.63/1.85 tff(3859,plain,
% 1.63/1.85 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[670, 65, 3846, 644])).
% 1.63/1.85 tff(3860,plain,
% 1.63/1.85 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 1.63/1.85 tff(3861,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[337, 3860, 3529])).
% 1.63/1.85 tff(3862,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3861, 1332])).
% 1.63/1.85 tff(3863,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3864,plain,
% 1.63/1.85 (((~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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(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(s(s(z)))), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3865,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[3864])).
% 1.63/1.85 tff(3866,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[3865, 3863])).
% 1.63/1.85 tff(3867,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(3868,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 1.63/1.85 tff(3869,plain,
% 1.63/1.85 (~b(s(z), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3868, 162, 298, 694, 1076, 3862, 3857])).
% 1.63/1.85 tff(3870,plain,
% 1.63/1.85 (r(s(z), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[493, 3869])).
% 1.63/1.85 tff(3871,plain,
% 1.63/1.85 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1211])).
% 1.63/1.85 tff(3872,plain,
% 1.63/1.85 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[3871, 2306])).
% 1.63/1.85 tff(3873,plain,
% 1.63/1.85 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1211])).
% 1.63/1.85 tff(3874,plain,
% 1.63/1.85 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.85 inference(symmetry,[status(thm)],[3873])).
% 1.63/1.85 tff(3875,plain,
% 1.63/1.85 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1214])).
% 1.63/1.85 tff(3876,plain,
% 1.63/1.85 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.63/1.85 inference(symmetry,[status(thm)],[3875])).
% 1.63/1.85 tff(3877,plain,
% 1.63/1.85 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.63/1.85 inference(transitivity,[status(thm)],[3876, 3874])).
% 1.63/1.85 tff(3878,plain,
% 1.63/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[298, 3877])).
% 1.63/1.85 tff(3879,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[1213, 1214])).
% 1.63/1.85 tff(3880,plain,
% 1.63/1.85 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.85 inference(symmetry,[status(thm)],[3879])).
% 1.63/1.85 tff(3881,plain,
% 1.63/1.85 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[444, 3880])).
% 1.63/1.85 tff(3882,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.63/1.85 tff(3883,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.63/1.85 tff(3884,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.63/1.85 tff(3885,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3886,plain,
% 1.63/1.85 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3887,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[3886])).
% 1.63/1.85 tff(3888,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.63/1.85 inference(transitivity,[status(thm)],[3887, 3885])).
% 1.63/1.85 tff(3889,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(3890,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3889, 3888])).
% 1.63/1.85 tff(3891,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3890, 162, 1600, 1248, 3884, 3883, 3882])).
% 1.63/1.85 tff(3892,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(3893,plain,
% 1.63/1.85 (~b(elem!1, s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3892, 3881, 1248, 3878, 1600])).
% 1.63/1.85 tff(3894,plain,
% 1.63/1.85 (r(elem!1, s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1483, 3893, 1473])).
% 1.63/1.85 tff(3895,plain,
% 1.63/1.85 (r(z, s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3894, 3872])).
% 1.63/1.85 tff(3896,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(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3897,plain,
% 1.63/1.85 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3898,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(z, s(s(s(z))))) | (~r(s(z), 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(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[3897])).
% 1.63/1.85 tff(3899,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(z, s(s(s(z))))) | (~r(s(z), 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(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[3898, 3896])).
% 1.63/1.85 tff(3900,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(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(3901,plain,
% 1.63/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3900, 3899])).
% 1.63/1.85 tff(3902,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3901, 65, 194, 3895, 3870, 803])).
% 1.63/1.85 tff(3903,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(3904,plain,
% 1.63/1.85 (~b(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3903, 3843, 803, 194, 694, 1076, 1211, 1275, 644, 3644, 538, 1248, 1600])).
% 1.63/1.85 tff(3905,plain,
% 1.63/1.85 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[441, 3904, 437])).
% 1.63/1.85 tff(3906,plain,
% 1.63/1.85 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3689, 3905, 1211, 788])).
% 1.63/1.85 tff(3907,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[337, 3906, 3529])).
% 1.63/1.85 tff(3908,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3907, 1332])).
% 1.63/1.85 tff(3909,plain,
% 1.63/1.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[796, 3905, 788])).
% 1.63/1.85 tff(3910,plain,
% 1.63/1.85 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3854, 3909, 1211])).
% 1.63/1.85 tff(3911,plain,
% 1.63/1.85 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1304, 3910, 1275])).
% 1.63/1.85 tff(3912,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3911, 3844])).
% 1.63/1.85 tff(3913,plain,
% 1.63/1.85 (~b(s(z), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3868, 162, 3843, 694, 1076, 3908, 3912])).
% 1.63/1.85 tff(3914,plain,
% 1.63/1.85 (r(s(z), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[493, 3913])).
% 1.63/1.85 tff(3915,plain,
% 1.63/1.85 (~r(s(z), s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3707, 65, 3914, 3905, 788])).
% 1.63/1.85 tff(3916,plain,
% 1.63/1.85 (b(s(z), s(s(z)))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3713, 3915])).
% 1.63/1.85 tff(3917,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), 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)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3918,plain,
% 1.63/1.85 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), 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)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3919,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), 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))))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[3918])).
% 1.63/1.85 tff(3920,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), 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)))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[3919, 3917])).
% 1.63/1.85 tff(3921,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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)))))))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(3922,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), 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))))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3921, 3920])).
% 1.63/1.85 tff(3923,plain,
% 1.63/1.85 (~b(z, s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3922, 162, 3644, 3916, 3843, 1076, 3908])).
% 1.63/1.85 tff(3924,plain,
% 1.63/1.85 (r(z, s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[117, 3923])).
% 1.63/1.85 tff(3925,plain,
% 1.63/1.85 (~r(z, s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2609, 65, 3924, 385])).
% 1.63/1.85 tff(3926,plain,
% 1.63/1.85 (~r(z, s(s(s(elem!1))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3925, 3840])).
% 1.63/1.85 tff(3927,plain,
% 1.63/1.85 (b(z, s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2296, 3926])).
% 1.63/1.85 tff(3928,plain,
% 1.63/1.85 (b(z, s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3927, 3839])).
% 1.63/1.85 tff(3929,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3930,plain,
% 1.63/1.85 (((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3931,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.63/1.85 inference(monotonicity,[status(thm)],[3930])).
% 1.63/1.85 tff(3932,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.63/1.85 inference(transitivity,[status(thm)],[3931, 3929])).
% 1.63/1.85 tff(3933,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.63/1.85 inference(quant_inst,[status(thm)],[])).
% 1.63/1.85 tff(3934,plain,
% 1.63/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3933, 3932])).
% 1.63/1.85 tff(3935,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3934, 162, 3843, 1076, 3908, 3912, 3928])).
% 1.63/1.85 tff(3936,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = 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(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(3937,plain,
% 1.63/1.85 (~r(s(s(s(z))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3936, 3538, 1211, 3535, 3616, 1275, 3639, 194, 3838, 3557, 3638, 1600])).
% 1.63/1.85 tff(3938,plain,
% 1.63/1.85 (b(s(s(s(z))), s(z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[595, 3937])).
% 1.63/1.85 tff(3939,plain,
% 1.63/1.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[796, 417, 788])).
% 1.63/1.85 tff(3940,plain,
% 1.63/1.85 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3854, 3939, 1211])).
% 1.63/1.85 tff(3941,plain,
% 1.63/1.85 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1304, 3940, 1275])).
% 1.63/1.85 tff(3942,plain,
% 1.63/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3941, 3844])).
% 1.63/1.85 tff(3943,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[337, 3728, 3529])).
% 1.63/1.85 tff(3944,plain,
% 1.63/1.85 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3943, 1332])).
% 1.63/1.85 tff(3945,plain,
% 1.63/1.85 ($false),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[1443, 162, 600, 694, 1437, 3944, 3942])).
% 1.63/1.85 tff(3946,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.85 tff(3947,plain,
% 1.63/1.85 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3946, 3938, 3616, 3605, 1211, 1275, 3535])).
% 1.63/1.85 tff(3948,plain,
% 1.63/1.85 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[441, 3947, 437])).
% 1.63/1.85 tff(3949,plain,
% 1.63/1.85 (~b(s(s(s(z))), z)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3903, 3948, 3639, 194, 3616, 3538, 1211, 1275, 3838, 3641, 3557, 3638, 1600])).
% 1.63/1.85 tff(3950,plain,
% 1.63/1.85 (~b(s(s(s(z))), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3761, 3949, 1211])).
% 1.63/1.85 tff(3951,plain,
% 1.63/1.85 (r(s(s(s(z))), elem!1)),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3664, 3950, 3620])).
% 1.63/1.85 tff(3952,plain,
% 1.63/1.85 (r(s(s(s(z))), z)),
% 1.63/1.85 inference(modus_ponens,[status(thm)],[3951, 1382])).
% 1.63/1.85 tff(3953,plain,
% 1.63/1.85 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[2269, 65, 194])).
% 1.63/1.85 tff(3954,plain,
% 1.63/1.85 (~r(s(z), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[3953, 3952])).
% 1.63/1.85 tff(3955,plain,
% 1.63/1.85 (b(s(z), s(s(s(z))))),
% 1.63/1.85 inference(unit_resolution,[status(thm)],[493, 3954])).
% 1.63/1.85 tff(3956,plain,
% 1.63/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.85 tff(3957,plain,
% 1.63/1.85 (((~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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.85 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(3958,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[3957])).
% 1.63/1.86 tff(3959,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[3958, 3956])).
% 1.63/1.86 tff(3960,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(3961,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3960, 3959])).
% 1.63/1.86 tff(3962,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3961, 162, 600, 599, 694, 1437, 693])).
% 1.63/1.86 tff(3963,plain,((~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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(3964,plain,
% 1.63/1.86 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3963, 3938, 3955, 3616, 3605])).
% 1.63/1.86 tff(3965,plain,
% 1.63/1.86 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3964, 3530])).
% 1.63/1.86 tff(3966,plain,
% 1.63/1.86 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[337, 3965, 3529])).
% 1.63/1.86 tff(3967,plain,
% 1.63/1.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3966, 3524])).
% 1.63/1.86 tff(3968,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3182, 65, 3639, 3952])).
% 1.63/1.86 tff(3969,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3968, 3967])).
% 1.63/1.86 tff(3970,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~(elem!1 = z)) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (elem!1 = s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(3971,plain,
% 1.63/1.86 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3970, 3487, 3522, 3498, 3513, 3521, 122, 3456, 3511, 3506])).
% 1.63/1.86 tff(3972,plain,
% 1.63/1.86 (((~![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))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(3973,plain,
% 1.63/1.86 ((~![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))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(3974,plain,
% 1.63/1.86 ((~![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)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3973, 3972])).
% 1.63/1.86 tff(3975,plain,
% 1.63/1.86 ((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)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3974, 47])).
% 1.63/1.86 tff(3976,plain,
% 1.63/1.86 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3975, 3971, 3455])).
% 1.63/1.86 tff(3977,plain,
% 1.63/1.86 (b(z, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3976, 3505])).
% 1.63/1.86 tff(3978,plain,
% 1.63/1.86 (b(z, s(s(s(s(z)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3977, 3504])).
% 1.63/1.86 tff(3979,plain,
% 1.63/1.86 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.63/1.86 inference(monotonicity,[status(thm)],[3492])).
% 1.63/1.86 tff(3980,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 1.63/1.86 inference(symmetry,[status(thm)],[3979])).
% 1.63/1.86 tff(3981,plain,
% 1.63/1.86 (b(s(s(s(s(z)))), z)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[122, 3980])).
% 1.63/1.86 tff(3982,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.63/1.86 inference(monotonicity,[status(thm)],[3487])).
% 1.63/1.86 tff(3983,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.86 inference(symmetry,[status(thm)],[3982])).
% 1.63/1.86 tff(3984,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[122, 3983])).
% 1.63/1.86 tff(3985,plain,
% 1.63/1.86 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.63/1.86 inference(monotonicity,[status(thm)],[3489])).
% 1.63/1.86 tff(3986,plain,
% 1.63/1.86 (b(s(s(z)), z)),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3521, 3985])).
% 1.63/1.86 tff(3987,plain,
% 1.63/1.86 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.86 tff(3988,plain,
% 1.63/1.86 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[3987])).
% 1.63/1.86 tff(3989,plain,
% 1.63/1.86 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[1211])).
% 1.63/1.86 tff(3990,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.86 tff(3991,plain,
% 1.63/1.86 (b(z, s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3990, 3989])).
% 1.63/1.86 tff(3992,plain,
% 1.63/1.86 (b(z, s(s(s(s(z)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3991, 3988])).
% 1.63/1.86 tff(3993,plain,
% 1.63/1.86 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[1762])).
% 1.63/1.86 tff(3994,plain,
% 1.63/1.86 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.63/1.86 inference(symmetry,[status(thm)],[3993])).
% 1.63/1.86 tff(3995,plain,
% 1.63/1.86 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[1213])).
% 1.63/1.86 tff(3996,plain,
% 1.63/1.86 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 1.63/1.86 inference(symmetry,[status(thm)],[3995])).
% 1.63/1.86 tff(3997,plain,
% 1.63/1.86 (r(z, s(s(elem!1)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[55, 3996])).
% 1.63/1.86 tff(3998,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.63/1.86 tff(3999,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(z), z)) | (~r(z, s(s(elem!1)))) | (~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(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4000,plain,
% 1.63/1.86 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4001,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(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~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(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[4000])).
% 1.63/1.86 tff(4002,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(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~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(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[4001, 3999])).
% 1.63/1.86 tff(4003,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(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(4004,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4003, 4002])).
% 1.63/1.86 tff(4005,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4004, 65, 3998, 1246, 194])).
% 1.63/1.86 tff(4006,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(4007,plain,
% 1.63/1.86 (~r(s(z), s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4006, 3997, 194])).
% 1.63/1.86 tff(4008,plain,
% 1.63/1.86 (b(s(z), s(s(elem!1)))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3591, 4007])).
% 1.63/1.86 tff(4009,plain,
% 1.63/1.86 (b(s(z), s(s(z)))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4008, 3994])).
% 1.63/1.86 tff(4010,plain,
% 1.63/1.86 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[3689, 417, 788, 1211])).
% 1.63/1.86 tff(4011,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[337, 4010, 3529])).
% 1.63/1.86 tff(4012,plain,
% 1.63/1.86 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4011, 1332])).
% 1.63/1.86 tff(4013,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[3941, 1293])).
% 1.63/1.86 tff(4014,plain,
% 1.63/1.86 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4013, 1339])).
% 1.63/1.86 tff(4015,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(z, s(s(elem!1)))) | (~r(s(s(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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4016,plain,
% 1.63/1.86 (((~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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4017,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(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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[4016])).
% 1.63/1.86 tff(4018,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(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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[4017, 4015])).
% 1.63/1.86 tff(4019,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(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(4020,plain,
% 1.63/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4019, 4018])).
% 1.63/1.86 tff(4021,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4020, 65, 3998, 2304, 2313])).
% 1.63/1.86 tff(4022,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(4023,plain,
% 1.63/1.86 (~r(z, s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4022, 3742, 3998])).
% 1.63/1.86 tff(4024,plain,
% 1.63/1.86 (b(z, s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[2296, 4023])).
% 1.63/1.86 tff(4025,plain,
% 1.63/1.86 (b(z, s(s(s(z))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4024, 3839])).
% 1.63/1.86 tff(4026,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(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))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4027,plain,
% 1.63/1.86 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(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(s(z)))), s(s(s(z))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4028,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(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)))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[4027])).
% 1.63/1.86 tff(4029,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(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))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[4028, 4026])).
% 1.63/1.86 tff(4030,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(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))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(4031,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4030, 4029])).
% 1.63/1.86 tff(4032,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4031, 162, 1076, 693, 1075, 4025, 4014])).
% 1.63/1.86 tff(4033,plain,((~r(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(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (~r(z, s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(4034,plain,
% 1.63/1.86 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4033, 417, 1075, 1076, 1211, 3998, 1275, 788])).
% 1.63/1.86 tff(4035,plain,
% 1.63/1.86 ($false),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4034, 4012])).
% 1.63/1.86 tff(4036,plain,((~r(s(s(z)), s(s(s(z))))) | (~(elem!1 = z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.86 tff(4037,plain,
% 1.63/1.86 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4036, 3992, 1211, 1076, 3997, 1275, 3535])).
% 1.63/1.86 tff(4038,plain,
% 1.63/1.86 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[441, 4037, 437])).
% 1.63/1.86 tff(4039,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.63/1.86 tff(4040,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4041,plain,
% 1.63/1.86 (((~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)))), 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4042,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[4041])).
% 1.63/1.86 tff(4043,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[4042, 4040])).
% 1.63/1.86 tff(4044,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(4045,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4044, 4043])).
% 1.63/1.86 tff(4046,plain,
% 1.63/1.86 (~b(z, s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4045, 162, 298, 1076, 693, 1075])).
% 1.63/1.86 tff(4047,plain,
% 1.63/1.86 (~b(z, s(s(s(elem!1))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4046, 2286])).
% 1.63/1.86 tff(4048,plain,
% 1.63/1.86 (r(z, s(s(s(elem!1))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[2296, 4047])).
% 1.63/1.86 tff(4049,plain,
% 1.63/1.86 (r(z, s(s(s(z))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4048, 2306])).
% 1.63/1.86 tff(4050,plain,
% 1.63/1.86 (~r(s(z), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[1966, 4049, 194])).
% 1.63/1.86 tff(4051,plain,
% 1.63/1.86 (b(s(z), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[493, 4050])).
% 1.63/1.86 tff(4052,plain,
% 1.63/1.86 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.86 inference(symmetry,[status(thm)],[1293])).
% 1.63/1.86 tff(4053,plain,
% 1.63/1.86 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[1338, 4052])).
% 1.63/1.86 tff(4054,plain,
% 1.63/1.86 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[4053])).
% 1.63/1.86 tff(4055,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4056,plain,
% 1.63/1.86 (((~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(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(s(s(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(s(z)))), s(s(s(z))))))),
% 1.63/1.86 inference(rewrite,[status(thm)],[])).
% 1.63/1.86 tff(4057,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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)))))))),
% 1.63/1.86 inference(monotonicity,[status(thm)],[4056])).
% 1.63/1.86 tff(4058,plain,
% 1.63/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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))))))),
% 1.63/1.86 inference(transitivity,[status(thm)],[4057, 4055])).
% 1.63/1.86 tff(4059,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(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)))),
% 1.63/1.86 inference(quant_inst,[status(thm)],[])).
% 1.63/1.86 tff(4060,plain,
% 1.63/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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)))))),
% 1.63/1.86 inference(modus_ponens,[status(thm)],[4059, 4058])).
% 1.63/1.86 tff(4061,plain,
% 1.63/1.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.86 inference(unit_resolution,[status(thm)],[4060, 162, 298, 1076, 693, 1075])).
% 1.63/1.87 tff(4062,plain,
% 1.63/1.87 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4061, 4054])).
% 1.63/1.87 tff(4063,plain,
% 1.63/1.87 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1304, 4062, 1275])).
% 1.63/1.87 tff(4064,plain,
% 1.63/1.87 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[3854, 4063, 1211])).
% 1.63/1.87 tff(4065,plain,
% 1.63/1.87 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[796, 4064, 788])).
% 1.63/1.87 tff(4066,plain,
% 1.63/1.87 (b(s(s(z)), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[441, 4065, 437])).
% 1.63/1.87 tff(4067,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(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(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(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(s(z))), s(s(s(s(z)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4068,plain,
% 1.63/1.87 (((~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)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), 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(s(z))), s(s(s(s(z)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4069,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(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(s(z))), s(s(s(s(z))))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[4068])).
% 1.63/1.87 tff(4070,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(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(s(z))), s(s(s(s(z)))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[4069, 4067])).
% 1.63/1.87 tff(4071,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(4072,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4071, 4070])).
% 1.63/1.87 tff(4073,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4072, 162, 4066, 4039, 298, 4051, 693, 1075])).
% 1.63/1.87 tff(4074,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~(elem!1 = z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(4075,plain,
% 1.63/1.87 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4074, 298, 1075, 4039, 194, 1211, 788, 1275, 1076])).
% 1.63/1.87 tff(4076,plain,
% 1.63/1.87 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1336, 4075, 1211])).
% 1.63/1.87 tff(4077,plain,
% 1.63/1.87 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[337, 4076, 3529])).
% 1.63/1.87 tff(4078,plain,
% 1.63/1.87 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4077, 3524])).
% 1.63/1.87 tff(4079,plain,
% 1.63/1.87 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2426, 65, 788])).
% 1.63/1.87 tff(4080,plain,
% 1.63/1.87 (~r(s(s(s(z))), s(s(z)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4079, 4078])).
% 1.63/1.87 tff(4081,plain,
% 1.63/1.87 (b(s(s(s(z))), s(s(z)))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[458, 4080, 436])).
% 1.63/1.87 tff(4082,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4083,plain,
% 1.63/1.87 (((~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(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4084,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[4083])).
% 1.63/1.87 tff(4085,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[4084, 4082])).
% 1.63/1.87 tff(4086,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(4087,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4086, 4085])).
% 1.63/1.87 tff(4088,plain,
% 1.63/1.87 (~b(s(z), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4087, 162, 538, 444, 4081, 4039, 298])).
% 1.63/1.87 tff(4089,plain,
% 1.63/1.87 (r(s(z), s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[493, 4088])).
% 1.63/1.87 tff(4090,plain,
% 1.63/1.87 (~r(z, s(s(s(z))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1966, 4089, 194])).
% 1.63/1.87 tff(4091,plain,
% 1.63/1.87 (~r(z, s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2309, 4090, 1211])).
% 1.63/1.87 tff(4092,plain,
% 1.63/1.87 (b(z, s(s(s(elem!1))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[2296, 4091])).
% 1.63/1.87 tff(4093,plain,
% 1.63/1.87 (b(z, s(s(s(z))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4092, 3839])).
% 1.63/1.87 tff(4094,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4095,plain,
% 1.63/1.87 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4096,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[4095])).
% 1.63/1.87 tff(4097,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[4096, 4094])).
% 1.63/1.87 tff(4098,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(4099,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4098, 4097])).
% 1.63/1.87 tff(4100,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4099, 162, 538, 444, 4081, 298, 4093])).
% 1.63/1.87 tff(4101,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(4102,plain,
% 1.63/1.87 (~b(s(s(s(z))), z)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4101, 4038, 538, 1211, 194, 4009, 3535, 3992, 1275, 1076])).
% 1.63/1.87 tff(4103,plain,
% 1.63/1.87 (~b(s(s(s(z))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[3761, 4102, 1211])).
% 1.63/1.87 tff(4104,plain,
% 1.63/1.87 (r(s(s(s(z))), elem!1)),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[3664, 4103, 3620])).
% 1.63/1.87 tff(4105,plain,
% 1.63/1.87 (r(s(s(s(z))), z)),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4104, 1382])).
% 1.63/1.87 tff(4106,plain,
% 1.63/1.87 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.63/1.87 inference(symmetry,[status(thm)],[1610])).
% 1.63/1.87 tff(4107,plain,
% 1.63/1.87 (b(elem!1, s(z))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[118, 4106])).
% 1.63/1.87 tff(4108,plain,
% 1.63/1.87 (r(s(s(elem!1)), s(z))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[2, 3646])).
% 1.63/1.87 tff(4109,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(elem!1)), s(z))) | (~r(s(z), 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(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4110,plain,
% 1.63/1.87 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4111,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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[4110])).
% 1.63/1.87 tff(4112,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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[4111, 4109])).
% 1.63/1.87 tff(4113,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(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(4114,plain,
% 1.63/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4113, 4112])).
% 1.63/1.87 tff(4115,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4114, 65, 3367, 193, 1495])).
% 1.63/1.87 tff(4116,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(4117,plain,
% 1.63/1.87 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4116, 4108, 1495])).
% 1.63/1.87 tff(4118,plain,
% 1.63/1.87 (b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[191, 4117])).
% 1.63/1.87 tff(4119,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.63/1.87 tff(4120,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4121,plain,
% 1.63/1.87 (((~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), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.87 inference(rewrite,[status(thm)],[])).
% 1.63/1.87 tff(4122,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.63/1.87 inference(monotonicity,[status(thm)],[4121])).
% 1.63/1.87 tff(4123,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.63/1.87 inference(transitivity,[status(thm)],[4122, 4120])).
% 1.63/1.87 tff(4124,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))),
% 1.63/1.87 inference(quant_inst,[status(thm)],[])).
% 1.63/1.87 tff(4125,plain,
% 1.63/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4124, 4123])).
% 1.63/1.87 tff(4126,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4125, 162, 4119, 3990, 177, 1240, 151])).
% 1.63/1.87 tff(4127,plain,((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(4128,plain,
% 1.63/1.87 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4127, 4118, 1240, 3990, 4107])).
% 1.63/1.87 tff(4129,plain,
% 1.63/1.87 (r(s(s(s(s(elem!1)))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[149, 4128])).
% 1.63/1.87 tff(4130,plain,
% 1.63/1.87 (r(s(s(s(s(z)))), s(z))),
% 1.63/1.87 inference(modus_ponens,[status(thm)],[4129, 3541])).
% 1.63/1.87 tff(4131,plain,
% 1.63/1.87 (~r(s(s(s(s(z)))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1139, 2, 3535])).
% 1.63/1.87 tff(4132,plain,
% 1.63/1.87 ($false),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4131, 4130])).
% 1.63/1.87 tff(4133,plain,((~r(s(s(z)), s(z))) | (~(elem!1 = z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.87 tff(4134,plain,
% 1.63/1.87 (~r(s(s(z)), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[4133, 55, 1240, 3990, 1495, 1211])).
% 1.63/1.87 tff(4135,plain,
% 1.63/1.87 (b(s(s(z)), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[271, 4134])).
% 1.63/1.87 tff(4136,plain,
% 1.63/1.87 (~r(s(s(s(z))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[1392, 4104, 194, 1211])).
% 1.63/1.87 tff(4137,plain,
% 1.63/1.87 (b(s(s(s(z))), s(z))),
% 1.63/1.87 inference(unit_resolution,[status(thm)],[595, 4136])).
% 1.63/1.87 tff(4138,plain,
% 1.63/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4139,plain,
% 1.63/1.88 (((~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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4140,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4139])).
% 1.63/1.88 tff(4141,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[4140, 4138])).
% 1.63/1.88 tff(4142,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(4143,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4142, 4141])).
% 1.63/1.88 tff(4144,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4143, 162, 444, 383, 4039, 600, 599])).
% 1.63/1.88 tff(4145,plain,((~b(s(s(z)), s(z))) | (~b(s(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)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4146,plain,
% 1.63/1.88 (~b(s(z), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4145, 4137, 4009, 4135, 4038])).
% 1.63/1.88 tff(4147,plain,
% 1.63/1.88 (r(s(z), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[493, 4146])).
% 1.63/1.88 tff(4148,plain,
% 1.63/1.88 (~r(s(s(s(z))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2269, 65, 194, 4147])).
% 1.63/1.88 tff(4149,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4148, 4105])).
% 1.63/1.88 tff(4150,plain,((~r(z, s(s(z)))) | (~(elem!1 = z)) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4151,plain,
% 1.63/1.88 (~r(z, s(s(z)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4150, 3487, 3522, 3986, 3498, 3981, 3984, 3976, 3506])).
% 1.63/1.88 tff(4152,plain,
% 1.63/1.88 (b(z, s(s(z)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[524, 4151])).
% 1.63/1.88 tff(4153,plain,
% 1.63/1.88 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1084, 3986, 4152, 3981, 3978])).
% 1.63/1.88 tff(4154,plain,
% 1.63/1.88 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4153, 3502])).
% 1.63/1.88 tff(4155,plain,
% 1.63/1.88 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[52, 4154])).
% 1.63/1.88 tff(4156,plain,
% 1.63/1.88 (r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4155, 3500])).
% 1.63/1.88 tff(4157,plain,
% 1.63/1.88 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = z)),
% 1.63/1.88 inference(monotonicity,[status(thm)],[3487])).
% 1.63/1.88 tff(4158,plain,
% 1.63/1.88 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.63/1.88 inference(symmetry,[status(thm)],[4157])).
% 1.63/1.88 tff(4159,plain,
% 1.63/1.88 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4158])).
% 1.63/1.88 tff(4160,plain,
% 1.63/1.88 (~(s(s(s(z))) = elem!1)),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[286, 4159])).
% 1.63/1.88 tff(4161,plain,
% 1.63/1.88 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1524, 3497])).
% 1.63/1.88 tff(4162,plain,
% 1.63/1.88 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[3487])).
% 1.63/1.88 tff(4163,plain,
% 1.63/1.88 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(symmetry,[status(thm)],[4162])).
% 1.63/1.88 tff(4164,plain,
% 1.63/1.88 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[3489])).
% 1.63/1.88 tff(4165,plain,
% 1.63/1.88 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.63/1.88 inference(symmetry,[status(thm)],[4164])).
% 1.63/1.88 tff(4166,plain,
% 1.63/1.88 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(transitivity,[status(thm)],[4165, 4163])).
% 1.63/1.88 tff(4167,plain,
% 1.63/1.88 (b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4152, 4166])).
% 1.63/1.88 tff(4168,plain,
% 1.63/1.88 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2077, 3497])).
% 1.63/1.88 tff(4169,plain,
% 1.63/1.88 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[3492])).
% 1.63/1.88 tff(4170,plain,
% 1.63/1.88 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.63/1.88 inference(symmetry,[status(thm)],[4169])).
% 1.63/1.88 tff(4171,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[3489])).
% 1.63/1.88 tff(4172,plain,
% 1.63/1.88 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[3506, 4171])).
% 1.63/1.88 tff(4173,plain,
% 1.63/1.88 (r(s(s(z)), s(s(s(s(z)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4172, 4170])).
% 1.63/1.88 tff(4174,plain,
% 1.63/1.88 (~r(z, s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1966, 395, 194])).
% 1.63/1.88 tff(4175,plain,
% 1.63/1.88 (~r(z, s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2309, 4174, 1211])).
% 1.63/1.88 tff(4176,plain,
% 1.63/1.88 (b(z, s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2296, 4175])).
% 1.63/1.88 tff(4177,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.63/1.88 tff(4178,plain,
% 1.63/1.88 (b(elem!1, s(s(s(elem!1))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4177, 1475])).
% 1.63/1.88 tff(4179,plain,
% 1.63/1.88 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3892, 3878, 1248, 4178, 1600])).
% 1.63/1.88 tff(4180,plain,
% 1.63/1.88 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2116, 4179, 1253])).
% 1.63/1.88 tff(4181,plain,
% 1.63/1.88 (r(s(s(z)), s(s(s(z))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4180, 2066])).
% 1.63/1.88 tff(4182,plain,
% 1.63/1.88 (b(s(s(s(elem!1))), z)),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[298, 3876])).
% 1.63/1.88 tff(4183,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4184,plain,
% 1.63/1.88 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4185,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4184])).
% 1.63/1.88 tff(4186,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[4185, 4183])).
% 1.63/1.88 tff(4187,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(4188,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4187, 4186])).
% 1.63/1.88 tff(4189,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4188, 162, 741, 122, 2219, 4177, 120])).
% 1.63/1.88 tff(4190,plain,((~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(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4191,plain,
% 1.63/1.88 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4190, 4182, 122, 120, 4177])).
% 1.63/1.88 tff(4192,plain,
% 1.63/1.88 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1304, 4191, 1275])).
% 1.63/1.88 tff(4193,plain,
% 1.63/1.88 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3854, 4192, 1211])).
% 1.63/1.88 tff(4194,plain,
% 1.63/1.88 (~r(s(s(z)), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[796, 4193, 788])).
% 1.63/1.88 tff(4195,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4194, 4181])).
% 1.63/1.88 tff(4196,plain,((~b(s(s(s(z))), z)) | (~(elem!1 = z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4197,plain,
% 1.63/1.88 (~b(s(s(s(z))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4196, 4176, 788, 1275, 1253, 122, 120, 1211, 1248, 1600])).
% 1.63/1.88 tff(4198,plain,
% 1.63/1.88 (~b(s(s(s(z))), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3761, 4197, 1211])).
% 1.63/1.88 tff(4199,plain,
% 1.63/1.88 (r(s(s(s(z))), elem!1)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[3664, 4198, 3620])).
% 1.63/1.88 tff(4200,plain,
% 1.63/1.88 (r(s(s(s(z))), z)),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4199, 1382])).
% 1.63/1.88 tff(4201,plain,
% 1.63/1.88 (~r(s(s(s(z))), z)),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[2269, 65, 194, 395])).
% 1.63/1.88 tff(4202,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4201, 4200])).
% 1.63/1.88 tff(4203,plain,((~r(s(z), s(s(s(z))))) | (~(elem!1 = z)) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4204,plain,
% 1.63/1.88 (~r(s(z), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4203, 3487, 3522, 4173, 3498, 4168, 122, 3977, 4167, 3513])).
% 1.63/1.88 tff(4205,plain,
% 1.63/1.88 (b(s(z), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[493, 4204])).
% 1.63/1.88 tff(4206,assumption,(s(elem!1) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.88 tff(4207,plain,
% 1.63/1.88 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.63/1.88 inference(symmetry,[status(thm)],[4206])).
% 1.63/1.88 tff(4208,plain,
% 1.63/1.88 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4207])).
% 1.63/1.88 tff(4209,plain,
% 1.63/1.88 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(symmetry,[status(thm)],[4208])).
% 1.63/1.88 tff(4210,plain,
% 1.63/1.88 (elem!1 = s(s(s(s(elem!1))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[1171, 4209, 909])).
% 1.63/1.88 tff(4211,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1538, 4210])).
% 1.63/1.88 tff(4212,plain,((~(s(elem!1) = s(s(s(s(s(elem!1))))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4213,plain,
% 1.63/1.88 (~(s(elem!1) = s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4212, 3455])).
% 1.63/1.88 tff(4214,assumption,(s(z) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.63/1.88 tff(4215,plain,
% 1.63/1.88 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[1212, 4214])).
% 1.63/1.88 tff(4216,assumption,(~(s(elem!1) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.63/1.88 tff(4217,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4216, 4215])).
% 1.63/1.88 tff(4218,plain,((~(s(z) = s(s(s(s(s(elem!1))))))) | (s(elem!1) = s(s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4219,plain,
% 1.63/1.88 (~(s(z) = s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4218, 3487, 4213])).
% 1.63/1.88 tff(4220,plain,
% 1.63/1.88 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.63/1.88 inference(monotonicity,[status(thm)],[1380])).
% 1.63/1.88 tff(4221,plain,
% 1.63/1.88 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), z)),
% 1.63/1.88 inference(symmetry,[status(thm)],[4220])).
% 1.63/1.88 tff(4222,plain,
% 1.63/1.88 (~r(s(s(s(z))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1392, 1313, 194, 1211])).
% 1.63/1.88 tff(4223,plain,
% 1.63/1.88 (b(s(s(s(z))), s(z))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[595, 4222])).
% 1.63/1.88 tff(4224,plain,
% 1.63/1.88 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(symmetry,[status(thm)],[1328])).
% 1.63/1.88 tff(4225,plain,
% 1.63/1.88 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(transitivity,[status(thm)],[3572, 4224])).
% 1.63/1.88 tff(4226,plain,
% 1.63/1.88 (b(elem!1, s(s(elem!1)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[537, 4225])).
% 1.63/1.88 tff(4227,plain,
% 1.63/1.88 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1084, 538, 537, 1076, 1075])).
% 1.63/1.88 tff(4228,plain,
% 1.63/1.88 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4227, 3539])).
% 1.63/1.88 tff(4229,plain,
% 1.63/1.88 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[52, 4228])).
% 1.63/1.88 tff(4230,plain,
% 1.63/1.88 (r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4229, 1345])).
% 1.63/1.88 tff(4231,plain,
% 1.63/1.88 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1517, 1275])).
% 1.63/1.88 tff(4232,plain,
% 1.63/1.88 (b(s(s(s(s(s(elem!1))))), z)),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[2174, 4221])).
% 1.63/1.88 tff(4233,plain,
% 1.63/1.88 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.88 tff(4234,plain,
% 1.63/1.88 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(symmetry,[status(thm)],[4233])).
% 1.63/1.88 tff(4235,plain,
% 1.63/1.88 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1741, 877, 1211])).
% 1.63/1.88 tff(4236,plain,
% 1.63/1.88 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1813, 4235, 1588])).
% 1.63/1.88 tff(4237,plain,
% 1.63/1.88 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1853, 4236, 1248, 2174, 1600])).
% 1.63/1.88 tff(4238,plain,
% 1.63/1.88 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1760, 4237, 1701])).
% 1.63/1.88 tff(4239,plain,
% 1.63/1.88 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1768, 4238, 1211])).
% 1.63/1.88 tff(4240,plain,
% 1.63/1.88 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1781, 4239, 644, 1211])).
% 1.63/1.88 tff(4241,plain,
% 1.63/1.88 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1789, 4240, 1692])).
% 1.63/1.88 tff(4242,plain,
% 1.63/1.88 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4241, 4234])).
% 1.63/1.88 tff(4243,plain,
% 1.63/1.88 (b(z, s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1821, 4236, 1211])).
% 1.63/1.88 tff(4244,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4245,plain,
% 1.63/1.88 (((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4246,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1)))))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4245])).
% 1.63/1.88 tff(4247,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[4246, 4244])).
% 1.63/1.88 tff(4248,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(4249,plain,
% 1.63/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4248, 4247])).
% 1.63/1.88 tff(4250,plain,
% 1.63/1.88 ($false),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4249, 162, 4243, 1076, 1075, 4242, 4232])).
% 1.63/1.88 tff(4251,plain,((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.88 tff(4252,plain,
% 1.63/1.88 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4251, 1383, 1075, 1211, 4231, 4230, 4226, 1600, 1076])).
% 1.63/1.88 tff(4253,plain,
% 1.63/1.88 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1001, 4252])).
% 1.63/1.88 tff(4254,plain,
% 1.63/1.88 (((~![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(s(elem!1))))), z)) | (~r(s(z), 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(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4255,plain,
% 1.63/1.88 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4256,plain,
% 1.63/1.88 (((~![X0: $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(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), 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(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4255])).
% 1.63/1.88 tff(4257,plain,
% 1.63/1.88 (((~![X0: $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(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), 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(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[4256, 4254])).
% 1.63/1.88 tff(4258,plain,
% 1.63/1.88 ((~![X0: $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(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(4259,plain,
% 1.63/1.88 ((~![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(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4258, 4257])).
% 1.63/1.88 tff(4260,plain,
% 1.63/1.88 ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4259, 65, 194])).
% 1.63/1.88 tff(4261,plain,
% 1.63/1.88 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4260, 878])).
% 1.63/1.88 tff(4262,plain,
% 1.63/1.88 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1049, 4261, 1043])).
% 1.63/1.88 tff(4263,plain,
% 1.63/1.88 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[1270])).
% 1.63/1.88 tff(4264,plain,
% 1.63/1.88 ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4263])).
% 1.63/1.88 tff(4265,plain,
% 1.63/1.88 (((~![X0: $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(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4266,plain,
% 1.63/1.88 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4267,plain,
% 1.63/1.88 (((~![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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.63/1.88 inference(monotonicity,[status(thm)],[4266])).
% 1.63/1.88 tff(4268,plain,
% 1.63/1.88 (((~![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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.63/1.88 inference(transitivity,[status(thm)],[4267, 4265])).
% 1.63/1.88 tff(4269,plain,
% 1.63/1.88 ((~![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(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.63/1.88 inference(quant_inst,[status(thm)],[])).
% 1.63/1.88 tff(4270,plain,
% 1.63/1.88 ((~![X0: $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(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4269, 4268])).
% 1.63/1.88 tff(4271,plain,
% 1.63/1.88 ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4270, 65, 866])).
% 1.63/1.88 tff(4272,plain,
% 1.63/1.88 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[4271, 878])).
% 1.63/1.88 tff(4273,plain,
% 1.63/1.88 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4272, 4264])).
% 1.63/1.88 tff(4274,plain,
% 1.63/1.88 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.63/1.88 inference(unit_resolution,[status(thm)],[1731, 4273, 1691])).
% 1.63/1.88 tff(4275,plain,
% 1.63/1.88 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.63/1.88 inference(modus_ponens,[status(thm)],[4274, 1835])).
% 1.63/1.88 tff(4276,plain,
% 1.63/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.88 inference(rewrite,[status(thm)],[])).
% 1.63/1.88 tff(4277,plain,
% 1.63/1.88 (((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4278,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4277])).
% 1.63/1.89 tff(4279,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[4278, 4276])).
% 1.63/1.89 tff(4280,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(4281,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4280, 4279])).
% 1.63/1.89 tff(4282,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4281, 162, 4275, 4262, 600, 1003, 599])).
% 1.63/1.89 tff(4283,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = z)) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(z) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(4284,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4283, 4253, 4223, 599, 1211, 1691, 1043, 1383, 194])).
% 1.63/1.89 tff(4285,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[888, 1863])).
% 1.63/1.89 tff(4286,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | r(s(s(s(s(s(elem!1))))), z) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(4287,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4286, 4284, 1211])).
% 1.63/1.89 tff(4288,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1858, 4287, 1834])).
% 1.63/1.89 tff(4289,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), z)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4288, 4221])).
% 1.63/1.89 tff(4290,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[1762])).
% 1.63/1.89 tff(4291,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.63/1.89 inference(symmetry,[status(thm)],[4290])).
% 1.63/1.89 tff(4292,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.89 tff(4293,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(symmetry,[status(thm)],[4292])).
% 1.63/1.89 tff(4294,plain,
% 1.63/1.89 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[1216])).
% 1.63/1.89 tff(4295,plain,
% 1.63/1.89 ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4294])).
% 1.63/1.89 tff(4296,plain,
% 1.63/1.89 (((~![X0: $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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(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(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4297,plain,
% 1.63/1.89 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4298,plain,
% 1.63/1.89 (((~![X0: $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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(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(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4297])).
% 1.63/1.89 tff(4299,plain,
% 1.63/1.89 (((~![X0: $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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(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(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[4298, 4296])).
% 1.63/1.89 tff(4300,plain,
% 1.63/1.89 ((~![X0: $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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(4301,plain,
% 1.63/1.89 ((~![X0: $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(elem!1))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 1.63/1.89 tff(4302,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4301, 65, 644, 896])).
% 1.63/1.89 tff(4303,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4302, 4295])).
% 1.63/1.89 tff(4304,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2214, 4303, 2378])).
% 1.63/1.89 tff(4305,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4304, 4293])).
% 1.63/1.89 tff(4306,plain,
% 1.63/1.89 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1781, 896, 644, 1211])).
% 1.63/1.89 tff(4307,plain,
% 1.63/1.89 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1789, 4306, 1692])).
% 1.63/1.89 tff(4308,plain,
% 1.63/1.89 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4307, 4234])).
% 1.63/1.89 tff(4309,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4310,plain,
% 1.63/1.89 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4311,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4310])).
% 1.63/1.89 tff(4312,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[4311, 4309])).
% 1.63/1.89 tff(4313,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(4314,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 1.63/1.89 tff(4315,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4314, 162, 1076, 1075, 4308, 926, 4305])).
% 1.63/1.89 tff(4316,plain,((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(4317,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4316, 4289, 1075, 1076, 1211, 4230, 4231])).
% 1.63/1.89 tff(4318,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1768, 4317, 1211])).
% 1.63/1.89 tff(4319,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1760, 4318, 1701])).
% 1.63/1.89 tff(4320,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4319, 4291])).
% 1.63/1.89 tff(4321,plain,
% 1.63/1.89 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[933, 162, 538, 537, 4320, 4289])).
% 1.63/1.89 tff(4322,plain,
% 1.63/1.89 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[943, 4321])).
% 1.63/1.89 tff(4323,plain,
% 1.63/1.89 (((~![X0: $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(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), 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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4324,plain,
% 1.63/1.89 (((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4325,plain,
% 1.63/1.89 (((~![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(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(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(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4324])).
% 1.63/1.89 tff(4326,plain,
% 1.63/1.89 (((~![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(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(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(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[4325, 4323])).
% 1.63/1.89 tff(4327,plain,
% 1.63/1.89 ((~![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(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(4328,plain,
% 1.63/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4327, 4326])).
% 1.63/1.89 tff(4329,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4328, 65, 54, 1004, 946])).
% 1.63/1.89 tff(4330,plain,((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.89 tff(4331,plain,
% 1.63/1.89 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4330, 4322, 4229])).
% 1.63/1.89 tff(4332,plain,
% 1.63/1.89 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1789, 4331, 4231])).
% 1.63/1.89 tff(4333,plain,
% 1.63/1.89 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4332, 4234])).
% 1.63/1.89 tff(4334,plain,
% 1.63/1.89 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[1417])).
% 1.63/1.89 tff(4335,plain,
% 1.63/1.89 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3689, 417, 3535, 1211])).
% 1.63/1.89 tff(4336,plain,
% 1.63/1.89 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[337, 4335, 3529])).
% 1.63/1.89 tff(4337,plain,
% 1.63/1.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1336, 4336, 1211])).
% 1.63/1.89 tff(4338,plain,
% 1.63/1.89 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[796, 417, 3535])).
% 1.63/1.89 tff(4339,plain,
% 1.63/1.89 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3854, 4338, 1211])).
% 1.63/1.89 tff(4340,plain,
% 1.63/1.89 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1304, 4339, 1275])).
% 1.63/1.89 tff(4341,plain,
% 1.63/1.89 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4340, 3844])).
% 1.63/1.89 tff(4342,plain,
% 1.63/1.89 (~b(s(z), s(s(s(s(z)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[702, 4341, 599, 4337, 600])).
% 1.63/1.89 tff(4343,plain,
% 1.63/1.89 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4342, 4334])).
% 1.63/1.89 tff(4344,plain,
% 1.63/1.89 (r(s(z), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[191, 4343])).
% 1.63/1.89 tff(4345,plain,
% 1.63/1.89 (~r(s(z), s(s(z)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[403, 4344, 54])).
% 1.63/1.89 tff(4346,plain,
% 1.63/1.89 (b(s(z), s(s(z)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3713, 4345])).
% 1.63/1.89 tff(4347,plain,
% 1.63/1.89 (~r(s(s(elem!1)), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4116, 4344, 1495])).
% 1.63/1.89 tff(4348,plain,
% 1.63/1.89 (b(s(s(elem!1)), s(z))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[3824, 4347])).
% 1.63/1.89 tff(4349,plain,
% 1.63/1.89 (b(s(s(z)), s(z))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4348, 3818])).
% 1.63/1.89 tff(4350,plain,
% 1.63/1.89 (r(s(s(s(s(z)))), s(s(z)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[54, 1345])).
% 1.63/1.89 tff(4351,plain,
% 1.63/1.89 ((~r(s(s(s(s(s(elem!1))))), z)) <=> (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[1860])).
% 1.63/1.89 tff(4352,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4283, 1003, 600, 599, 1211, 1691, 1043, 866, 194])).
% 1.63/1.89 tff(4353,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4352, 4351])).
% 1.63/1.89 tff(4354,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1858, 4353, 1834])).
% 1.63/1.89 tff(4355,plain,
% 1.63/1.89 (b(s(s(s(s(s(elem!1))))), z)),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4354, 4221])).
% 1.63/1.89 tff(4356,plain,
% 1.63/1.89 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4292])).
% 1.63/1.89 tff(4357,plain,
% 1.63/1.89 ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4290])).
% 1.63/1.89 tff(4358,plain,
% 1.63/1.89 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[935, 926, 537, 927, 538])).
% 1.63/1.89 tff(4359,plain,
% 1.63/1.89 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4358, 4357])).
% 1.63/1.89 tff(4360,plain,
% 1.63/1.89 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1760, 4359, 1701])).
% 1.63/1.89 tff(4361,plain,
% 1.63/1.89 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1768, 4360, 1211])).
% 1.63/1.89 tff(4362,plain,
% 1.63/1.89 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1781, 4361, 644, 1211])).
% 1.63/1.89 tff(4363,plain,
% 1.63/1.89 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[1789, 4362, 1692])).
% 1.63/1.89 tff(4364,plain,
% 1.63/1.89 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4363, 4234])).
% 1.63/1.89 tff(4365,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4366,plain,
% 1.63/1.89 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(rewrite,[status(thm)],[])).
% 1.63/1.89 tff(4367,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 1.63/1.89 inference(monotonicity,[status(thm)],[4366])).
% 1.63/1.89 tff(4368,plain,
% 1.63/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.63/1.89 inference(transitivity,[status(thm)],[4367, 4365])).
% 1.63/1.89 tff(4369,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.63/1.89 inference(quant_inst,[status(thm)],[])).
% 1.63/1.89 tff(4370,plain,
% 1.63/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4369, 4368])).
% 1.63/1.89 tff(4371,plain,
% 1.63/1.89 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4370, 162, 1003, 1076, 692, 4364, 926])).
% 1.63/1.89 tff(4372,plain,
% 1.63/1.89 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4371, 4356])).
% 1.63/1.89 tff(4373,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[4301, 65, 644, 4361])).
% 1.63/1.89 tff(4374,plain,
% 1.63/1.89 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.63/1.89 inference(modus_ponens,[status(thm)],[4373, 4295])).
% 1.63/1.89 tff(4375,plain,
% 1.63/1.89 ($false),
% 1.63/1.89 inference(unit_resolution,[status(thm)],[2214, 4374, 4372, 2378])).
% 1.63/1.89 tff(4376,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~(elem!1 = z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(4377,plain,
% 1.73/1.90 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4376, 4355, 1003, 1076, 692, 4350, 1692, 537, 1211, 538])).
% 1.73/1.90 tff(4378,plain,
% 1.73/1.90 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[943, 4377])).
% 1.73/1.90 tff(4379,plain,
% 1.73/1.90 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4330, 4378, 54])).
% 1.73/1.90 tff(4380,plain,
% 1.73/1.90 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1789, 4379, 1692])).
% 1.73/1.90 tff(4381,plain,
% 1.73/1.90 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4380, 4234])).
% 1.73/1.90 tff(4382,plain,
% 1.73/1.90 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/1.90 inference(symmetry,[status(thm)],[4263])).
% 1.73/1.90 tff(4383,plain,
% 1.73/1.90 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[1718, 4382])).
% 1.73/1.90 tff(4384,plain,
% 1.73/1.90 (((~![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(elem!1))))))) | (~r(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(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4385,plain,
% 1.73/1.90 (((~r(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(elem!1))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4386,plain,
% 1.73/1.90 (((~![X0: $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(elem!1))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(z)), 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(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[4385])).
% 1.73/1.90 tff(4387,plain,
% 1.73/1.90 (((~![X0: $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(elem!1))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(z)), 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(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[4386, 4384])).
% 1.73/1.90 tff(4388,plain,
% 1.73/1.90 ((~![X0: $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(elem!1))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(4389,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4388, 4387])).
% 1.73/1.90 tff(4390,plain,
% 1.73/1.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4389, 65, 946, 417])).
% 1.73/1.90 tff(4391,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4390, 4383])).
% 1.73/1.90 tff(4392,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(elem!1 = z)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(4393,plain,
% 1.73/1.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4392, 4378, 1211, 417])).
% 1.73/1.90 tff(4394,plain,
% 1.73/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1731, 4393, 1691])).
% 1.73/1.90 tff(4395,plain,
% 1.73/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4394, 1835])).
% 1.73/1.90 tff(4396,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1800, 162, 4395, 1003, 693, 692, 4381])).
% 1.73/1.90 tff(4397,plain,((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = z)) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(z) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(4398,plain,
% 1.73/1.90 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4397, 4337, 4341, 1211, 1691, 4231, 417, 54, 1076, 537, 538, 600, 599, 1043, 866, 194])).
% 1.73/1.90 tff(4399,plain,
% 1.73/1.90 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1001, 4398])).
% 1.73/1.90 tff(4400,plain,
% 1.73/1.90 (~r(s(s(s(z))), s(s(z)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[2179, 4399, 1211, 4226, 1600, 866])).
% 1.73/1.90 tff(4401,plain,
% 1.73/1.90 (b(s(s(s(z))), s(s(z)))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[458, 4400, 436])).
% 1.73/1.90 tff(4402,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4403,plain,
% 1.73/1.90 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4404,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[4403])).
% 1.73/1.90 tff(4405,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[4404, 4402])).
% 1.73/1.90 tff(4406,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(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)))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(4407,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4406, 4405])).
% 1.73/1.90 tff(4408,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4407, 162, 4401, 4349, 4346, 600, 599])).
% 1.73/1.90 tff(4409,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~(elem!1 = z)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), z)) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (s(z) = s(s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(4410,plain,
% 1.73/1.90 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4409, 4223, 599, 1211, 1600, 1383, 1691, 4229, 1076, 537, 538, 1043, 194, 1495, 1275])).
% 1.73/1.90 tff(4411,plain,
% 1.73/1.90 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[441, 4410, 437])).
% 1.73/1.90 tff(4412,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4413,plain,
% 1.73/1.90 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4414,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[4413])).
% 1.73/1.90 tff(4415,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[4414, 4412])).
% 1.73/1.90 tff(4416,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(4417,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4416, 4415])).
% 1.73/1.90 tff(4418,plain,
% 1.73/1.90 (~b(s(s(z)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4417, 162, 537, 4411, 599, 4320, 4289])).
% 1.73/1.90 tff(4419,plain,
% 1.73/1.90 (r(s(s(z)), s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[271, 4418])).
% 1.73/1.90 tff(4420,plain,
% 1.73/1.90 (r(s(s(elem!1)), s(z))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4419, 3646])).
% 1.73/1.90 tff(4421,plain,
% 1.73/1.90 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4116, 4420, 1495])).
% 1.73/1.90 tff(4422,plain,
% 1.73/1.90 (b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[191, 4421])).
% 1.73/1.90 tff(4423,plain,
% 1.73/1.90 (b(s(z), s(s(s(s(z)))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4422, 1418])).
% 1.73/1.90 tff(4424,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4425,plain,
% 1.73/1.90 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4426,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[4425])).
% 1.73/1.90 tff(4427,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[4426, 4424])).
% 1.73/1.90 tff(4428,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(4429,plain,
% 1.73/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4428, 4427])).
% 1.73/1.90 tff(4430,plain,
% 1.73/1.90 (~b(z, s(z))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4429, 162, 1076, 4423, 1075, 4333, 4289])).
% 1.73/1.90 tff(4431,plain,
% 1.73/1.90 (b(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[1845, 4221])).
% 1.73/1.90 tff(4432,plain,
% 1.73/1.90 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[1844, 4291])).
% 1.73/1.90 tff(4433,plain,
% 1.73/1.90 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1853, 1845, 1248, 1844, 1600])).
% 1.73/1.90 tff(4434,plain,
% 1.73/1.90 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1813, 4433, 1588])).
% 1.73/1.90 tff(4435,plain,
% 1.73/1.90 (r(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1741, 4434, 1211])).
% 1.73/1.90 tff(4436,plain,
% 1.73/1.90 (((~![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(z), s(s(s(s(s(elem!1))))))) | (~r(z, 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(z, s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4437,plain,
% 1.73/1.90 (((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(rewrite,[status(thm)],[])).
% 1.73/1.90 tff(4438,plain,
% 1.73/1.90 (((~![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(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))))),
% 1.73/1.90 inference(monotonicity,[status(thm)],[4437])).
% 1.73/1.90 tff(4439,plain,
% 1.73/1.90 (((~![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(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.73/1.90 inference(transitivity,[status(thm)],[4438, 4436])).
% 1.73/1.90 tff(4440,plain,
% 1.73/1.90 ((~![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(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))))),
% 1.73/1.90 inference(quant_inst,[status(thm)],[])).
% 1.73/1.90 tff(4441,plain,
% 1.73/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 1.73/1.90 inference(modus_ponens,[status(thm)],[4440, 4439])).
% 1.73/1.90 tff(4442,plain,
% 1.73/1.90 ($false),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4441, 65, 97, 2860, 868])).
% 1.73/1.90 tff(4443,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.90 tff(4444,plain,
% 1.73/1.90 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[4443, 4435, 97])).
% 1.73/1.90 tff(4445,plain,
% 1.73/1.90 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/1.90 inference(unit_resolution,[status(thm)],[1049, 4444, 1043])).
% 1.73/1.90 tff(4446,plain,
% 1.73/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4447,plain,
% 1.73/1.91 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4448,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[4447])).
% 1.73/1.91 tff(4449,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[4448, 4446])).
% 1.73/1.91 tff(4450,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(4451,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4450, 4449])).
% 1.73/1.91 tff(4452,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4451, 162, 538, 4445, 694, 1793, 4432, 4431])).
% 1.73/1.91 tff(4453,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~(elem!1 = z)) | (s(z) = s(s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(4454,plain,
% 1.73/1.91 (~r(z, s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4453, 4423, 4288, 538, 1211, 1043, 4333, 4226, 4319, 1600])).
% 1.73/1.91 tff(4455,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[117, 4454, 4430])).
% 1.73/1.91 tff(4456,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~(elem!1 = z)) | (s(z) = s(s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(4457,plain,
% 1.73/1.91 (~r(s(s(s(z))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4456, 3986, 3487, 4219, 3513, 3981, 3978, 3506, 4152, 4205, 4161, 3522, 3498])).
% 1.73/1.91 tff(4458,plain,
% 1.73/1.91 (b(s(s(s(z))), elem!1)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3664, 4457, 4160])).
% 1.73/1.91 tff(4459,plain,
% 1.73/1.91 (b(s(s(s(z))), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3761, 4458, 3487])).
% 1.73/1.91 tff(4460,plain,
% 1.73/1.91 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1336, 4011, 1211])).
% 1.73/1.91 tff(4461,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4060, 162, 298, 1076, 693, 1075, 692])).
% 1.73/1.91 tff(4462,plain,((~b(s(s(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)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(4463,plain,
% 1.73/1.91 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4462, 4460, 298, 1075, 1076])).
% 1.73/1.91 tff(4464,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4463, 3942])).
% 1.73/1.91 tff(4465,plain,((~r(s(s(z)), s(s(s(z))))) | (~(elem!1 = z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(4466,plain,
% 1.73/1.91 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4465, 3487, 4459, 3978, 3981, 3498, 4173])).
% 1.73/1.91 tff(4467,plain,
% 1.73/1.91 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[441, 4466, 437])).
% 1.73/1.91 tff(4468,plain,
% 1.73/1.91 (~b(s(s(s(z))), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3150, 4467, 4152, 3986, 4459])).
% 1.73/1.91 tff(4469,plain,
% 1.73/1.91 (r(s(s(s(z))), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[458, 4468, 436])).
% 1.73/1.91 tff(4470,plain,
% 1.73/1.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[685, 65, 4469, 4156])).
% 1.73/1.91 tff(4471,plain,
% 1.73/1.91 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3854, 4470, 3487])).
% 1.73/1.91 tff(4472,plain,
% 1.73/1.91 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1304, 4471, 3498])).
% 1.73/1.91 tff(4473,plain,
% 1.73/1.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4472, 3496])).
% 1.73/1.91 tff(4474,plain,
% 1.73/1.91 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[3492])).
% 1.73/1.91 tff(4475,plain,
% 1.73/1.91 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.73/1.91 inference(symmetry,[status(thm)],[4474])).
% 1.73/1.91 tff(4476,plain,
% 1.73/1.91 (~b(s(z), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4101, 4467, 3978, 3487, 3522, 4459, 4173, 3986, 3498, 3981])).
% 1.73/1.91 tff(4477,plain,
% 1.73/1.91 (r(s(z), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3713, 4476])).
% 1.73/1.91 tff(4478,plain,
% 1.73/1.91 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[403, 4477, 4155])).
% 1.73/1.91 tff(4479,plain,
% 1.73/1.91 (b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[191, 4478])).
% 1.73/1.91 tff(4480,plain,
% 1.73/1.91 (b(s(z), s(s(s(s(z)))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4479, 4475])).
% 1.73/1.91 tff(4481,plain,
% 1.73/1.91 (((~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(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4482,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[4481])).
% 1.73/1.91 tff(4483,plain,
% 1.73/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[4482, 3863])).
% 1.73/1.91 tff(4484,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(4485,plain,
% 1.73/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4484, 4483])).
% 1.73/1.91 tff(4486,plain,
% 1.73/1.91 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4485, 162, 4459, 4205, 3981, 4480, 4473])).
% 1.73/1.91 tff(4487,plain,
% 1.73/1.91 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[3490])).
% 1.73/1.91 tff(4488,plain,
% 1.73/1.91 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[4487, 3525])).
% 1.73/1.91 tff(4489,plain,
% 1.73/1.91 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[4488])).
% 1.73/1.91 tff(4490,plain,
% 1.73/1.91 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[3498, 4489])).
% 1.73/1.91 tff(4491,plain,
% 1.73/1.91 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[3492])).
% 1.73/1.91 tff(4492,plain,
% 1.73/1.91 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[4491])).
% 1.73/1.91 tff(4493,plain,
% 1.73/1.91 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[670, 65, 4469, 4156])).
% 1.73/1.91 tff(4494,plain,
% 1.73/1.91 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4493, 4492])).
% 1.73/1.91 tff(4495,plain,
% 1.73/1.91 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[337, 4494, 4490])).
% 1.73/1.91 tff(4496,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1336, 4495, 4486, 3487])).
% 1.73/1.91 tff(4497,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | b(elem!1, z) | b(s(elem!1), elem!1) | r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(4498,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4497, 3441, 3434, 122, 3421, 3411, 3404])).
% 1.73/1.91 tff(4499,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | r(s(s(z)), z) | b(s(z), z) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(4500,plain,
% 1.73/1.91 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4499, 3360, 97, 3332, 3345, 3361, 2])).
% 1.73/1.91 tff(4501,plain,
% 1.73/1.91 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2727, 4500, 3332, 3358, 340])).
% 1.73/1.91 tff(4502,plain,
% 1.73/1.91 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[690, 4501, 679])).
% 1.73/1.91 tff(4503,plain,
% 1.73/1.91 (((~![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(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(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4504,plain,
% 1.73/1.91 (((~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(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4505,plain,
% 1.73/1.91 (((~![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(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[4504])).
% 1.73/1.91 tff(4506,plain,
% 1.73/1.91 (((~![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(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[4505, 4503])).
% 1.73/1.91 tff(4507,plain,
% 1.73/1.91 ((~![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)))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(4508,plain,
% 1.73/1.91 ((~![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(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 1.73/1.91 tff(4509,plain,
% 1.73/1.91 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4508, 65, 2, 1131])).
% 1.73/1.91 tff(4510,plain,
% 1.73/1.91 (b(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[709, 4509, 635])).
% 1.73/1.91 tff(4511,plain,
% 1.73/1.91 (((~![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(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(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4512,plain,
% 1.73/1.91 (((~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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4513,plain,
% 1.73/1.91 (((~![X0: $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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[4512])).
% 1.73/1.91 tff(4514,plain,
% 1.73/1.91 (((~![X0: $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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[4513, 4511])).
% 1.73/1.91 tff(4515,plain,
% 1.73/1.91 ((~![X0: $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)))))))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(4516,plain,
% 1.73/1.91 ((~![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(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4515, 4514])).
% 1.73/1.91 tff(4517,plain,
% 1.73/1.91 (~r(z, s(s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4516, 65, 97, 1131])).
% 1.73/1.91 tff(4518,plain,
% 1.73/1.91 (b(z, s(s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[823, 4517])).
% 1.73/1.91 tff(4519,plain,
% 1.73/1.91 (((~![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(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(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4520,plain,
% 1.73/1.91 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), 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(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(rewrite,[status(thm)],[])).
% 1.73/1.91 tff(4521,plain,
% 1.73/1.91 (((~![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)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.73/1.91 inference(monotonicity,[status(thm)],[4520])).
% 1.73/1.91 tff(4522,plain,
% 1.73/1.91 (((~![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)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.73/1.91 inference(transitivity,[status(thm)],[4521, 4519])).
% 1.73/1.91 tff(4523,plain,
% 1.73/1.91 ((~![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)))),
% 1.73/1.91 inference(quant_inst,[status(thm)],[])).
% 1.73/1.91 tff(4524,plain,
% 1.73/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.73/1.91 inference(modus_ponens,[status(thm)],[4523, 4522])).
% 1.73/1.91 tff(4525,plain,
% 1.73/1.91 (~r(s(s(s(s(z)))), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4524, 65, 97, 1131])).
% 1.73/1.91 tff(4526,plain,
% 1.73/1.91 (b(s(s(s(s(z)))), z)),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1089, 4525])).
% 1.73/1.91 tff(4527,plain,
% 1.73/1.91 ($false),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[1084, 4526, 4518, 537, 538, 4510])).
% 1.73/1.91 tff(4528,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.91 tff(4529,plain,
% 1.73/1.91 (~r(s(s(s(s(z)))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[4528, 97, 3346, 2, 3352])).
% 1.73/1.91 tff(4530,plain,
% 1.73/1.91 (b(s(s(s(s(z)))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[775, 4529, 642])).
% 1.73/1.91 tff(4531,plain,
% 1.73/1.91 (~r(s(z), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3102, 3358, 97])).
% 1.73/1.91 tff(4532,plain,
% 1.73/1.91 (b(s(z), s(s(s(z))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[493, 4531])).
% 1.73/1.91 tff(4533,plain,
% 1.73/1.91 (~r(s(s(s(z))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[3058, 97, 3352, 3346, 384])).
% 1.73/1.91 tff(4534,plain,
% 1.73/1.91 (b(s(s(s(z))), s(z))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[595, 4533])).
% 1.73/1.91 tff(4535,plain,
% 1.73/1.91 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[2699, 4502, 2, 4534, 3356, 3354, 4532])).
% 1.73/1.91 tff(4536,plain,
% 1.73/1.91 (r(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[709, 4535, 635])).
% 1.73/1.91 tff(4537,plain,
% 1.73/1.91 (~r(s(z), s(s(s(s(z)))))),
% 1.73/1.91 inference(unit_resolution,[status(thm)],[653, 4536, 384])).
% 1.73/1.91 tff(4538,plain,
% 1.73/1.91 (b(s(z), s(s(s(s(z)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[658, 4537, 643])).
% 1.73/1.92 tff(4539,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2465, 162, 4534, 4532, 4538, 4530, 4502])).
% 1.73/1.92 tff(4540,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(4541,plain,
% 1.73/1.92 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4540, 97, 2, 384, 54])).
% 1.73/1.92 tff(4542,plain,
% 1.73/1.92 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[360, 4541])).
% 1.73/1.92 tff(4543,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4544,plain,
% 1.73/1.92 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4545,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[4544])).
% 1.73/1.92 tff(4546,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[4545, 4543])).
% 1.73/1.92 tff(4547,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), 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))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(4548,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[4547, 4546])).
% 1.73/1.92 tff(4549,plain,
% 1.73/1.92 ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4548, 162, 3018, 3042, 3332, 4534])).
% 1.73/1.92 tff(4550,plain,
% 1.73/1.92 (~b(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4549, 4542])).
% 1.73/1.92 tff(4551,plain,
% 1.73/1.92 (r(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[175, 4550])).
% 1.73/1.92 tff(4552,plain,
% 1.73/1.92 (~b(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3066, 395, 537, 538, 384])).
% 1.73/1.92 tff(4553,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[295, 4174, 4552])).
% 1.73/1.92 tff(4554,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(4555,plain,
% 1.73/1.92 (~r(s(z), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4554, 4551, 3352, 3346, 384])).
% 1.73/1.92 tff(4556,plain,
% 1.73/1.92 (b(s(z), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[493, 4555])).
% 1.73/1.92 tff(4557,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4558,plain,
% 1.73/1.92 (((~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(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(s(s(z))), s(z))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4559,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[4558])).
% 1.73/1.92 tff(4560,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[4559, 4557])).
% 1.73/1.92 tff(4561,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(4562,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[4561, 4560])).
% 1.73/1.92 tff(4563,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4562, 162, 3018, 3042, 4542, 4534, 4556])).
% 1.73/1.92 tff(4564,plain,((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(4565,plain,
% 1.73/1.92 (~r(z, s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4564, 54, 2, 384])).
% 1.73/1.92 tff(4566,plain,
% 1.73/1.92 (b(z, s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[117, 4565])).
% 1.73/1.92 tff(4567,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4568,plain,
% 1.73/1.92 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4569,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[4568])).
% 1.73/1.92 tff(4570,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[4569, 4567])).
% 1.73/1.92 tff(4571,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(4572,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[4571, 4570])).
% 1.73/1.92 tff(4573,plain,
% 1.73/1.92 (~b(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4572, 162, 4566, 3018, 3042, 3332])).
% 1.73/1.92 tff(4574,plain,
% 1.73/1.92 (r(s(z), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[175, 4573])).
% 1.73/1.92 tff(4575,plain,
% 1.73/1.92 (~r(s(z), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4554, 4574, 3352, 3346, 384])).
% 1.73/1.92 tff(4576,plain,
% 1.73/1.92 (b(s(z), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[493, 4575])).
% 1.73/1.92 tff(4577,plain,
% 1.73/1.92 (~b(s(s(s(z))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3150, 588, 538, 578, 537])).
% 1.73/1.92 tff(4578,plain,
% 1.73/1.92 (r(s(s(s(z))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[381, 4577])).
% 1.73/1.92 tff(4579,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1389, 65, 194, 385, 4578])).
% 1.73/1.92 tff(4580,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(4581,plain,
% 1.73/1.92 (~r(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4580, 4574, 3346, 3352, 2, 384])).
% 1.73/1.92 tff(4582,plain,
% 1.73/1.92 (b(s(s(s(z))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[595, 4581])).
% 1.73/1.92 tff(4583,plain,
% 1.73/1.92 (~r(s(s(s(z))), s(s(z)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3288, 4582, 4576, 3042, 54])).
% 1.73/1.92 tff(4584,plain,
% 1.73/1.92 (b(s(s(s(z))), s(s(z)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[459, 4583])).
% 1.73/1.92 tff(4585,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4586,plain,
% 1.73/1.92 (((~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(z, s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4587,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[4586])).
% 1.73/1.92 tff(4588,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[4587, 4585])).
% 1.73/1.92 tff(4589,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(4590,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 1.73/1.92 tff(4591,plain,
% 1.73/1.92 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4590, 162, 4566, 3018, 3042, 3332, 4582])).
% 1.73/1.92 tff(4592,plain,
% 1.73/1.92 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[360, 4591])).
% 1.73/1.92 tff(4593,plain,
% 1.73/1.92 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3094, 4592, 54])).
% 1.73/1.92 tff(4594,plain,
% 1.73/1.92 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[442, 4593])).
% 1.73/1.92 tff(4595,plain,
% 1.73/1.92 (~b(s(s(s(s(elem!1)))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[185, 4566, 3018, 3042, 3332])).
% 1.73/1.92 tff(4596,plain,
% 1.73/1.92 (r(s(s(s(s(elem!1)))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[95, 4595])).
% 1.73/1.92 tff(4597,plain,
% 1.73/1.92 (~r(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2601, 4592, 4596])).
% 1.73/1.92 tff(4598,plain,
% 1.73/1.92 (b(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[295, 4597])).
% 1.73/1.92 tff(4599,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[1465, 4598, 4594, 3352, 3346, 4584])).
% 1.73/1.92 tff(4600,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(4601,plain,
% 1.73/1.92 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4600, 2, 384])).
% 1.73/1.92 tff(4602,plain,
% 1.73/1.92 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[52, 4601])).
% 1.73/1.92 tff(4603,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2986, 588, 578, 4602, 3034, 712])).
% 1.73/1.92 tff(4604,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(4605,plain,
% 1.73/1.92 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4604, 385, 2, 384])).
% 1.73/1.92 tff(4606,plain,
% 1.73/1.92 (b(s(s(s(s(elem!1)))), s(z))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[149, 4605])).
% 1.73/1.92 tff(4607,plain,
% 1.73/1.92 (~b(s(s(s(s(elem!1)))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[3122, 4606, 3018, 3032, 3022])).
% 1.73/1.92 tff(4608,plain,
% 1.73/1.92 (r(s(s(s(s(elem!1)))), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[95, 4607])).
% 1.73/1.92 tff(4609,plain,
% 1.73/1.92 ($false),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4572, 162, 152, 121, 177, 151, 120])).
% 1.73/1.92 tff(4610,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.92 tff(4611,plain,
% 1.73/1.92 (~b(z, s(s(s(s(elem!1)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4610, 4606, 3032, 3018, 3022])).
% 1.73/1.92 tff(4612,plain,
% 1.73/1.92 (r(z, s(s(s(s(elem!1)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[83, 4611])).
% 1.73/1.92 tff(4613,plain,
% 1.73/1.92 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2986, 363, 4602, 578, 588])).
% 1.73/1.92 tff(4614,plain,
% 1.73/1.92 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[590, 363, 4602, 385, 2, 384])).
% 1.73/1.92 tff(4615,plain,
% 1.73/1.92 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[338, 4614])).
% 1.73/1.92 tff(4616,plain,
% 1.73/1.92 (~r(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[2507, 4615, 495])).
% 1.73/1.92 tff(4617,plain,
% 1.73/1.92 (b(z, s(s(s(z))))),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[295, 4616])).
% 1.73/1.92 tff(4618,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4619,plain,
% 1.73/1.92 (((~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(s(s(elem!1)))), 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(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4620,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[4619])).
% 1.73/1.92 tff(4621,plain,
% 1.73/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.73/1.92 inference(transitivity,[status(thm)],[4620, 4618])).
% 1.73/1.92 tff(4622,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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))))))),
% 1.73/1.92 inference(quant_inst,[status(thm)],[])).
% 1.73/1.92 tff(4623,plain,
% 1.73/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.73/1.92 inference(modus_ponens,[status(thm)],[4622, 4621])).
% 1.73/1.92 tff(4624,plain,
% 1.73/1.92 (~b(s(s(z)), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[4623, 162, 4602, 588, 363, 578, 4617])).
% 1.73/1.92 tff(4625,plain,
% 1.73/1.92 (r(s(s(z)), z)),
% 1.73/1.92 inference(unit_resolution,[status(thm)],[245, 4624])).
% 1.73/1.92 tff(4626,plain,
% 1.73/1.92 (((~![X0: $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)))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4627,plain,
% 1.73/1.92 (((~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)))))))),
% 1.73/1.92 inference(rewrite,[status(thm)],[])).
% 1.73/1.92 tff(4628,plain,
% 1.73/1.92 (((~![X0: $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))))))))),
% 1.73/1.92 inference(monotonicity,[status(thm)],[4627])).
% 1.73/1.92 tff(4629,plain,
% 1.73/1.92 (((~![X0: $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)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4628, 4626])).
% 1.73/1.93 tff(4630,plain,
% 1.73/1.93 ((~![X0: $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)))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(4631,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4630, 4629])).
% 1.73/1.93 tff(4632,plain,
% 1.73/1.93 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4631, 65, 2252, 4625])).
% 1.73/1.93 tff(4633,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[214, 47, 4632, 4613, 209])).
% 1.73/1.93 tff(4634,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(4635,plain,
% 1.73/1.93 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4634, 4608, 4612, 385, 2, 384])).
% 1.73/1.93 tff(4636,plain,
% 1.73/1.93 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[360, 4635])).
% 1.73/1.93 tff(4637,plain,
% 1.73/1.93 (~r(z, s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2601, 4636, 4608])).
% 1.73/1.93 tff(4638,plain,
% 1.73/1.93 (b(z, s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[295, 4637])).
% 1.73/1.93 tff(4639,plain,
% 1.73/1.93 (b(z, s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[117, 3347])).
% 1.73/1.93 tff(4640,plain,
% 1.73/1.93 (~b(s(s(s(s(z)))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2657, 2649, 4639, 3114, 659])).
% 1.73/1.93 tff(4641,plain,
% 1.73/1.93 (r(s(s(s(s(z)))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[775, 4640, 642])).
% 1.73/1.93 tff(4642,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1594, 65, 384, 4641, 644])).
% 1.73/1.93 tff(4643,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(4644,plain,
% 1.73/1.93 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4643, 3020, 384])).
% 1.73/1.93 tff(4645,plain,
% 1.73/1.93 (b(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[709, 4644, 635])).
% 1.73/1.93 tff(4646,plain,
% 1.73/1.93 (((~![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(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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4647,plain,
% 1.73/1.93 (((~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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4648,plain,
% 1.73/1.93 (((~![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(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4647])).
% 1.73/1.93 tff(4649,plain,
% 1.73/1.93 (((~![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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4648, 4646])).
% 1.73/1.93 tff(4650,plain,
% 1.73/1.93 ((~![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))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(4651,plain,
% 1.73/1.93 ((~![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(s(z)))), s(s(s(z)))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4650, 4649])).
% 1.73/1.93 tff(4652,plain,
% 1.73/1.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4651, 65, 385, 1131])).
% 1.73/1.93 tff(4653,plain,
% 1.73/1.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[690, 4652, 679])).
% 1.73/1.93 tff(4654,plain,
% 1.73/1.93 (((~![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(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(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4655,plain,
% 1.73/1.93 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4656,plain,
% 1.73/1.93 (((~![X0: $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(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(z))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4655])).
% 1.73/1.93 tff(4657,plain,
% 1.73/1.93 (((~![X0: $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(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(z)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4656, 4654])).
% 1.73/1.93 tff(4658,plain,
% 1.73/1.93 ((~![X0: $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(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(4659,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4658, 4657])).
% 1.73/1.93 tff(4660,plain,
% 1.73/1.93 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4659, 65, 385, 1131])).
% 1.73/1.93 tff(4661,plain,
% 1.73/1.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[675, 4660, 664])).
% 1.73/1.93 tff(4662,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2340, 162, 445, 825, 4661, 4653, 2806])).
% 1.73/1.93 tff(4663,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(4664,plain,
% 1.73/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4663, 578, 4645, 385, 2])).
% 1.73/1.93 tff(4665,plain,
% 1.73/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[775, 4664, 642])).
% 1.73/1.93 tff(4666,plain,
% 1.73/1.93 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.73/1.93 inference(commutativity,[status(thm)],[])).
% 1.73/1.93 tff(4667,plain,
% 1.73/1.93 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(symmetry,[status(thm)],[4666])).
% 1.73/1.93 tff(4668,plain,
% 1.73/1.93 ((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(elem!1))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4667])).
% 1.73/1.93 tff(4669,plain,
% 1.73/1.93 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[753, 4668])).
% 1.73/1.93 tff(4670,plain,
% 1.73/1.93 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3219, 694, 151, 177, 1437])).
% 1.73/1.93 tff(4671,plain,
% 1.73/1.93 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[763, 47, 4670, 753])).
% 1.73/1.93 tff(4672,plain,
% 1.73/1.93 (~b(s(s(s(s(z)))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3198, 694, 121, 152, 1437])).
% 1.73/1.93 tff(4673,plain,
% 1.73/1.93 (r(s(s(s(s(z)))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[1089, 4672])).
% 1.73/1.93 tff(4674,plain,
% 1.73/1.93 (~b(s(s(s(s(elem!1)))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3122, 151, 177, 121, 152])).
% 1.73/1.93 tff(4675,plain,
% 1.73/1.93 (r(s(s(s(s(elem!1)))), z)),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[95, 4674])).
% 1.73/1.93 tff(4676,plain,
% 1.73/1.93 (((~![X0: $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)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4677,plain,
% 1.73/1.93 (((~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)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4678,plain,
% 1.73/1.93 (((~![X0: $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))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4677])).
% 1.73/1.93 tff(4679,plain,
% 1.73/1.93 (((~![X0: $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)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4678, 4676])).
% 1.73/1.93 tff(4680,plain,
% 1.73/1.93 ((~![X0: $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)))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(4681,plain,
% 1.73/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4680, 4679])).
% 1.73/1.93 tff(4682,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4681, 65, 4675, 4673, 4671])).
% 1.73/1.93 tff(4683,plain,((~b(s(z), s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = 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(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(4684,plain,
% 1.73/1.93 (~b(s(z), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4683, 753, 151, 177, 1437, 121, 152])).
% 1.73/1.93 tff(4685,plain,
% 1.73/1.93 (r(s(z), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[658, 4684, 643])).
% 1.73/1.93 tff(4686,plain,
% 1.73/1.93 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[3172, 4685, 2])).
% 1.73/1.93 tff(4687,plain,
% 1.73/1.93 (b(s(s(z)), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[801, 4686, 634])).
% 1.73/1.93 tff(4688,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2685, 162, 444, 445, 825, 692, 1369])).
% 1.73/1.93 tff(4689,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(4690,plain,
% 1.73/1.93 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4689, 4687, 445, 825, 444])).
% 1.73/1.93 tff(4691,plain,
% 1.73/1.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[690, 4690, 679])).
% 1.73/1.93 tff(4692,plain,
% 1.73/1.93 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[2707, 65, 4691, 340])).
% 1.73/1.93 tff(4693,plain,
% 1.73/1.93 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[763, 47, 753, 4692])).
% 1.73/1.93 tff(4694,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(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)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4695,plain,
% 1.73/1.93 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(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(elem!1)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4696,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4695])).
% 1.73/1.93 tff(4697,plain,
% 1.73/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(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)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4696, 4694])).
% 1.73/1.93 tff(4698,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(elem!1)))), s(s(z)))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(4699,plain,
% 1.73/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(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))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4698, 4697])).
% 1.73/1.93 tff(4700,plain,
% 1.73/1.93 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4699, 162, 416, 825, 4687, 4693])).
% 1.73/1.93 tff(4701,plain,
% 1.73/1.93 (((~![X0: $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(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)))), 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(s(s(elem!1)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4702,plain,
% 1.73/1.93 (((~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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), 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(s(s(elem!1)))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4703,plain,
% 1.73/1.93 (((~![X0: $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)))), 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)))), 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(s(s(elem!1))))))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4702])).
% 1.73/1.93 tff(4704,plain,
% 1.73/1.93 (((~![X0: $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)))), 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)))), 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(s(s(elem!1)))))))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4703, 4701])).
% 1.73/1.93 tff(4705,plain,
% 1.73/1.93 ((~![X0: $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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(4706,plain,
% 1.73/1.93 ((~![X0: $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(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))))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4705, 4704])).
% 1.73/1.93 tff(4707,plain,
% 1.73/1.93 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4706, 65, 4675, 4691, 340])).
% 1.73/1.93 tff(4708,plain,
% 1.73/1.93 (((~![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))))))),
% 1.73/1.93 inference(rewrite,[status(thm)],[])).
% 1.73/1.93 tff(4709,plain,
% 1.73/1.93 ((~![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))))))),
% 1.73/1.93 inference(quant_inst,[status(thm)],[])).
% 1.73/1.93 tff(4710,plain,
% 1.73/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[4709, 4708])).
% 1.73/1.93 tff(4711,plain,
% 1.73/1.93 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4710, 47, 4707])).
% 1.73/1.93 tff(4712,plain,
% 1.73/1.93 ($false),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4711, 4700, 4669])).
% 1.73/1.93 tff(4713,plain,((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.93 tff(4714,plain,
% 1.73/1.93 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.73/1.93 inference(unit_resolution,[status(thm)],[4713, 4636, 4645, 4602, 578, 588, 2, 4606, 3018, 4665, 3032, 3022])).
% 1.73/1.93 tff(4715,plain,
% 1.73/1.93 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4714])).
% 1.73/1.93 tff(4716,plain,
% 1.73/1.93 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[20, 4715, 630])).
% 1.73/1.93 tff(4717,plain,
% 1.73/1.93 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4716])).
% 1.73/1.93 tff(4718,plain,
% 1.73/1.93 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4716])).
% 1.73/1.93 tff(4719,plain,
% 1.73/1.93 (s(s(elem!1)) = s(s(z))),
% 1.73/1.93 inference(transitivity,[status(thm)],[25, 4718, 312])).
% 1.73/1.93 tff(4720,plain,
% 1.73/1.93 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4719])).
% 1.73/1.93 tff(4721,plain,
% 1.73/1.93 (s(elem!1) = s(z)),
% 1.73/1.93 inference(transitivity,[status(thm)],[325, 4720, 15])).
% 1.73/1.93 tff(4722,plain,
% 1.73/1.93 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4721])).
% 1.73/1.93 tff(4723,plain,
% 1.73/1.93 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.73/1.93 inference(symmetry,[status(thm)],[4722])).
% 1.73/1.93 tff(4724,plain,
% 1.73/1.93 (z = elem!1),
% 1.73/1.93 inference(transitivity,[status(thm)],[1182, 4723, 1170])).
% 1.73/1.93 tff(4725,plain,
% 1.73/1.93 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4724])).
% 1.73/1.93 tff(4726,plain,
% 1.73/1.93 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4725, 1179])).
% 1.73/1.93 tff(4727,plain,
% 1.73/1.93 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.73/1.93 inference(transitivity,[status(thm)],[4726, 1180])).
% 1.73/1.93 tff(4728,plain,
% 1.73/1.93 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4727])).
% 1.73/1.93 tff(4729,plain,
% 1.73/1.93 (~(s(z) = elem!1)),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[111, 4728])).
% 1.73/1.93 tff(4730,plain,
% 1.73/1.93 (elem!1 = z),
% 1.73/1.93 inference(transitivity,[status(thm)],[1171, 4722, 13])).
% 1.73/1.93 tff(4731,plain,
% 1.73/1.93 (b(elem!1, z) <=> b(z, z)),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4730])).
% 1.73/1.93 tff(4732,plain,
% 1.73/1.93 (b(z, z) <=> b(elem!1, z)),
% 1.73/1.93 inference(symmetry,[status(thm)],[4731])).
% 1.73/1.93 tff(4733,plain,
% 1.73/1.93 ((~b(z, z)) <=> (~b(elem!1, z))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4732])).
% 1.73/1.93 tff(4734,plain,
% 1.73/1.93 (~b(elem!1, z)),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[3433, 4733])).
% 1.73/1.93 tff(4735,plain,
% 1.73/1.93 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4719])).
% 1.73/1.93 tff(4736,plain,
% 1.73/1.93 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.73/1.93 inference(symmetry,[status(thm)],[4735])).
% 1.73/1.93 tff(4737,plain,
% 1.73/1.93 (r(s(z), s(s(elem!1)))),
% 1.73/1.93 inference(modus_ponens,[status(thm)],[384, 4736])).
% 1.73/1.93 tff(4738,plain,
% 1.73/1.93 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4719])).
% 1.73/1.93 tff(4739,plain,
% 1.73/1.93 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.73/1.93 inference(symmetry,[status(thm)],[4738])).
% 1.73/1.93 tff(4740,plain,
% 1.73/1.93 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4730])).
% 1.73/1.93 tff(4741,plain,
% 1.73/1.93 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.73/1.93 inference(symmetry,[status(thm)],[4740])).
% 1.73/1.93 tff(4742,plain,
% 1.73/1.93 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.73/1.93 inference(transitivity,[status(thm)],[4741, 4739])).
% 1.73/1.93 tff(4743,plain,
% 1.73/1.93 ((~b(z, s(s(z)))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.73/1.93 inference(monotonicity,[status(thm)],[4742])).
% 1.73/1.93 tff(4744,plain,
% 1.73/1.94 (~b(elem!1, s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[3019, 4743])).
% 1.73/1.94 tff(4745,plain,
% 1.73/1.94 ((elem!1 = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4714])).
% 1.73/1.94 tff(4746,plain,
% 1.73/1.94 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[4745])).
% 1.73/1.94 tff(4747,plain,
% 1.73/1.94 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4730])).
% 1.73/1.94 tff(4748,plain,
% 1.73/1.94 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.73/1.94 inference(transitivity,[status(thm)],[4747, 813])).
% 1.73/1.94 tff(4749,plain,
% 1.73/1.94 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[4748])).
% 1.73/1.94 tff(4750,plain,
% 1.73/1.94 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[4749, 4746])).
% 1.73/1.94 tff(4751,plain,
% 1.73/1.94 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4750])).
% 1.73/1.94 tff(4752,plain,
% 1.73/1.94 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[817, 4751])).
% 1.73/1.94 tff(4753,plain,
% 1.73/1.94 (~(elem!1 = s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1555, 1538])).
% 1.73/1.94 tff(4754,plain,
% 1.73/1.94 (r(elem!1, s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3637, 3632, 4753])).
% 1.73/1.94 tff(4755,plain,
% 1.73/1.94 (((~![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(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(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4756,plain,
% 1.73/1.94 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4757,plain,
% 1.73/1.94 (((~![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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~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(z), s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4756])).
% 1.73/1.94 tff(4758,plain,
% 1.73/1.94 (((~![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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~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(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[4757, 4755])).
% 1.73/1.94 tff(4759,plain,
% 1.73/1.94 ((~![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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(4760,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 1.73/1.94 tff(4761,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4760, 65, 1246, 1616, 3621])).
% 1.73/1.94 tff(4762,plain,((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4763,plain,
% 1.73/1.94 (~r(elem!1, s(z))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4762, 4754, 1246])).
% 1.73/1.94 tff(4764,plain,
% 1.73/1.94 (b(elem!1, s(z))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1651, 4763, 1615])).
% 1.73/1.94 tff(4765,plain,
% 1.73/1.94 (((~![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), elem!1)) | (~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(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4766,plain,
% 1.73/1.94 (((~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), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4767,plain,
% 1.73/1.94 (((~![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), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4766])).
% 1.73/1.94 tff(4768,plain,
% 1.73/1.94 (((~![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), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[4767, 4765])).
% 1.73/1.94 tff(4769,plain,
% 1.73/1.94 ((~![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)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(4770,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4769, 4768])).
% 1.73/1.94 tff(4771,plain,
% 1.73/1.94 (~r(s(z), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4770, 65, 1246, 4754])).
% 1.73/1.94 tff(4772,plain,
% 1.73/1.94 (b(s(z), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1682, 4771, 1247])).
% 1.73/1.94 tff(4773,plain,
% 1.73/1.94 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1540, 1538])).
% 1.73/1.94 tff(4774,plain,
% 1.73/1.94 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1259, 4773])).
% 1.73/1.94 tff(4775,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.94 tff(4776,plain,
% 1.73/1.94 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.73/1.94 inference(symmetry,[status(thm)],[4775])).
% 1.73/1.94 tff(4777,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1275, 4776])).
% 1.73/1.94 tff(4778,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4779,plain,
% 1.73/1.94 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4778, 4774])).
% 1.73/1.94 tff(4780,plain,
% 1.73/1.94 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1267, 65, 1261, 2252])).
% 1.73/1.94 tff(4781,assumption,(~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.94 tff(4782,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.94 tff(4783,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2109, 47, 1280, 4782, 4781])).
% 1.73/1.94 tff(4784,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4785,plain,
% 1.73/1.94 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4784, 4780, 4779])).
% 1.73/1.94 tff(4786,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1299, 65, 1261, 2252])).
% 1.73/1.94 tff(4787,plain,
% 1.73/1.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1304, 4786, 4774])).
% 1.73/1.94 tff(4788,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.94 tff(4789,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.94 tff(4790,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.73/1.94 tff(4791,plain,
% 1.73/1.94 (elem!1 = s(s(s(s(elem!1))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4790, 1162])).
% 1.73/1.94 tff(4792,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1538, 4791])).
% 1.73/1.94 tff(4793,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4794,plain,
% 1.73/1.94 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4793, 1538])).
% 1.73/1.94 tff(4795,plain,
% 1.73/1.94 (((~![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(s(s(s(elem!1)))), z)) | (~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, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4796,plain,
% 1.73/1.94 (((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4797,plain,
% 1.73/1.94 (((~![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(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~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, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4796])).
% 1.73/1.94 tff(4798,plain,
% 1.73/1.94 (((~![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(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~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, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.94 inference(transitivity,[status(thm)],[4797, 4795])).
% 1.73/1.94 tff(4799,plain,
% 1.73/1.94 ((~![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(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(4800,plain,
% 1.73/1.94 ((~![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(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4799, 4798])).
% 1.73/1.94 tff(4801,plain,
% 1.73/1.94 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4800, 65, 3473, 2252])).
% 1.73/1.94 tff(4802,plain,
% 1.73/1.94 (((~![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(s(s(s(elem!1)))), z)) | (~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, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4803,plain,
% 1.73/1.94 (((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4804,plain,
% 1.73/1.94 (((~![X0: $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(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4803])).
% 1.73/1.94 tff(4805,plain,
% 1.73/1.94 (((~![X0: $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(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[4804, 4802])).
% 1.73/1.94 tff(4806,plain,
% 1.73/1.94 ((~![X0: $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(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(4807,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4806, 4805])).
% 1.73/1.94 tff(4808,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4807, 65, 3473, 3532, 2252])).
% 1.73/1.94 tff(4809,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4810,plain,
% 1.73/1.94 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4809, 3473, 2252])).
% 1.73/1.94 tff(4811,plain,
% 1.73/1.94 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3975, 4810, 1538])).
% 1.73/1.94 tff(4812,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4813,plain,
% 1.73/1.94 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4814,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4813])).
% 1.73/1.94 tff(4815,plain,
% 1.73/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[4814, 4812])).
% 1.73/1.94 tff(4816,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(4817,plain,
% 1.73/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 1.73/1.94 tff(4818,plain,
% 1.73/1.94 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4817, 162, 4811, 2219, 3884, 4789])).
% 1.73/1.94 tff(4819,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1529, 4818, 4801, 4794])).
% 1.73/1.94 tff(4820,plain,((~r(elem!1, z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4821,plain,
% 1.73/1.94 (~r(elem!1, z)),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4820, 3884, 2219, 4789, 2252, 1538])).
% 1.73/1.94 tff(4822,plain,
% 1.73/1.94 (elem!1 = z),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3486, 4821, 3442])).
% 1.73/1.94 tff(4823,plain,
% 1.73/1.94 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4822])).
% 1.73/1.94 tff(4824,plain,
% 1.73/1.94 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(symmetry,[status(thm)],[4823])).
% 1.73/1.94 tff(4825,plain,
% 1.73/1.94 ((~b(z, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4824])).
% 1.73/1.94 tff(4826,plain,
% 1.73/1.94 (~b(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4788, 4825])).
% 1.73/1.94 tff(4827,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3884, 4826])).
% 1.73/1.94 tff(4828,plain,((~b(elem!1, s(s(s(elem!1))))) | b(z, s(s(s(elem!1)))) | b(elem!1, z) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4829,plain,
% 1.73/1.94 (~b(elem!1, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4828, 4788, 3442, 4787, 4785, 2252, 1538])).
% 1.73/1.94 tff(4830,plain,
% 1.73/1.94 (r(z, s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2296, 4788])).
% 1.73/1.94 tff(4831,plain,
% 1.73/1.94 (r(s(s(s(s(z)))), z)),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[2252, 1228])).
% 1.73/1.94 tff(4832,plain,
% 1.73/1.94 (b(elem!1, s(s(elem!1)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[1149, 4224])).
% 1.73/1.94 tff(4833,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3632, 4832])).
% 1.73/1.94 tff(4834,plain,((~(elem!1 = z)) | b(elem!1, s(s(elem!1))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4835,plain,
% 1.73/1.94 (~b(z, s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4834, 1211, 3632])).
% 1.73/1.94 tff(4836,plain,
% 1.73/1.94 (r(z, s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[3401, 4835])).
% 1.73/1.94 tff(4837,plain,
% 1.73/1.94 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4022, 4836, 2304])).
% 1.73/1.94 tff(4838,plain,
% 1.73/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, 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(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4839,plain,
% 1.73/1.94 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4840,plain,
% 1.73/1.94 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(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(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4839])).
% 1.73/1.94 tff(4841,plain,
% 1.73/1.94 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(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(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.73/1.94 inference(transitivity,[status(thm)],[4840, 4838])).
% 1.73/1.94 tff(4842,plain,
% 1.73/1.94 ((~![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(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))),
% 1.73/1.94 inference(quant_inst,[status(thm)],[])).
% 1.73/1.94 tff(4843,plain,
% 1.73/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4842, 4841])).
% 1.73/1.94 tff(4844,plain,
% 1.73/1.94 ($false),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4843, 65, 3998, 1495, 495])).
% 1.73/1.94 tff(4845,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.94 tff(4846,plain,
% 1.73/1.94 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[4845, 4836, 495])).
% 1.73/1.94 tff(4847,plain,
% 1.73/1.94 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[1493, 4846, 1232])).
% 1.73/1.94 tff(4848,plain,
% 1.73/1.94 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2126, 4847, 2001, 1280, 2078, 4837])).
% 1.73/1.94 tff(4849,plain,
% 1.73/1.94 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[2302, 4848, 1237])).
% 1.73/1.94 tff(4850,plain,
% 1.73/1.94 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.94 inference(unit_resolution,[status(thm)],[52, 4849])).
% 1.73/1.94 tff(4851,plain,
% 1.73/1.94 (r(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4850, 1345])).
% 1.73/1.94 tff(4852,plain,
% 1.73/1.94 (r(z, s(s(z)))),
% 1.73/1.94 inference(modus_ponens,[status(thm)],[4836, 3995])).
% 1.73/1.94 tff(4853,plain,
% 1.73/1.94 (((~![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(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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4854,plain,
% 1.73/1.94 (((~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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.73/1.94 inference(rewrite,[status(thm)],[])).
% 1.73/1.94 tff(4855,plain,
% 1.73/1.94 (((~![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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.73/1.94 inference(monotonicity,[status(thm)],[4854])).
% 1.73/1.94 tff(4856,plain,
% 1.73/1.94 (((~![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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[4855, 4853])).
% 1.73/1.95 tff(4857,plain,
% 1.73/1.95 ((~![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)))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4858,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4857, 4856])).
% 1.73/1.95 tff(4859,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4858, 65, 4852, 4851, 4831])).
% 1.73/1.95 tff(4860,plain,((~(elem!1 = z)) | (~r(s(s(s(s(elem!1)))), z)) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4861,plain,
% 1.73/1.95 (~(elem!1 = z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4860, 4830, 4786, 4780, 4773, 2252, 495, 3632])).
% 1.73/1.95 tff(4862,plain,
% 1.73/1.95 (r(elem!1, z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3486, 4861, 3442])).
% 1.73/1.95 tff(4863,plain,
% 1.73/1.95 (((~![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(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(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4864,plain,
% 1.73/1.95 (((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4865,plain,
% 1.73/1.95 (((~![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(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~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, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4864])).
% 1.73/1.95 tff(4866,plain,
% 1.73/1.95 (((~![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(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~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, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[4865, 4863])).
% 1.73/1.95 tff(4867,plain,
% 1.73/1.95 ((~![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(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4868,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4867, 4866])).
% 1.73/1.95 tff(4869,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4868, 65, 3473, 1261, 1507])).
% 1.73/1.95 tff(4870,plain,((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4871,plain,
% 1.73/1.95 (~r(elem!1, s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4870, 4862, 1261])).
% 1.73/1.95 tff(4872,plain,
% 1.73/1.95 (elem!1 = s(s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1483, 4871, 4829])).
% 1.73/1.95 tff(4873,plain,
% 1.73/1.95 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4872])).
% 1.73/1.95 tff(4874,plain,
% 1.73/1.95 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4873])).
% 1.73/1.95 tff(4875,plain,
% 1.73/1.95 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4874])).
% 1.73/1.95 tff(4876,plain,
% 1.73/1.95 (~(z = elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1208, 4861])).
% 1.73/1.95 tff(4877,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.73/1.95 tff(4878,plain,
% 1.73/1.95 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4877])).
% 1.73/1.95 tff(4879,plain,
% 1.73/1.95 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 1.73/1.95 inference(symmetry,[status(thm)],[4878])).
% 1.73/1.95 tff(4880,plain,
% 1.73/1.95 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, elem!1))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4879])).
% 1.73/1.95 tff(4881,plain,
% 1.73/1.95 (~b(z, elem!1)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4788, 4880])).
% 1.73/1.95 tff(4882,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.73/1.95 tff(4883,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4882, 4881])).
% 1.73/1.95 tff(4884,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(z, elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4885,plain,
% 1.73/1.95 (~b(z, elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4884, 4872, 4788])).
% 1.73/1.95 tff(4886,plain,
% 1.73/1.95 (((~![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))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4887,plain,
% 1.73/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4888,plain,
% 1.73/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4887, 4886])).
% 1.73/1.95 tff(4889,plain,
% 1.73/1.95 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4888, 47])).
% 1.73/1.95 tff(4890,plain,
% 1.73/1.95 (r(z, elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4889, 4885, 4876])).
% 1.73/1.95 tff(4891,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.73/1.95 tff(4892,plain,
% 1.73/1.95 (((~![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(z, 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(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4893,plain,
% 1.73/1.95 (((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4894,plain,
% 1.73/1.95 (((~![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(z, s(s(elem!1)))) | (~r(elem!1, 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(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4893])).
% 1.73/1.95 tff(4895,plain,
% 1.73/1.95 (((~![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(z, s(s(elem!1)))) | (~r(elem!1, 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(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[4894, 4892])).
% 1.73/1.95 tff(4896,plain,
% 1.73/1.95 ((~![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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4897,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4896, 4895])).
% 1.73/1.95 tff(4898,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4897, 65, 4891, 3998, 3621])).
% 1.73/1.95 tff(4899,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4900,plain,
% 1.73/1.95 (~r(z, s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4899, 4890, 4754])).
% 1.73/1.95 tff(4901,plain,
% 1.73/1.95 (b(z, s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3401, 4900])).
% 1.73/1.95 tff(4902,plain,
% 1.73/1.95 (b(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4901, 4875])).
% 1.73/1.95 tff(4903,plain,
% 1.73/1.95 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4904,plain,
% 1.73/1.95 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4905,plain,
% 1.73/1.95 (((~![X0: $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)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), 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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4904])).
% 1.73/1.95 tff(4906,plain,
% 1.73/1.95 (((~![X0: $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)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), 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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[4905, 4903])).
% 1.73/1.95 tff(4907,plain,
% 1.73/1.95 ((~![X0: $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)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4908,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4907, 4906])).
% 1.73/1.95 tff(4909,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4908, 65, 4891, 1572, 495])).
% 1.73/1.95 tff(4910,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4911,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4910, 4890, 495])).
% 1.73/1.95 tff(4912,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1529, 4911, 4794])).
% 1.73/1.95 tff(4913,plain,
% 1.73/1.95 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4809, 4862, 2252])).
% 1.73/1.95 tff(4914,plain,
% 1.73/1.95 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3975, 4913, 1538])).
% 1.73/1.95 tff(4915,plain,
% 1.73/1.95 (s(s(s(elem!1))) = elem!1),
% 1.73/1.95 inference(symmetry,[status(thm)],[4872])).
% 1.73/1.95 tff(4916,plain,
% 1.73/1.95 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4915])).
% 1.73/1.95 tff(4917,plain,
% 1.73/1.95 ((~r(s(z), s(s(s(elem!1))))) <=> (~r(s(z), elem!1))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4916])).
% 1.73/1.95 tff(4918,plain,
% 1.73/1.95 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4915])).
% 1.73/1.95 tff(4919,plain,
% 1.73/1.95 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(symmetry,[status(thm)],[4918])).
% 1.73/1.95 tff(4920,plain,
% 1.73/1.95 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4874])).
% 1.73/1.95 tff(4921,plain,
% 1.73/1.95 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4754, 4920])).
% 1.73/1.95 tff(4922,plain,
% 1.73/1.95 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4921, 4919])).
% 1.73/1.95 tff(4923,plain,
% 1.73/1.95 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4874])).
% 1.73/1.95 tff(4924,plain,
% 1.73/1.95 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[1246, 4923])).
% 1.73/1.95 tff(4925,plain,
% 1.73/1.95 (((~![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(elem!1))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), 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(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4926,plain,
% 1.73/1.95 (((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4927,plain,
% 1.73/1.95 (((~![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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~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(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4926])).
% 1.73/1.95 tff(4928,plain,
% 1.73/1.95 (((~![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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~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(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[4927, 4925])).
% 1.73/1.95 tff(4929,plain,
% 1.73/1.95 ((~![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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4930,plain,
% 1.73/1.95 ((~![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(elem!1))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4929, 4928])).
% 1.73/1.95 tff(4931,plain,
% 1.73/1.95 ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4930, 65, 4924])).
% 1.73/1.95 tff(4932,plain,
% 1.73/1.95 (~r(s(z), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4931, 4922])).
% 1.73/1.95 tff(4933,plain,
% 1.73/1.95 (~r(s(z), elem!1)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4932, 4917])).
% 1.73/1.95 tff(4934,plain,
% 1.73/1.95 (b(s(z), elem!1)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1682, 4933, 1247])).
% 1.73/1.95 tff(4935,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.73/1.95 tff(4936,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4937,plain,
% 1.73/1.95 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4938,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4937])).
% 1.73/1.95 tff(4939,plain,
% 1.73/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(transitivity,[status(thm)],[4938, 4936])).
% 1.73/1.95 tff(4940,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4941,plain,
% 1.73/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4940, 4939])).
% 1.73/1.95 tff(4942,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4941, 162, 4119, 4935, 3990, 177, 1240])).
% 1.73/1.95 tff(4943,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4944,plain,
% 1.73/1.95 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4943, 4934, 4914, 4912, 4764])).
% 1.73/1.95 tff(4945,plain,
% 1.73/1.95 (r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[191, 4944])).
% 1.73/1.95 tff(4946,plain,
% 1.73/1.95 (~r(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2561, 4945, 2252])).
% 1.73/1.95 tff(4947,plain,
% 1.73/1.95 (b(s(z), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[175, 4946])).
% 1.73/1.95 tff(4948,plain,
% 1.73/1.95 (~r(z, s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[534, 4945, 495])).
% 1.73/1.95 tff(4949,plain,
% 1.73/1.95 (b(z, s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[117, 4948])).
% 1.73/1.95 tff(4950,plain,
% 1.73/1.95 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4874])).
% 1.73/1.95 tff(4951,plain,
% 1.73/1.95 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1503, 1495, 1246])).
% 1.73/1.95 tff(4952,plain,
% 1.73/1.95 (b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[191, 4951])).
% 1.73/1.95 tff(4953,plain,
% 1.73/1.95 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3629, 1495, 3621])).
% 1.73/1.95 tff(4954,plain,
% 1.73/1.95 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3975, 4953, 1538])).
% 1.73/1.95 tff(4955,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4943, 4954, 4952, 4935, 4119, 1240])).
% 1.73/1.95 tff(4956,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4957,plain,
% 1.73/1.95 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4956, 4934, 4764, 4912, 1538, 4754, 1246])).
% 1.73/1.95 tff(4958,plain,
% 1.73/1.95 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1493, 4957, 4773])).
% 1.73/1.95 tff(4959,plain,
% 1.73/1.95 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2077, 4773])).
% 1.73/1.95 tff(4960,plain,
% 1.73/1.95 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2082, 4773])).
% 1.73/1.95 tff(4961,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2092, 4945, 1246])).
% 1.73/1.95 tff(4962,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2101, 4961, 4960])).
% 1.73/1.95 tff(4963,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2126, 4962, 4786, 4780, 4959, 4958])).
% 1.73/1.95 tff(4964,plain,
% 1.73/1.95 (((~![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(s(elem!1)), s(s(s(elem!1))))) | (~r(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(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4965,plain,
% 1.73/1.95 (((~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)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4966,plain,
% 1.73/1.95 (((~![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)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4965])).
% 1.73/1.95 tff(4967,plain,
% 1.73/1.95 (((~![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)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.73/1.95 inference(transitivity,[status(thm)],[4966, 4964])).
% 1.73/1.95 tff(4968,plain,
% 1.73/1.95 ((~![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))))))),
% 1.73/1.95 inference(quant_inst,[status(thm)],[])).
% 1.73/1.95 tff(4969,plain,
% 1.73/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4968, 4967])).
% 1.73/1.95 tff(4970,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4969, 65, 3375, 1261, 2313])).
% 1.73/1.95 tff(4971,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,[]))).
% 1.73/1.95 tff(4972,plain,
% 1.73/1.95 (~r(s(s(elem!1)), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4971, 4963, 1261])).
% 1.73/1.95 tff(4973,plain,
% 1.73/1.95 (b(s(s(elem!1)), z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2783, 4972])).
% 1.73/1.95 tff(4974,plain,
% 1.73/1.95 (b(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4973, 4950])).
% 1.73/1.95 tff(4975,plain,
% 1.73/1.95 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[979, 4974, 4949, 4947, 4902])).
% 1.73/1.95 tff(4976,plain,
% 1.73/1.95 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[968, 4975])).
% 1.73/1.95 tff(4977,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4874])).
% 1.73/1.95 tff(4978,plain,
% 1.73/1.95 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.95 inference(modus_ponens,[status(thm)],[4963, 4977])).
% 1.73/1.95 tff(4979,plain,
% 1.73/1.95 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4784, 1280, 4779])).
% 1.73/1.95 tff(4980,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.95 tff(4981,plain,
% 1.73/1.95 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3138, 65, 2252, 230])).
% 1.73/1.95 tff(4982,plain,
% 1.73/1.95 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[52, 4981])).
% 1.73/1.95 tff(4983,plain,
% 1.73/1.95 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[2326, 1211, 1280, 2078, 2001, 230, 416, 2304])).
% 1.73/1.95 tff(4984,plain,
% 1.73/1.95 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[1493, 4983, 1232])).
% 1.73/1.95 tff(4985,plain,
% 1.73/1.95 ($false),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4845, 4984, 4836, 495])).
% 1.73/1.95 tff(4986,plain,((~(elem!1 = z)) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.95 tff(4987,plain,
% 1.73/1.95 (~(elem!1 = z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4986, 230, 4773, 1280, 2001, 495, 4982, 2304, 3632])).
% 1.73/1.95 tff(4988,plain,
% 1.73/1.95 (r(elem!1, z)),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[3486, 4987, 3442])).
% 1.73/1.95 tff(4989,plain,
% 1.73/1.95 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[4631, 65, 2252, 230])).
% 1.73/1.95 tff(4990,plain,
% 1.73/1.95 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.95 inference(unit_resolution,[status(thm)],[214, 47, 4989, 209])).
% 1.73/1.95 tff(4991,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.73/1.95 tff(4992,plain,
% 1.73/1.95 (((~![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(s(z)), z)) | (~r(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, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4993,plain,
% 1.73/1.95 (((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 1.73/1.95 inference(rewrite,[status(thm)],[])).
% 1.73/1.95 tff(4994,plain,
% 1.73/1.95 (((~![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(s(z)), z)) | (~r(elem!1, z)) | (~r(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, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))))),
% 1.73/1.95 inference(monotonicity,[status(thm)],[4993])).
% 1.73/1.95 tff(4995,plain,
% 1.73/1.95 (((~![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(s(z)), z)) | (~r(elem!1, z)) | (~r(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, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[4994, 4992])).
% 1.73/1.96 tff(4996,plain,
% 1.73/1.96 ((~![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(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(4997,plain,
% 1.73/1.96 ((~![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(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[4996, 4995])).
% 1.73/1.96 tff(4998,plain,
% 1.73/1.96 (~r(s(s(z)), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4997, 65, 3473, 230])).
% 1.73/1.96 tff(4999,plain,
% 1.73/1.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5000,plain,
% 1.73/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(5001,plain,
% 1.73/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[5000, 4999])).
% 1.73/1.96 tff(5002,plain,
% 1.73/1.96 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5001, 47])).
% 1.73/1.96 tff(5003,plain,
% 1.73/1.96 (b(s(s(z)), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5002, 4998, 4991])).
% 1.73/1.96 tff(5004,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1529, 4801, 4794])).
% 1.73/1.96 tff(5005,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5006,plain,
% 1.73/1.96 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5007,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5006])).
% 1.73/1.96 tff(5008,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[5007, 5005])).
% 1.73/1.96 tff(5009,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), elem!1)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(5010,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[5009, 5008])).
% 1.73/1.96 tff(5011,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5010, 162, 4982, 4811, 5004, 5003, 4990])).
% 1.73/1.96 tff(5012,plain,((~r(elem!1, z)) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5013,plain,
% 1.73/1.96 (s(s(z)) = elem!1),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5012, 4988, 230, 2252, 1538])).
% 1.73/1.96 tff(5014,plain,
% 1.73/1.96 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[4877])).
% 1.73/1.96 tff(5015,plain,
% 1.73/1.96 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5014])).
% 1.73/1.96 tff(5016,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.73/1.96 tff(5017,plain,
% 1.73/1.96 (s(s(z)) = s(s(s(elem!1)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[5016, 4877])).
% 1.73/1.96 tff(5018,plain,
% 1.73/1.96 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5017])).
% 1.73/1.96 tff(5019,plain,
% 1.73/1.96 (s(z) = s(s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[261, 5018, 24, 5015])).
% 1.73/1.96 tff(5020,plain,
% 1.73/1.96 ((s(s(elem!1)) = s(z)) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5015])).
% 1.73/1.96 tff(5021,plain,
% 1.73/1.96 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[5020, 1039])).
% 1.73/1.96 tff(5022,plain,
% 1.73/1.96 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5021])).
% 1.73/1.96 tff(5023,plain,
% 1.73/1.96 (~(s(z) = s(s(s(s(s(elem!1))))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[331, 5022])).
% 1.73/1.96 tff(5024,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5023, 5019])).
% 1.73/1.96 tff(5025,plain,((~(s(s(z)) = elem!1)) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5026,plain,
% 1.73/1.96 (~(elem!1 = s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5025, 5013])).
% 1.73/1.96 tff(5027,plain,
% 1.73/1.96 (b(elem!1, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1483, 5026, 4980])).
% 1.73/1.96 tff(5028,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1304, 2001, 4774])).
% 1.73/1.96 tff(5029,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5013])).
% 1.73/1.96 tff(5030,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[4982, 5029])).
% 1.73/1.96 tff(5031,plain,
% 1.73/1.96 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4809, 4988, 2252])).
% 1.73/1.96 tff(5032,plain,
% 1.73/1.96 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3975, 5031, 1538])).
% 1.73/1.96 tff(5033,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4817, 162, 5032, 5030, 5028, 5027, 4979])).
% 1.73/1.96 tff(5034,plain,((~r(s(s(z)), z)) | r(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | b(elem!1, z) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5035,plain,
% 1.73/1.96 (~r(s(s(z)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5034, 4871, 1538, 2252, 3442, 4780, 4786, 495, 4830, 3632])).
% 1.73/1.96 tff(5036,plain,
% 1.73/1.96 (b(s(s(z)), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[245, 5035])).
% 1.73/1.96 tff(5037,plain,
% 1.73/1.96 (~r(s(s(z)), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1945, 5036, 4902, 4974, 4978, 4976])).
% 1.73/1.96 tff(5038,plain,
% 1.73/1.96 (b(s(s(z)), s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[271, 5037])).
% 1.73/1.96 tff(5039,plain,
% 1.73/1.96 (~b(z, s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1400, 162, 4947, 4949, 5036, 5038])).
% 1.73/1.96 tff(5040,plain,
% 1.73/1.96 (r(z, s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[524, 5039])).
% 1.73/1.96 tff(5041,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.73/1.96 tff(5042,plain,
% 1.73/1.96 (((~![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(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(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5043,plain,
% 1.73/1.96 (((~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5044,plain,
% 1.73/1.96 (((~![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(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~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(z)))) | (~r(z, s(s(z))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5043])).
% 1.73/1.96 tff(5045,plain,
% 1.73/1.96 (((~![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(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~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(z)))) | (~r(z, s(s(z)))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[5044, 5042])).
% 1.73/1.96 tff(5046,plain,
% 1.73/1.96 ((~![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(elem!1, s(s(z)))) | (~r(z, s(s(z)))) | (~r(elem!1, z)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(5047,plain,
% 1.73/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[5046, 5045])).
% 1.73/1.96 tff(5048,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5047, 65, 3473, 55, 5041])).
% 1.73/1.96 tff(5049,plain,((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5050,plain,
% 1.73/1.96 (~r(elem!1, s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5049, 5040, 4862])).
% 1.73/1.96 tff(5051,plain,
% 1.73/1.96 (s(s(s(elem!1))) = elem!1),
% 1.73/1.96 inference(symmetry,[status(thm)],[4877])).
% 1.73/1.96 tff(5052,plain,
% 1.73/1.96 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5051])).
% 1.73/1.96 tff(5053,plain,
% 1.73/1.96 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.96 inference(symmetry,[status(thm)],[5052])).
% 1.73/1.96 tff(5054,plain,
% 1.73/1.96 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(z))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5053])).
% 1.73/1.96 tff(5055,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 1.73/1.96 tff(5056,plain,
% 1.73/1.96 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[5055, 5054])).
% 1.73/1.96 tff(5057,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.73/1.96 tff(5058,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5057, 5056])).
% 1.73/1.96 tff(5059,plain,((~r(s(s(s(elem!1))), s(s(z)))) | r(elem!1, s(s(z))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5060,plain,
% 1.73/1.96 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5059, 5050, 4872])).
% 1.73/1.96 tff(5061,plain,
% 1.73/1.96 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5051])).
% 1.73/1.96 tff(5062,plain,
% 1.73/1.96 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.73/1.96 inference(symmetry,[status(thm)],[5061])).
% 1.73/1.96 tff(5063,assumption,(~(s(elem!1) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.96 tff(5064,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5063, 5062])).
% 1.73/1.96 tff(5065,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5066,plain,
% 1.73/1.96 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5065, 4872])).
% 1.73/1.96 tff(5067,assumption,(s(elem!1) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.73/1.96 tff(5068,plain,
% 1.73/1.96 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5067])).
% 1.73/1.96 tff(5069,plain,
% 1.73/1.96 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.73/1.96 inference(symmetry,[status(thm)],[5068])).
% 1.73/1.96 tff(5070,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 1.73/1.96 tff(5071,plain,
% 1.73/1.96 (s(s(z)) = s(s(s(elem!1)))),
% 1.73/1.96 inference(symmetry,[status(thm)],[5070])).
% 1.73/1.96 tff(5072,plain,
% 1.73/1.96 (s(s(z)) = elem!1),
% 1.73/1.96 inference(transitivity,[status(thm)],[5071, 20, 5069, 1170])).
% 1.73/1.96 tff(5073,plain,
% 1.73/1.96 (elem!1 = s(s(s(elem!1)))),
% 1.73/1.96 inference(transitivity,[status(thm)],[1171, 5068, 19])).
% 1.73/1.96 tff(5074,plain,
% 1.73/1.96 (~(s(s(z)) = elem!1)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5025, 5073])).
% 1.73/1.96 tff(5075,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5074, 5072])).
% 1.73/1.96 tff(5076,plain,((~(s(s(s(elem!1))) = s(s(z)))) | (~(s(elem!1) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5077,plain,
% 1.73/1.96 (~(s(s(s(elem!1))) = s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5076, 5066])).
% 1.73/1.96 tff(5078,plain,
% 1.73/1.96 (((~![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))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5079,plain,
% 1.73/1.96 ((~![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))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(5080,plain,
% 1.73/1.96 ((~![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)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[5079, 5078])).
% 1.73/1.96 tff(5081,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5080, 47, 5077, 5060])).
% 1.73/1.96 tff(5082,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5083,plain,
% 1.73/1.96 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5084,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5083])).
% 1.73/1.96 tff(5085,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[5084, 5082])).
% 1.73/1.96 tff(5086,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(5087,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 1.73/1.96 tff(5088,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5087, 162, 152, 121, 538, 383, 4039])).
% 1.73/1.96 tff(5089,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5090,plain,
% 1.73/1.96 (~b(s(z), s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5089, 5038, 5036, 4947, 4949])).
% 1.73/1.96 tff(5091,plain,
% 1.73/1.96 (r(s(z), s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[3713, 5090])).
% 1.73/1.96 tff(5092,plain,
% 1.73/1.96 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[403, 5091, 4945])).
% 1.73/1.96 tff(5093,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[52, 5092])).
% 1.73/1.96 tff(5094,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5095,plain,
% 1.73/1.96 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5096,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5095])).
% 1.73/1.96 tff(5097,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.73/1.96 inference(transitivity,[status(thm)],[5096, 5094])).
% 1.73/1.96 tff(5098,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.73/1.96 inference(quant_inst,[status(thm)],[])).
% 1.73/1.96 tff(5099,plain,
% 1.73/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[5098, 5097])).
% 1.73/1.96 tff(5100,plain,
% 1.73/1.96 ($false),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5099, 162, 4947, 5093, 5036, 5038, 4785, 5081])).
% 1.73/1.96 tff(5101,plain,(b(z, s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (elem!1 = s(s(s(s(elem!1))))) | (s(z) = elem!1) | b(elem!1, z) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.96 tff(5102,plain,
% 1.73/1.96 (b(z, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[5101, 3632, 1246, 2252, 495, 1538, 1247, 3442, 1261])).
% 1.73/1.96 tff(5103,plain,
% 1.73/1.96 (~b(elem!1, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4820, 3473, 4787, 4785, 2252, 1538])).
% 1.73/1.96 tff(5104,plain,
% 1.73/1.96 (~r(elem!1, s(s(s(elem!1))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4870, 3473, 1261])).
% 1.73/1.96 tff(5105,plain,
% 1.73/1.96 (elem!1 = s(s(s(elem!1)))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[1483, 5104, 5103])).
% 1.73/1.96 tff(5106,plain,
% 1.73/1.96 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5105])).
% 1.73/1.96 tff(5107,plain,
% 1.73/1.96 (b(s(z), s(s(s(elem!1))))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[4935, 5106])).
% 1.73/1.96 tff(5108,plain,
% 1.73/1.96 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5105])).
% 1.73/1.96 tff(5109,plain,
% 1.73/1.96 (b(s(s(s(elem!1))), s(z))),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[4119, 5108])).
% 1.73/1.96 tff(5110,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/1.96 inference(monotonicity,[status(thm)],[5105])).
% 1.73/1.96 tff(5111,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(symmetry,[status(thm)],[5110])).
% 1.73/1.96 tff(5112,plain,
% 1.73/1.96 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.73/1.96 inference(modus_ponens,[status(thm)],[4787, 5111])).
% 1.73/1.96 tff(5113,plain,
% 1.73/1.96 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[4943, 5112, 4935, 4811, 4119])).
% 1.73/1.96 tff(5114,plain,
% 1.73/1.96 (r(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[191, 5113])).
% 1.73/1.96 tff(5115,plain,
% 1.73/1.96 (~r(z, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[534, 5114, 495])).
% 1.73/1.96 tff(5116,plain,
% 1.73/1.96 (b(z, s(z))),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[117, 5115])).
% 1.73/1.96 tff(5117,plain,
% 1.73/1.96 (~r(s(z), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[2561, 5114, 2252])).
% 1.73/1.96 tff(5118,plain,
% 1.73/1.96 (b(s(z), z)),
% 1.73/1.96 inference(unit_resolution,[status(thm)],[175, 5117])).
% 1.73/1.96 tff(5119,plain,
% 1.73/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.73/1.96 inference(rewrite,[status(thm)],[])).
% 1.73/1.96 tff(5120,plain,
% 1.73/1.96 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5121,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5120])).
% 1.73/1.97 tff(5122,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5121, 5119])).
% 1.73/1.97 tff(5123,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(5124,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5123, 5122])).
% 1.73/1.97 tff(5125,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5124, 162, 5118, 5116, 4177, 5109, 5107])).
% 1.73/1.97 tff(5126,plain,((~r(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(5127,plain,
% 1.73/1.97 (~r(elem!1, z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5126, 5102, 2252, 495, 4772, 4764, 1538, 1261])).
% 1.73/1.97 tff(5128,plain,
% 1.73/1.97 (elem!1 = z),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3486, 5127, 3442])).
% 1.73/1.97 tff(5129,plain,
% 1.73/1.97 (s(elem!1) = s(z)),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5128])).
% 1.73/1.97 tff(5130,plain,
% 1.73/1.97 (s(s(elem!1)) = s(s(z))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5129])).
% 1.73/1.97 tff(5131,plain,
% 1.73/1.97 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5130])).
% 1.73/1.97 tff(5132,plain,
% 1.73/1.97 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5131])).
% 1.73/1.97 tff(5133,plain,
% 1.73/1.97 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5132])).
% 1.73/1.97 tff(5134,plain,
% 1.73/1.97 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5133])).
% 1.73/1.97 tff(5135,plain,
% 1.73/1.97 (b(z, s(s(s(z))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5102, 5134])).
% 1.73/1.97 tff(5136,plain,
% 1.73/1.97 (s(s(elem!1)) = s(s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1316, 5128])).
% 1.73/1.97 tff(5137,plain,
% 1.73/1.97 (r(s(z), s(s(z)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1325, 5136, 1246])).
% 1.73/1.97 tff(5138,plain,
% 1.73/1.97 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5130, 5131])).
% 1.73/1.97 tff(5139,plain,
% 1.73/1.97 (~b(z, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4834, 5128, 3632])).
% 1.73/1.97 tff(5140,plain,
% 1.73/1.97 (r(z, s(s(elem!1)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[3401, 5139])).
% 1.73/1.97 tff(5141,plain,
% 1.73/1.97 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4845, 5140, 495])).
% 1.73/1.97 tff(5142,plain,
% 1.73/1.97 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1493, 5141, 4773])).
% 1.73/1.97 tff(5143,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5130])).
% 1.73/1.97 tff(5144,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5143])).
% 1.73/1.97 tff(5145,plain,
% 1.73/1.97 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5131])).
% 1.73/1.97 tff(5146,plain,
% 1.73/1.97 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5145])).
% 1.73/1.97 tff(5147,plain,
% 1.73/1.97 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5146])).
% 1.73/1.97 tff(5148,plain,
% 1.73/1.97 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5147, 5144])).
% 1.73/1.97 tff(5149,plain,
% 1.73/1.97 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5146])).
% 1.73/1.97 tff(5150,plain,
% 1.73/1.97 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5149, 1210])).
% 1.73/1.97 tff(5151,plain,
% 1.73/1.97 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5150])).
% 1.73/1.97 tff(5152,plain,
% 1.73/1.97 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5151, 624])).
% 1.73/1.97 tff(5153,plain,
% 1.73/1.97 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5152])).
% 1.73/1.97 tff(5154,plain,
% 1.73/1.97 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[37, 5153])).
% 1.73/1.97 tff(5155,plain,
% 1.73/1.97 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5130])).
% 1.73/1.97 tff(5156,plain,
% 1.73/1.97 (r(z, s(s(z)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5140, 5155])).
% 1.73/1.97 tff(5157,plain,
% 1.73/1.97 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5145])).
% 1.73/1.97 tff(5158,plain,
% 1.73/1.97 (r(z, s(s(s(s(z)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[495, 5157])).
% 1.73/1.97 tff(5159,plain,
% 1.73/1.97 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2647, 5158, 5156])).
% 1.73/1.97 tff(5160,plain,
% 1.73/1.97 (b(s(s(s(s(z)))), s(s(z)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[709, 5159, 5154])).
% 1.73/1.97 tff(5161,plain,
% 1.73/1.97 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5160, 5148])).
% 1.73/1.97 tff(5162,plain,
% 1.73/1.97 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2126, 5161, 4786, 4780, 4959, 5142])).
% 1.73/1.97 tff(5163,plain,
% 1.73/1.97 (r(s(s(z)), s(s(s(z))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5162, 5138])).
% 1.73/1.97 tff(5164,plain,
% 1.73/1.97 (~r(s(z), s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[425, 5163, 5137])).
% 1.73/1.97 tff(5165,plain,
% 1.73/1.97 (b(s(z), s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[493, 5164])).
% 1.73/1.97 tff(5166,plain,
% 1.73/1.97 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5146])).
% 1.73/1.97 tff(5167,plain,
% 1.73/1.97 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5166])).
% 1.73/1.97 tff(5168,plain,
% 1.73/1.97 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5130])).
% 1.73/1.97 tff(5169,plain,
% 1.73/1.97 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5142, 5168])).
% 1.73/1.97 tff(5170,plain,
% 1.73/1.97 (b(s(s(z)), s(s(s(s(z)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5169, 5167])).
% 1.73/1.97 tff(5171,plain,
% 1.73/1.97 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1285, 5128, 4780, 4774])).
% 1.73/1.97 tff(5172,plain,
% 1.73/1.97 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1336, 5171, 5128])).
% 1.73/1.97 tff(5173,plain,
% 1.73/1.97 (~r(s(z), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4006, 5140, 1246])).
% 1.73/1.97 tff(5174,plain,
% 1.73/1.97 (b(s(z), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[175, 5173])).
% 1.73/1.97 tff(5175,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5176,plain,
% 1.73/1.97 (((~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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5177,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5176])).
% 1.73/1.97 tff(5178,plain,
% 1.73/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5177, 5175])).
% 1.73/1.97 tff(5179,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(5180,plain,
% 1.73/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5179, 5178])).
% 1.73/1.97 tff(5181,plain,
% 1.73/1.97 (~b(s(s(s(z))), s(s(z)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5180, 162, 5174, 5165, 5172, 5135, 5170])).
% 1.73/1.97 tff(5182,plain,
% 1.73/1.97 (r(s(s(s(z))), s(s(z)))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[459, 5181])).
% 1.73/1.97 tff(5183,plain,
% 1.73/1.97 (~r(s(s(s(z))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[576, 5182, 5137])).
% 1.73/1.97 tff(5184,plain,
% 1.73/1.97 (b(s(s(s(z))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[595, 5183])).
% 1.73/1.97 tff(5185,plain,
% 1.73/1.97 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5128])).
% 1.73/1.97 tff(5186,plain,
% 1.73/1.97 (b(z, s(z))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[4764, 5185])).
% 1.73/1.97 tff(5187,plain,
% 1.73/1.97 ($false),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2037, 162, 5174, 5186, 5184, 5165, 5135])).
% 1.73/1.97 tff(5188,plain,(b(elem!1, s(s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | b(elem!1, z) | (~r(s(s(s(s(elem!1)))), z)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.73/1.97 tff(5189,plain,
% 1.73/1.97 (~r(s(s(s(elem!1))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5188, 4752, 4612, 4744, 4608, 4737, 4734, 4729])).
% 1.73/1.97 tff(5190,plain,
% 1.73/1.97 (((~![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))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5191,plain,
% 1.73/1.97 ((~![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))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(5192,plain,
% 1.73/1.97 ((~![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)),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5191, 5190])).
% 1.73/1.97 tff(5193,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5192, 47, 141])).
% 1.73/1.97 tff(5194,plain,
% 1.73/1.97 (b(s(s(s(elem!1))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5193, 5189])).
% 1.73/1.97 tff(5195,plain,
% 1.73/1.97 (b(s(s(s(z))), z)),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5194, 4717])).
% 1.73/1.97 tff(5196,plain,
% 1.73/1.97 (~r(s(s(s(s(z)))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4663, 445, 825, 385, 2])).
% 1.73/1.97 tff(5197,plain,
% 1.73/1.97 (b(s(s(s(s(z)))), s(z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[775, 5196, 642])).
% 1.73/1.97 tff(5198,plain,
% 1.73/1.97 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[4681, 65, 4675, 4673])).
% 1.73/1.97 tff(5199,plain,
% 1.73/1.97 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[763, 47, 4670])).
% 1.73/1.97 tff(5200,plain,
% 1.73/1.97 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5199, 5198])).
% 1.73/1.97 tff(5201,plain,
% 1.73/1.97 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5200])).
% 1.73/1.97 tff(5202,plain,
% 1.73/1.97 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5201])).
% 1.73/1.97 tff(5203,plain,
% 1.73/1.97 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5202])).
% 1.73/1.97 tff(5204,plain,
% 1.73/1.97 (b(s(s(z)), s(s(s(s(s(elem!1)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5203])).
% 1.73/1.97 tff(5205,plain,
% 1.73/1.97 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5200])).
% 1.73/1.97 tff(5206,plain,
% 1.73/1.97 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[20, 5205, 630])).
% 1.73/1.97 tff(5207,plain,
% 1.73/1.97 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5206])).
% 1.73/1.97 tff(5208,plain,
% 1.73/1.97 (s(s(elem!1)) = s(s(z))),
% 1.73/1.97 inference(transitivity,[status(thm)],[25, 5207, 312])).
% 1.73/1.97 tff(5209,plain,
% 1.73/1.97 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5208])).
% 1.73/1.97 tff(5210,plain,
% 1.73/1.97 (s(elem!1) = s(z)),
% 1.73/1.97 inference(transitivity,[status(thm)],[325, 5209, 15])).
% 1.73/1.97 tff(5211,plain,
% 1.73/1.97 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5210, 5200])).
% 1.73/1.97 tff(5212,plain,
% 1.73/1.97 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5211])).
% 1.73/1.97 tff(5213,plain,
% 1.73/1.97 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[694, 5212])).
% 1.73/1.97 tff(5214,plain,
% 1.73/1.97 (~b(z, s(s(s(s(z)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2657, 694, 121, 152, 1437])).
% 1.73/1.97 tff(5215,plain,
% 1.73/1.97 (r(z, s(s(s(s(z)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[823, 5214])).
% 1.73/1.97 tff(5216,plain,
% 1.73/1.97 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[2788])).
% 1.73/1.97 tff(5217,plain,
% 1.73/1.97 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5216])).
% 1.73/1.97 tff(5218,plain,
% 1.73/1.97 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.73/1.97 inference(symmetry,[status(thm)],[3414])).
% 1.73/1.97 tff(5219,plain,
% 1.73/1.97 (z = elem!1),
% 1.73/1.97 inference(transitivity,[status(thm)],[1182, 5218, 1170])).
% 1.73/1.97 tff(5220,plain,
% 1.73/1.97 (elem!1 = z),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[1208, 5219])).
% 1.73/1.97 tff(5221,plain,
% 1.73/1.97 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(z))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[3415, 2787])).
% 1.73/1.97 tff(5222,plain,
% 1.73/1.97 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.73/1.97 inference(transitivity,[status(thm)],[5221, 2881])).
% 1.73/1.97 tff(5223,plain,
% 1.73/1.97 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5222])).
% 1.73/1.97 tff(5224,plain,
% 1.73/1.97 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5223])).
% 1.73/1.97 tff(5225,plain,
% 1.73/1.97 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[2888, 5224])).
% 1.73/1.97 tff(5226,plain,
% 1.73/1.97 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[3415])).
% 1.73/1.97 tff(5227,plain,
% 1.73/1.97 (r(z, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5226])).
% 1.73/1.97 tff(5228,plain,
% 1.73/1.97 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[2788])).
% 1.73/1.97 tff(5229,plain,
% 1.73/1.97 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5228, 5227])).
% 1.73/1.97 tff(5230,plain,
% 1.73/1.97 ((~r(z, s(s(s(s(s(z))))))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5229])).
% 1.73/1.97 tff(5231,plain,
% 1.73/1.97 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[2197, 2798])).
% 1.73/1.97 tff(5232,plain,
% 1.73/1.97 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[727])).
% 1.73/1.97 tff(5233,plain,
% 1.73/1.97 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(symmetry,[status(thm)],[5232])).
% 1.73/1.97 tff(5234,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[2788])).
% 1.73/1.97 tff(5235,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5234, 5233])).
% 1.73/1.97 tff(5236,plain,
% 1.73/1.97 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5235])).
% 1.73/1.97 tff(5237,plain,
% 1.73/1.97 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(monotonicity,[status(thm)],[2787])).
% 1.73/1.97 tff(5238,plain,
% 1.73/1.97 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.97 inference(symmetry,[status(thm)],[5237])).
% 1.73/1.97 tff(5239,plain,
% 1.73/1.97 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(s(elem!1))))), z))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5238])).
% 1.73/1.97 tff(5240,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.73/1.97 tff(5241,plain,
% 1.73/1.97 (((~![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(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5242,plain,
% 1.73/1.97 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5243,plain,
% 1.73/1.97 (((~![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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(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(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5242])).
% 1.73/1.97 tff(5244,plain,
% 1.73/1.97 (((~![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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(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(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5243, 5241])).
% 1.73/1.97 tff(5245,plain,
% 1.73/1.97 ((~![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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(5246,plain,
% 1.73/1.97 ((~![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(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5245, 5244])).
% 1.73/1.97 tff(5247,plain,
% 1.73/1.97 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5246, 65, 55, 803])).
% 1.73/1.97 tff(5248,plain,
% 1.73/1.97 (~r(s(s(s(s(s(z))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5247, 5240])).
% 1.73/1.97 tff(5249,plain,
% 1.73/1.97 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5248, 5239])).
% 1.73/1.97 tff(5250,plain,
% 1.73/1.97 (b(s(s(s(s(s(elem!1))))), z)),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[894, 5249])).
% 1.73/1.97 tff(5251,plain,
% 1.73/1.97 (((~![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(s(s(s(z))))))) | (~r(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(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5252,plain,
% 1.73/1.97 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.73/1.97 inference(rewrite,[status(thm)],[])).
% 1.73/1.97 tff(5253,plain,
% 1.73/1.97 (((~![X0: $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(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, 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(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.73/1.97 inference(monotonicity,[status(thm)],[5252])).
% 1.73/1.97 tff(5254,plain,
% 1.73/1.97 (((~![X0: $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(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, 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(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.73/1.97 inference(transitivity,[status(thm)],[5253, 5251])).
% 1.73/1.97 tff(5255,plain,
% 1.73/1.97 ((~![X0: $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(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.73/1.97 inference(quant_inst,[status(thm)],[])).
% 1.73/1.97 tff(5256,plain,
% 1.73/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.73/1.97 inference(modus_ponens,[status(thm)],[5255, 5254])).
% 1.73/1.97 tff(5257,plain,
% 1.73/1.97 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.73/1.97 inference(unit_resolution,[status(thm)],[5256, 65, 803])).
% 1.73/1.97 tff(5258,plain,
% 1.73/1.97 (~r(z, s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5257, 5240])).
% 1.73/1.98 tff(5259,plain,
% 1.73/1.98 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5258, 5230])).
% 1.73/1.98 tff(5260,plain,
% 1.73/1.98 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1813, 5259, 5225])).
% 1.73/1.98 tff(5261,plain,
% 1.73/1.98 (b(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1821, 5260, 5220])).
% 1.73/1.98 tff(5262,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[979, 5261, 5250, 121, 152, 970])).
% 1.73/1.98 tff(5263,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5264,plain,
% 1.73/1.98 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5263, 970, 152, 121, 727, 55, 803])).
% 1.73/1.98 tff(5265,plain,
% 1.73/1.98 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5264, 5236])).
% 1.73/1.98 tff(5266,plain,
% 1.73/1.98 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[2214, 5265, 5231])).
% 1.73/1.98 tff(5267,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5268,plain,
% 1.73/1.98 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5269,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[5268])).
% 1.73/1.98 tff(5270,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[5269, 5267])).
% 1.73/1.98 tff(5271,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(5272,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5271, 5270])).
% 1.73/1.98 tff(5273,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5272, 162, 177, 151, 2218, 970, 2217])).
% 1.73/1.98 tff(5274,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5275,plain,
% 1.73/1.98 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5274, 5266, 151, 177, 970])).
% 1.73/1.98 tff(5276,plain,
% 1.73/1.98 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1789, 5275, 2798])).
% 1.73/1.98 tff(5277,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.73/1.98 tff(5278,plain,
% 1.73/1.98 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[2786, 2788])).
% 1.73/1.98 tff(5279,plain,
% 1.73/1.98 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[5278])).
% 1.73/1.98 tff(5280,plain,
% 1.73/1.98 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[1004, 5279])).
% 1.73/1.98 tff(5281,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5282,plain,
% 1.73/1.98 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5283,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(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(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[5282])).
% 1.73/1.98 tff(5284,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(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(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[5283, 5281])).
% 1.73/1.98 tff(5285,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(5286,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5285, 5284])).
% 1.73/1.98 tff(5287,plain,
% 1.73/1.98 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5286, 65, 1341])).
% 1.73/1.98 tff(5288,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5287, 5280, 5277])).
% 1.73/1.98 tff(5289,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5290,plain,
% 1.73/1.98 (~r(z, s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5289, 5276, 1341, 727])).
% 1.73/1.98 tff(5291,plain,
% 1.73/1.98 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5290, 5230])).
% 1.73/1.98 tff(5292,plain,
% 1.73/1.98 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1813, 5291, 5225])).
% 1.73/1.98 tff(5293,plain,
% 1.73/1.98 (b(z, s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1821, 5292, 5220])).
% 1.73/1.98 tff(5294,plain,
% 1.73/1.98 (b(z, s(s(s(s(s(z))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5293, 5217])).
% 1.73/1.98 tff(5295,plain,
% 1.73/1.98 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[727])).
% 1.73/1.98 tff(5296,plain,
% 1.73/1.98 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[5295, 2801])).
% 1.73/1.98 tff(5297,plain,
% 1.73/1.98 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5266, 5296])).
% 1.73/1.98 tff(5298,plain,
% 1.73/1.98 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[2787])).
% 1.73/1.98 tff(5299,plain,
% 1.73/1.98 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[970, 5298])).
% 1.73/1.98 tff(5300,plain,
% 1.73/1.98 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[2788])).
% 1.73/1.98 tff(5301,plain,
% 1.73/1.98 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[5300])).
% 1.73/1.98 tff(5302,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[727, 3406])).
% 1.73/1.98 tff(5303,plain,
% 1.73/1.98 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.98 inference(symmetry,[status(thm)],[5302])).
% 1.73/1.98 tff(5304,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[1437, 5303])).
% 1.73/1.98 tff(5305,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.73/1.98 tff(5306,plain,
% 1.73/1.98 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[2787, 3406])).
% 1.73/1.98 tff(5307,plain,
% 1.73/1.98 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.73/1.98 inference(symmetry,[status(thm)],[5306])).
% 1.73/1.98 tff(5308,plain,
% 1.73/1.98 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.73/1.98 inference(transitivity,[status(thm)],[5298, 5307])).
% 1.73/1.98 tff(5309,plain,
% 1.73/1.98 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[970, 5308])).
% 1.73/1.98 tff(5310,plain,
% 1.73/1.98 (r(s(z), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[2787])).
% 1.73/1.98 tff(5311,assumption,(b(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.73/1.98 tff(5312,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.73/1.98 tff(5313,plain,
% 1.73/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), 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(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5314,plain,
% 1.73/1.98 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5315,plain,
% 1.73/1.98 (((~![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(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(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(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[5314])).
% 1.73/1.98 tff(5316,plain,
% 1.73/1.98 (((~![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(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(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(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[5315, 5313])).
% 1.73/1.98 tff(5317,plain,
% 1.73/1.98 ((~![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(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(5318,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5317, 5316])).
% 1.73/1.98 tff(5319,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5318, 65, 1004, 867, 340])).
% 1.73/1.98 tff(5320,plain,((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5321,plain,
% 1.73/1.98 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5320, 867, 340])).
% 1.73/1.98 tff(5322,plain,
% 1.73/1.98 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1789, 5321, 2798])).
% 1.73/1.98 tff(5323,assumption,(b(s(elem!1), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.73/1.98 tff(5324,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5325,plain,
% 1.73/1.98 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5326,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[5325])).
% 1.73/1.98 tff(5327,plain,
% 1.73/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[5326, 5324])).
% 1.73/1.98 tff(5328,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(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(s(s(elem!1))))))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(5329,plain,
% 1.73/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 1.73/1.98 tff(5330,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5329, 162, 5312, 5305, 2218, 5323, 5311])).
% 1.73/1.98 tff(5331,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5332,plain,
% 1.73/1.98 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5331, 5322, 5305, 5312, 5311])).
% 1.73/1.98 tff(5333,plain,
% 1.73/1.98 (s(z) = s(elem!1)),
% 1.73/1.98 inference(symmetry,[status(thm)],[1212])).
% 1.73/1.98 tff(5334,plain,
% 1.73/1.98 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[5333])).
% 1.73/1.98 tff(5335,plain,
% 1.73/1.98 (b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[1029, 5334])).
% 1.73/1.98 tff(5336,assumption,(~b(s(elem!1), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.73/1.98 tff(5337,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5336, 5335])).
% 1.73/1.98 tff(5338,plain,((~b(s(z), s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5339,plain,
% 1.73/1.98 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5338, 5332, 5220])).
% 1.73/1.98 tff(5340,plain,
% 1.73/1.98 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[1050, 5339])).
% 1.73/1.98 tff(5341,plain,
% 1.73/1.98 (r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5340, 5310])).
% 1.73/1.98 tff(5342,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[1705])).
% 1.73/1.98 tff(5343,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(symmetry,[status(thm)],[5342])).
% 1.73/1.98 tff(5344,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[867, 5343])).
% 1.73/1.98 tff(5345,assumption,(~r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.73/1.98 tff(5346,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5345, 5344])).
% 1.73/1.98 tff(5347,plain,(r(s(s(s(z))), s(s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5348,plain,
% 1.73/1.98 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5347, 867, 5220])).
% 1.73/1.98 tff(5349,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.73/1.98 tff(5350,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.73/1.98 tff(5351,plain,
% 1.73/1.98 (((~![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(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), 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(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5352,plain,
% 1.73/1.98 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(rewrite,[status(thm)],[])).
% 1.73/1.98 tff(5353,plain,
% 1.73/1.98 (((~![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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(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(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.73/1.98 inference(monotonicity,[status(thm)],[5352])).
% 1.73/1.98 tff(5354,plain,
% 1.73/1.98 (((~![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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(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(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/1.98 inference(transitivity,[status(thm)],[5353, 5351])).
% 1.73/1.98 tff(5355,plain,
% 1.73/1.98 ((~![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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 1.73/1.98 inference(quant_inst,[status(thm)],[])).
% 1.73/1.98 tff(5356,plain,
% 1.73/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.73/1.98 inference(modus_ponens,[status(thm)],[5355, 5354])).
% 1.73/1.98 tff(5357,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5356, 65, 385, 5350, 5349])).
% 1.73/1.98 tff(5358,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5359,plain,
% 1.73/1.98 (~r(s(z), s(s(s(s(s(z))))))),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5358, 5348, 385])).
% 1.73/1.98 tff(5360,plain,
% 1.73/1.98 ($false),
% 1.73/1.98 inference(unit_resolution,[status(thm)],[5359, 5341])).
% 1.73/1.98 tff(5361,plain,((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.98 tff(5362,plain,
% 1.73/1.98 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5361, 5309, 5305, 5304, 727, 385, 340])).
% 1.73/1.99 tff(5363,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1001, 5362])).
% 1.73/1.99 tff(5364,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5363, 5301])).
% 1.73/1.99 tff(5365,plain,
% 1.73/1.99 (~r(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2601, 340, 4675])).
% 1.73/1.99 tff(5366,plain,
% 1.73/1.99 (b(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[295, 5365])).
% 1.73/1.99 tff(5367,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5368,plain,
% 1.73/1.99 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5369,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5368])).
% 1.73/1.99 tff(5370,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[5369, 5367])).
% 1.73/1.99 tff(5371,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(5372,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5371, 5370])).
% 1.73/1.99 tff(5373,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5372, 162, 1437, 5366, 5364, 5299, 5297, 5294])).
% 1.73/1.99 tff(5374,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(5375,plain,
% 1.73/1.99 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5374, 5200, 1437, 4673, 151, 177, 152, 121, 55, 5215, 5213, 385, 340])).
% 1.73/1.99 tff(5376,plain,
% 1.73/1.99 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[968, 5375])).
% 1.73/1.99 tff(5377,plain,
% 1.73/1.99 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[954, 5376, 2])).
% 1.73/1.99 tff(5378,plain,
% 1.73/1.99 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[943, 5377])).
% 1.73/1.99 tff(5379,plain,
% 1.73/1.99 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5378, 5204])).
% 1.73/1.99 tff(5380,plain,
% 1.73/1.99 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5202])).
% 1.73/1.99 tff(5381,plain,
% 1.73/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.99 inference(symmetry,[status(thm)],[5380])).
% 1.73/1.99 tff(5382,plain,
% 1.73/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5206])).
% 1.73/1.99 tff(5383,plain,
% 1.73/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[5382, 5381])).
% 1.73/1.99 tff(5384,plain,
% 1.73/1.99 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5206])).
% 1.73/1.99 tff(5385,plain,
% 1.73/1.99 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[5384, 987])).
% 1.73/1.99 tff(5386,plain,
% 1.73/1.99 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.73/1.99 inference(symmetry,[status(thm)],[5385])).
% 1.73/1.99 tff(5387,plain,
% 1.73/1.99 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5386])).
% 1.73/1.99 tff(5388,plain,
% 1.73/1.99 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[996, 5387])).
% 1.73/1.99 tff(5389,plain,
% 1.73/1.99 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(symmetry,[status(thm)],[5205])).
% 1.73/1.99 tff(5390,plain,
% 1.73/1.99 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.73/1.99 inference(transitivity,[status(thm)],[631, 5389, 19])).
% 1.73/1.99 tff(5391,plain,
% 1.73/1.99 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5202, 5390])).
% 1.73/1.99 tff(5392,plain,
% 1.73/1.99 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5391])).
% 1.73/1.99 tff(5393,plain,
% 1.73/1.99 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5201])).
% 1.73/1.99 tff(5394,plain,
% 1.73/1.99 (r(s(s(s(s(s(z))))), s(z))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5376, 5393])).
% 1.73/1.99 tff(5395,plain,
% 1.73/1.99 (((~![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))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5396,plain,
% 1.73/1.99 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5397,plain,
% 1.73/1.99 (((~![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))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5396])).
% 1.73/1.99 tff(5398,plain,
% 1.73/1.99 (((~![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))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[5397, 5395])).
% 1.73/1.99 tff(5399,plain,
% 1.73/1.99 ((~![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))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(5400,plain,
% 1.73/1.99 ((~![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))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5399, 5398])).
% 1.73/1.99 tff(5401,plain,
% 1.73/1.99 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5400, 65, 385, 5394])).
% 1.73/1.99 tff(5402,plain,
% 1.73/1.99 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5401, 5392])).
% 1.73/1.99 tff(5403,plain,
% 1.73/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1731, 5402, 5388])).
% 1.73/1.99 tff(5404,plain,
% 1.73/1.99 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5403, 5383])).
% 1.73/1.99 tff(5405,plain,
% 1.73/1.99 (b(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5201, 5208])).
% 1.73/1.99 tff(5406,plain,
% 1.73/1.99 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5208])).
% 1.73/1.99 tff(5407,plain,
% 1.73/1.99 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[5406, 1917])).
% 1.73/1.99 tff(5408,plain,
% 1.73/1.99 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.73/1.99 inference(symmetry,[status(thm)],[5407])).
% 1.73/1.99 tff(5409,plain,
% 1.73/1.99 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5408])).
% 1.73/1.99 tff(5410,plain,
% 1.73/1.99 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[914, 5409])).
% 1.73/1.99 tff(5411,plain,
% 1.73/1.99 (r(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5201, 5208])).
% 1.73/1.99 tff(5412,plain,
% 1.73/1.99 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.73/1.99 inference(symmetry,[status(thm)],[5411])).
% 1.73/1.99 tff(5413,plain,
% 1.73/1.99 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5412])).
% 1.73/1.99 tff(5414,plain,
% 1.73/1.99 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2817, 65, 230, 2, 5394])).
% 1.73/1.99 tff(5415,plain,
% 1.73/1.99 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5414, 5413])).
% 1.73/1.99 tff(5416,plain,
% 1.73/1.99 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[1760, 5415, 5410])).
% 1.73/1.99 tff(5417,plain,
% 1.73/1.99 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5416, 5405])).
% 1.73/1.99 tff(5418,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5419,plain,
% 1.73/1.99 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5420,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5419])).
% 1.73/1.99 tff(5421,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[5420, 5418])).
% 1.73/1.99 tff(5422,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(5423,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5422, 5421])).
% 1.73/1.99 tff(5424,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5423, 162, 588, 445, 5417, 5404, 5379])).
% 1.73/1.99 tff(5425,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(5426,plain,
% 1.73/1.99 (~b(s(z), s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5425, 230, 445, 2, 385, 5197, 151, 177, 152, 121, 55, 340])).
% 1.73/1.99 tff(5427,plain,
% 1.73/1.99 (r(s(z), s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[658, 5426, 643])).
% 1.73/1.99 tff(5428,plain,
% 1.73/1.99 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[3172, 5427, 2])).
% 1.73/1.99 tff(5429,plain,
% 1.73/1.99 (b(s(s(z)), s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[801, 5428, 634])).
% 1.73/1.99 tff(5430,plain,
% 1.73/1.99 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4689, 5429, 445, 825, 588])).
% 1.73/1.99 tff(5431,plain,
% 1.73/1.99 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[690, 5430, 679])).
% 1.73/1.99 tff(5432,plain,
% 1.73/1.99 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2707, 65, 5431, 340])).
% 1.73/1.99 tff(5433,plain,
% 1.73/1.99 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[727])).
% 1.73/1.99 tff(5434,plain,
% 1.73/1.99 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(symmetry,[status(thm)],[5433])).
% 1.73/1.99 tff(5435,plain,
% 1.73/1.99 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5434])).
% 1.73/1.99 tff(5436,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.73/1.99 tff(5437,plain,
% 1.73/1.99 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5436, 5435])).
% 1.73/1.99 tff(5438,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[177, 5437])).
% 1.73/1.99 tff(5439,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(5440,plain,
% 1.73/1.99 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5439, 5426, 177])).
% 1.73/1.99 tff(5441,plain,
% 1.73/1.99 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[763, 47, 5440, 5432])).
% 1.73/1.99 tff(5442,plain,
% 1.73/1.99 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4631, 65, 4675, 230])).
% 1.73/1.99 tff(5443,plain,
% 1.73/1.99 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[214, 47, 5442, 209])).
% 1.73/1.99 tff(5444,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5445,plain,
% 1.73/1.99 (((~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(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(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.73/1.99 inference(rewrite,[status(thm)],[])).
% 1.73/1.99 tff(5446,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.73/1.99 inference(monotonicity,[status(thm)],[5445])).
% 1.73/1.99 tff(5447,plain,
% 1.73/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.73/1.99 inference(transitivity,[status(thm)],[5446, 5444])).
% 1.73/1.99 tff(5448,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.73/1.99 inference(quant_inst,[status(thm)],[])).
% 1.73/1.99 tff(5449,plain,
% 1.73/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.73/1.99 inference(modus_ponens,[status(thm)],[5448, 5447])).
% 1.73/1.99 tff(5450,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5449, 162, 416, 5443, 825, 5429, 5441])).
% 1.73/1.99 tff(5451,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(5452,plain,
% 1.73/1.99 (~r(s(s(z)), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5451, 4636, 4645, 4602, 578, 2, 3018, 385, 4606, 3022, 3032, 3020])).
% 1.73/1.99 tff(5453,plain,
% 1.73/1.99 (b(s(s(z)), z)),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[245, 5452])).
% 1.73/1.99 tff(5454,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[4099, 162, 5453, 588, 578, 5195, 4638])).
% 1.73/1.99 tff(5455,plain,((~r(s(s(s(z))), s(z))) | b(z, s(s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(5456,plain,
% 1.73/1.99 (~r(s(s(s(z))), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5455, 3019, 384, 2])).
% 1.73/1.99 tff(5457,plain,
% 1.73/1.99 (b(s(s(s(z))), s(z))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[595, 5456])).
% 1.73/1.99 tff(5458,plain,
% 1.73/1.99 (~b(s(z), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2039, 296, 4639, 3114, 600])).
% 1.73/1.99 tff(5459,plain,
% 1.73/1.99 (r(s(z), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[493, 5458])).
% 1.73/1.99 tff(5460,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[466, 65, 384, 5459, 273])).
% 1.73/1.99 tff(5461,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(5462,plain,
% 1.73/1.99 (~r(s(s(s(z))), s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5461, 5457, 384, 3020])).
% 1.73/1.99 tff(5463,plain,
% 1.73/1.99 (b(s(s(s(z))), s(s(z)))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[459, 5462])).
% 1.73/1.99 tff(5464,plain,
% 1.73/1.99 (~r(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[833, 417, 55])).
% 1.73/1.99 tff(5465,plain,
% 1.73/1.99 (b(z, s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[295, 5464])).
% 1.73/1.99 tff(5466,plain,
% 1.73/1.99 (~r(s(z), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[425, 417, 384])).
% 1.73/1.99 tff(5467,plain,
% 1.73/1.99 (b(s(z), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[493, 5466])).
% 1.73/1.99 tff(5468,plain,
% 1.73/1.99 ($false),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2039, 5467, 5465, 4639, 3114, 600])).
% 1.73/1.99 tff(5469,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/1.99 tff(5470,plain,
% 1.73/1.99 (~r(s(s(z)), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[5469, 5457, 384, 3020])).
% 1.73/1.99 tff(5471,plain,
% 1.73/1.99 (b(s(s(z)), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[442, 5470])).
% 1.73/1.99 tff(5472,plain,
% 1.73/1.99 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[2986, 712, 416, 445, 444])).
% 1.73/1.99 tff(5473,plain,
% 1.73/1.99 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/1.99 inference(unit_resolution,[status(thm)],[360, 5472])).
% 1.73/1.99 tff(5474,plain,
% 1.73/1.99 (((~![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(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))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5475,plain,
% 1.73/2.00 (((~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))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5476,plain,
% 1.73/2.00 (((~![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(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)))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[5475])).
% 1.73/2.00 tff(5477,plain,
% 1.73/2.00 (((~![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(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))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[5476, 5474])).
% 1.73/2.00 tff(5478,plain,
% 1.73/2.00 ((~![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(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))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(5479,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[5478, 5477])).
% 1.73/2.00 tff(5480,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5479, 65, 123, 395, 340])).
% 1.73/2.00 tff(5481,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,[]))).
% 1.73/2.00 tff(5482,plain,
% 1.73/2.00 (~r(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5481, 5473, 123])).
% 1.73/2.00 tff(5483,plain,
% 1.73/2.00 (b(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[493, 5482])).
% 1.73/2.00 tff(5484,plain,
% 1.73/2.00 (~b(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2039, 5483, 121, 152, 600])).
% 1.73/2.00 tff(5485,plain,
% 1.73/2.00 (r(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[295, 5484])).
% 1.73/2.00 tff(5486,plain,
% 1.73/2.00 (~r(z, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[566, 5485, 5473])).
% 1.73/2.00 tff(5487,plain,
% 1.73/2.00 (b(z, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[83, 5486])).
% 1.73/2.00 tff(5488,plain,
% 1.73/2.00 (~r(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2601, 5485, 5473])).
% 1.73/2.00 tff(5489,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[95, 5488])).
% 1.73/2.00 tff(5490,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5491,plain,
% 1.73/2.00 (((~b(s(z), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5492,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[5491])).
% 1.73/2.00 tff(5493,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.73/2.00 inference(transitivity,[status(thm)],[5492, 5490])).
% 1.73/2.00 tff(5494,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1)))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(5495,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[5494, 5493])).
% 1.73/2.00 tff(5496,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5495, 162, 152, 121, 177, 122, 120])).
% 1.73/2.00 tff(5497,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5498,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5497, 5489, 5487, 177, 152, 121])).
% 1.73/2.00 tff(5499,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5500,plain,
% 1.73/2.00 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5499, 3022, 3018, 3032, 5457, 4602, 5463, 5471, 2])).
% 1.73/2.00 tff(5501,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[149, 5500])).
% 1.73/2.00 tff(5502,plain,
% 1.73/2.00 (~b(z, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[4610, 5501, 3032, 3018, 3022])).
% 1.73/2.00 tff(5503,plain,
% 1.73/2.00 (r(z, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[83, 5502])).
% 1.73/2.00 tff(5504,plain,
% 1.73/2.00 (~r(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2507, 299, 495])).
% 1.73/2.00 tff(5505,plain,
% 1.73/2.00 (b(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[295, 5504])).
% 1.73/2.00 tff(5506,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5507,plain,
% 1.73/2.00 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5508,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[5507])).
% 1.73/2.00 tff(5509,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[5508, 5506])).
% 1.73/2.00 tff(5510,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(5511,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[5510, 5509])).
% 1.73/2.00 tff(5512,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5511, 162, 152, 121, 298, 600, 297])).
% 1.73/2.00 tff(5513,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5514,plain,
% 1.73/2.00 (~b(s(s(s(z))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5513, 5505, 121, 600, 152])).
% 1.73/2.00 tff(5515,plain,
% 1.73/2.00 (r(s(s(s(z))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[381, 5514])).
% 1.73/2.00 tff(5516,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3304, 65, 495, 299, 5515])).
% 1.73/2.00 tff(5517,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5518,plain,
% 1.73/2.00 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5517, 5503, 3032, 5457, 3022])).
% 1.73/2.00 tff(5519,plain,
% 1.73/2.00 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[338, 5518])).
% 1.73/2.00 tff(5520,plain,
% 1.73/2.00 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[453, 5519, 4602, 5471, 5463])).
% 1.73/2.00 tff(5521,plain,
% 1.73/2.00 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[360, 5520])).
% 1.73/2.00 tff(5522,plain,
% 1.73/2.00 (~b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3122, 5501, 3018, 3032, 3022])).
% 1.73/2.00 tff(5523,plain,
% 1.73/2.00 (r(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[95, 5522])).
% 1.73/2.00 tff(5524,plain,
% 1.73/2.00 (~r(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2601, 5521, 5523])).
% 1.73/2.00 tff(5525,plain,
% 1.73/2.00 (b(z, s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[295, 5524])).
% 1.73/2.00 tff(5526,plain,
% 1.73/2.00 (~b(s(s(s(z))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5513, 5525, 3032, 5457, 3022])).
% 1.73/2.00 tff(5527,plain,
% 1.73/2.00 (r(s(s(s(z))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[381, 5526])).
% 1.73/2.00 tff(5528,plain,
% 1.73/2.00 (((~![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)))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5529,plain,
% 1.73/2.00 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5530,plain,
% 1.73/2.00 (((~![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(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[5529])).
% 1.73/2.00 tff(5531,plain,
% 1.73/2.00 (((~![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(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.73/2.00 inference(transitivity,[status(thm)],[5530, 5528])).
% 1.73/2.00 tff(5532,plain,
% 1.73/2.00 ((~![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(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(5533,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 1.73/2.00 tff(5534,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5533, 65, 5523, 5527, 5521])).
% 1.73/2.00 tff(5535,plain,(b(z, s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5536,plain,
% 1.73/2.00 (b(z, s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5535, 2, 384])).
% 1.73/2.00 tff(5537,plain,
% 1.73/2.00 (~r(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[3066, 297, 5536, 3044, 384])).
% 1.73/2.00 tff(5538,plain,
% 1.73/2.00 (b(s(z), s(s(s(z))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[493, 5537])).
% 1.73/2.00 tff(5539,plain,
% 1.73/2.00 (((~![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(s(s(s(elem!1))))), z)) | (~r(s(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(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5540,plain,
% 1.73/2.00 (((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5541,plain,
% 1.73/2.00 (((~![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(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(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(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[5540])).
% 1.73/2.00 tff(5542,plain,
% 1.73/2.00 (((~![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(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(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(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[5541, 5539])).
% 1.73/2.00 tff(5543,plain,
% 1.73/2.00 ((~![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(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(5544,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 1.73/2.00 tff(5545,plain,
% 1.73/2.00 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5544, 65, 97, 945])).
% 1.73/2.00 tff(5546,plain,
% 1.73/2.00 (b(s(s(s(s(s(elem!1))))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[894, 5545])).
% 1.73/2.00 tff(5547,plain,
% 1.73/2.00 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[952, 65, 945, 2])).
% 1.73/2.00 tff(5548,plain,
% 1.73/2.00 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[943, 5547])).
% 1.73/2.00 tff(5549,plain,
% 1.73/2.00 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[935, 5548, 2565, 5546, 3044])).
% 1.73/2.00 tff(5550,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[921, 47, 1942, 5549, 916])).
% 1.73/2.00 tff(5551,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5552,plain,
% 1.73/2.00 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5551, 97, 2])).
% 1.73/2.00 tff(5553,plain,
% 1.73/2.00 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[968, 5552])).
% 1.73/2.00 tff(5554,plain,
% 1.73/2.00 (((~![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(s(s(elem!1)))), 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(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5555,plain,
% 1.73/2.00 (((~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(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5556,plain,
% 1.73/2.00 (((~![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(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(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[5555])).
% 1.73/2.00 tff(5557,plain,
% 1.73/2.00 (((~![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(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(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[5556, 5554])).
% 1.73/2.00 tff(5558,plain,
% 1.73/2.00 ((~![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(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.73/2.00 inference(quant_inst,[status(thm)],[])).
% 1.73/2.00 tff(5559,plain,
% 1.73/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.73/2.00 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 1.73/2.00 tff(5560,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5559, 65, 97, 123, 2252])).
% 1.73/2.00 tff(5561,plain,((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5562,plain,
% 1.73/2.00 (~r(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5561, 123, 97])).
% 1.73/2.00 tff(5563,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[95, 5562])).
% 1.73/2.00 tff(5564,plain,
% 1.73/2.00 (~r(z, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[1431, 123, 97])).
% 1.73/2.00 tff(5565,plain,
% 1.73/2.00 (b(z, s(s(s(s(elem!1)))))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[83, 5564])).
% 1.73/2.00 tff(5566,plain,
% 1.73/2.00 ($false),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2573, 5565, 5563, 416, 537, 538])).
% 1.73/2.00 tff(5567,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.00 tff(5568,plain,
% 1.73/2.00 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[5567, 3044, 5536, 4602, 97])).
% 1.73/2.00 tff(5569,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[149, 5568])).
% 1.73/2.00 tff(5570,plain,
% 1.73/2.00 (~r(s(s(z)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[238, 194, 2])).
% 1.73/2.00 tff(5571,plain,
% 1.73/2.00 (b(s(s(z)), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[245, 5570])).
% 1.73/2.00 tff(5572,plain,
% 1.73/2.00 (~r(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[2260, 123, 194])).
% 1.73/2.00 tff(5573,plain,
% 1.73/2.00 (b(s(s(s(s(elem!1)))), z)),
% 1.73/2.00 inference(unit_resolution,[status(thm)],[95, 5572])).
% 1.73/2.00 tff(5574,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5575,plain,
% 1.73/2.00 (((~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(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.73/2.00 inference(rewrite,[status(thm)],[])).
% 1.73/2.00 tff(5576,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.73/2.00 inference(monotonicity,[status(thm)],[5575])).
% 1.73/2.00 tff(5577,plain,
% 1.73/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.73/2.00 inference(transitivity,[status(thm)],[5576, 5574])).
% 1.73/2.00 tff(5578,plain,
% 1.73/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(5579,plain,
% 1.73/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5578, 5577])).
% 1.73/2.01 tff(5580,plain,
% 1.73/2.01 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5579, 162, 416, 5573, 5571, 537])).
% 1.73/2.01 tff(5581,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[214, 47, 711, 5580, 209])).
% 1.73/2.01 tff(5582,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5583,plain,
% 1.73/2.01 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5582, 194, 5536, 2, 4602])).
% 1.73/2.01 tff(5584,plain,
% 1.73/2.01 (b(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[149, 5583])).
% 1.73/2.01 tff(5585,plain,
% 1.73/2.01 (~r(s(z), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4554, 5571, 5536, 194, 384])).
% 1.73/2.01 tff(5586,plain,
% 1.73/2.01 (b(s(z), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[493, 5585])).
% 1.73/2.01 tff(5587,plain,
% 1.73/2.01 (~r(s(s(s(z))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4580, 5571, 194, 5536, 2, 384])).
% 1.73/2.01 tff(5588,plain,
% 1.73/2.01 (b(s(s(s(z))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[595, 5587])).
% 1.73/2.01 tff(5589,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2573, 5573, 5565, 416, 537, 538])).
% 1.73/2.01 tff(5590,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5591,plain,
% 1.73/2.01 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5590, 97, 5536, 5571, 194, 4602])).
% 1.73/2.01 tff(5592,plain,
% 1.73/2.01 (b(s(s(s(s(elem!1)))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[149, 5591])).
% 1.73/2.01 tff(5593,plain,
% 1.73/2.01 (((~![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(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)))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(5594,plain,
% 1.73/2.01 (((~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)))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(5595,plain,
% 1.73/2.01 (((~![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(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))))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5594])).
% 1.73/2.01 tff(5596,plain,
% 1.73/2.01 (((~![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(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)))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[5595, 5593])).
% 1.73/2.01 tff(5597,plain,
% 1.73/2.01 ((~![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(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(5598,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5597, 5596])).
% 1.73/2.01 tff(5599,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5598, 65, 194, 1341, 645])).
% 1.73/2.01 tff(5600,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5601,plain,
% 1.73/2.01 (~r(s(s(s(s(z)))), z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5600, 645, 194])).
% 1.73/2.01 tff(5602,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2016, 65, 194, 803, 645])).
% 1.73/2.01 tff(5603,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5604,plain,
% 1.73/2.01 (~r(z, s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5603, 645, 194])).
% 1.73/2.01 tff(5605,plain,
% 1.73/2.01 (b(z, s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[823, 5604])).
% 1.73/2.01 tff(5606,plain,
% 1.73/2.01 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1084, 5605, 538, 1076, 537])).
% 1.73/2.01 tff(5607,plain,
% 1.73/2.01 (r(s(s(s(s(z)))), s(s(z)))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[709, 5606, 635])).
% 1.73/2.01 tff(5608,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[651, 65, 384, 5607, 645])).
% 1.73/2.01 tff(5609,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5610,plain,
% 1.73/2.01 (~b(s(s(s(s(z)))), z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5609, 645, 384, 194, 538, 537])).
% 1.73/2.01 tff(5611,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1089, 5610, 5601])).
% 1.73/2.01 tff(5612,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5613,plain,
% 1.73/2.01 (~r(s(z), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5612, 194, 384, 5571, 5536])).
% 1.73/2.01 tff(5614,plain,
% 1.73/2.01 (b(s(z), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[658, 5613, 643])).
% 1.73/2.01 tff(5615,plain,
% 1.73/2.01 (~r(s(s(s(s(z)))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4528, 97, 5571, 2, 5536])).
% 1.73/2.01 tff(5616,plain,
% 1.73/2.01 (b(s(s(s(s(z)))), s(z))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[775, 5615, 642])).
% 1.73/2.01 tff(5617,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2465, 162, 600, 599, 694, 1437, 692])).
% 1.73/2.01 tff(5618,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5619,plain,
% 1.73/2.01 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5618, 5616, 5586, 5614, 5588])).
% 1.73/2.01 tff(5620,plain,
% 1.73/2.01 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[3219, 5616, 5614, 3018, 5592])).
% 1.73/2.01 tff(5621,plain,
% 1.73/2.01 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[3963, 5616, 5586, 5588, 5614])).
% 1.73/2.01 tff(5622,plain,
% 1.73/2.01 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[675, 5621, 664])).
% 1.73/2.01 tff(5623,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.73/2.01 tff(5624,plain,
% 1.73/2.01 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[608, 363, 599, 151, 600])).
% 1.73/2.01 tff(5625,plain,
% 1.73/2.01 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[338, 5624])).
% 1.73/2.01 tff(5626,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.73/2.01 tff(5627,plain,
% 1.73/2.01 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[727])).
% 1.73/2.01 tff(5628,plain,
% 1.73/2.01 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5627])).
% 1.73/2.01 tff(5629,plain,
% 1.73/2.01 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5628])).
% 1.73/2.01 tff(5630,plain,
% 1.73/2.01 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5626, 5629])).
% 1.73/2.01 tff(5631,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[363, 5630])).
% 1.73/2.01 tff(5632,plain,((~(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))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5633,plain,
% 1.73/2.01 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5632, 363, 5626])).
% 1.73/2.01 tff(5634,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 1.73/2.01 tff(5635,plain,
% 1.73/2.01 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[763, 47, 5634])).
% 1.73/2.01 tff(5636,plain,
% 1.73/2.01 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5635, 5633])).
% 1.73/2.01 tff(5637,plain,
% 1.73/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(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(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(5638,plain,
% 1.73/2.01 (((~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(5639,plain,
% 1.73/2.01 (((~![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)))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(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(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5638])).
% 1.73/2.01 tff(5640,plain,
% 1.73/2.01 (((~![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)))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(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(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[5639, 5637])).
% 1.73/2.01 tff(5641,plain,
% 1.73/2.01 ((~![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)))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(5642,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5641, 5640])).
% 1.73/2.01 tff(5643,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5642, 65, 299, 5623, 3201])).
% 1.73/2.01 tff(5644,plain,((~r(s(s(s(s(elem!1)))), 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))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5645,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5644, 5636, 5625, 5623])).
% 1.73/2.01 tff(5646,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5647,plain,
% 1.73/2.01 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5646, 5622, 5620, 5619, 5586, 5592, 5588])).
% 1.73/2.01 tff(5648,plain,
% 1.73/2.01 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[360, 5647])).
% 1.73/2.01 tff(5649,plain,
% 1.73/2.01 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[690, 5619, 679])).
% 1.73/2.01 tff(5650,plain,
% 1.73/2.01 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2707, 65, 5649, 5648])).
% 1.73/2.01 tff(5651,plain,
% 1.73/2.01 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[763, 47, 5620])).
% 1.73/2.01 tff(5652,plain,
% 1.73/2.01 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5651, 5650])).
% 1.73/2.01 tff(5653,plain,
% 1.73/2.01 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5652])).
% 1.73/2.01 tff(5654,plain,
% 1.73/2.01 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5653])).
% 1.73/2.01 tff(5655,plain,
% 1.73/2.01 (b(s(s(s(s(s(z))))), s(z))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5553, 5654])).
% 1.73/2.01 tff(5656,plain,
% 1.73/2.01 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5653])).
% 1.73/2.01 tff(5657,plain,
% 1.73/2.01 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5656])).
% 1.73/2.01 tff(5658,plain,
% 1.73/2.01 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5657])).
% 1.73/2.01 tff(5659,plain,
% 1.73/2.01 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5652])).
% 1.73/2.01 tff(5660,plain,
% 1.73/2.01 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[20, 5659, 630])).
% 1.73/2.01 tff(5661,plain,
% 1.73/2.01 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5660])).
% 1.73/2.01 tff(5662,plain,
% 1.73/2.01 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[5661, 987])).
% 1.73/2.01 tff(5663,plain,
% 1.73/2.01 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5662])).
% 1.73/2.01 tff(5664,plain,
% 1.73/2.01 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5663])).
% 1.73/2.01 tff(5665,plain,
% 1.73/2.01 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[996, 5664])).
% 1.73/2.01 tff(5666,plain,
% 1.73/2.01 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2746, 5665])).
% 1.73/2.01 tff(5667,plain,
% 1.73/2.01 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5660])).
% 1.73/2.01 tff(5668,plain,
% 1.73/2.01 (s(s(elem!1)) = s(s(z))),
% 1.73/2.01 inference(transitivity,[status(thm)],[25, 5667, 312])).
% 1.73/2.01 tff(5669,plain,
% 1.73/2.01 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5668])).
% 1.73/2.01 tff(5670,plain,
% 1.73/2.01 (s(elem!1) = s(z)),
% 1.73/2.01 inference(transitivity,[status(thm)],[325, 5669, 15])).
% 1.73/2.01 tff(5671,plain,
% 1.73/2.01 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5652, 5670])).
% 1.73/2.01 tff(5672,plain,
% 1.73/2.01 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5671])).
% 1.73/2.01 tff(5673,plain,
% 1.73/2.01 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5616, 5672])).
% 1.73/2.01 tff(5674,plain,
% 1.73/2.01 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5670, 5652])).
% 1.73/2.01 tff(5675,plain,
% 1.73/2.01 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5674])).
% 1.73/2.01 tff(5676,plain,
% 1.73/2.01 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5614, 5675])).
% 1.73/2.01 tff(5677,plain,
% 1.73/2.01 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5668])).
% 1.73/2.01 tff(5678,plain,
% 1.73/2.01 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.73/2.01 inference(symmetry,[status(thm)],[5677])).
% 1.73/2.01 tff(5679,plain,
% 1.73/2.01 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5670])).
% 1.73/2.01 tff(5680,plain,
% 1.73/2.01 (elem!1 = z),
% 1.73/2.01 inference(transitivity,[status(thm)],[1171, 5679, 13])).
% 1.73/2.01 tff(5681,plain,
% 1.73/2.01 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5680])).
% 1.73/2.01 tff(5682,plain,
% 1.73/2.01 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.73/2.01 inference(symmetry,[status(thm)],[5681])).
% 1.73/2.01 tff(5683,plain,
% 1.73/2.01 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.73/2.01 inference(transitivity,[status(thm)],[5682, 5678])).
% 1.73/2.01 tff(5684,plain,
% 1.73/2.01 (b(s(s(elem!1)), elem!1)),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5571, 5683])).
% 1.73/2.01 tff(5685,plain,
% 1.73/2.01 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5668])).
% 1.73/2.01 tff(5686,plain,
% 1.73/2.01 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5685])).
% 1.73/2.01 tff(5687,plain,
% 1.73/2.01 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5680])).
% 1.73/2.01 tff(5688,plain,
% 1.73/2.01 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5687])).
% 1.73/2.01 tff(5689,plain,
% 1.73/2.01 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.73/2.01 inference(transitivity,[status(thm)],[5688, 5686])).
% 1.73/2.01 tff(5690,plain,
% 1.73/2.01 (b(elem!1, s(s(elem!1)))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5536, 5689])).
% 1.73/2.01 tff(5691,plain,
% 1.73/2.01 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5234])).
% 1.73/2.01 tff(5692,plain,
% 1.73/2.01 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[5232, 5691])).
% 1.73/2.01 tff(5693,plain,
% 1.73/2.01 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5274, 2218, 151, 177, 970])).
% 1.73/2.01 tff(5694,plain,
% 1.73/2.01 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[2214, 5693, 5231])).
% 1.73/2.01 tff(5695,plain,
% 1.73/2.01 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5694, 5692])).
% 1.73/2.01 tff(5696,plain,
% 1.73/2.01 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5299, 5307])).
% 1.73/2.01 tff(5697,plain,
% 1.73/2.01 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5331, 2218, 5305, 5312, 5696])).
% 1.73/2.01 tff(5698,plain,
% 1.73/2.01 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5338, 5697, 5220])).
% 1.73/2.01 tff(5699,plain,
% 1.73/2.01 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1050, 5698])).
% 1.73/2.01 tff(5700,plain,
% 1.73/2.01 (r(s(z), s(s(s(s(s(z))))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5699, 5310])).
% 1.73/2.01 tff(5701,plain,
% 1.73/2.01 (r(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[2787, 3363])).
% 1.73/2.01 tff(5702,plain,
% 1.73/2.01 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[3363])).
% 1.73/2.01 tff(5703,plain,
% 1.73/2.01 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[5702, 1917])).
% 1.73/2.01 tff(5704,plain,
% 1.73/2.01 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.73/2.01 inference(symmetry,[status(thm)],[5703])).
% 1.73/2.01 tff(5705,plain,
% 1.73/2.01 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5704])).
% 1.73/2.01 tff(5706,plain,
% 1.73/2.01 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[914, 5705])).
% 1.73/2.01 tff(5707,plain,
% 1.73/2.01 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4443, 5699, 97])).
% 1.73/2.01 tff(5708,plain,
% 1.73/2.01 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1741, 5707, 5220])).
% 1.73/2.01 tff(5709,plain,
% 1.73/2.01 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1813, 5708, 5225])).
% 1.73/2.01 tff(5710,plain,
% 1.73/2.01 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.73/2.01 inference(transitivity,[status(thm)],[5223, 1831])).
% 1.73/2.01 tff(5711,plain,
% 1.73/2.01 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5710])).
% 1.73/2.01 tff(5712,plain,
% 1.73/2.01 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[2888, 5711])).
% 1.73/2.01 tff(5713,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4259, 65, 194, 2860, 878])).
% 1.73/2.01 tff(5714,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5715,plain,
% 1.73/2.01 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5714, 5699, 194])).
% 1.73/2.01 tff(5716,plain,
% 1.73/2.01 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[4286, 5715, 5220])).
% 1.73/2.01 tff(5717,plain,
% 1.73/2.01 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1858, 5716, 5712])).
% 1.73/2.01 tff(5718,plain,
% 1.73/2.01 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1853, 5717, 1248, 5709, 1600])).
% 1.73/2.01 tff(5719,plain,
% 1.73/2.01 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[1760, 5718, 5706])).
% 1.73/2.01 tff(5720,plain,
% 1.73/2.01 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5719, 5701])).
% 1.73/2.01 tff(5721,plain,
% 1.73/2.01 (((~![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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(5722,plain,
% 1.73/2.01 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.73/2.01 inference(rewrite,[status(thm)],[])).
% 1.73/2.01 tff(5723,plain,
% 1.73/2.01 (((~![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(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.73/2.01 inference(monotonicity,[status(thm)],[5722])).
% 1.73/2.01 tff(5724,plain,
% 1.73/2.01 (((~![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(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), 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(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.73/2.01 inference(transitivity,[status(thm)],[5723, 5721])).
% 1.73/2.01 tff(5725,plain,
% 1.73/2.01 ((~![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(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.73/2.01 inference(quant_inst,[status(thm)],[])).
% 1.73/2.01 tff(5726,plain,
% 1.73/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.73/2.01 inference(modus_ponens,[status(thm)],[5725, 5724])).
% 1.73/2.01 tff(5727,plain,
% 1.73/2.01 ($false),
% 1.73/2.01 inference(unit_resolution,[status(thm)],[5726, 65, 384, 5720, 5700, 5695])).
% 1.73/2.01 tff(5728,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(z)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.01 tff(5729,plain,
% 1.73/2.02 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5728, 5652, 384, 5690, 5684, 97, 194, 5676, 5673, 5592, 3018, 5553])).
% 1.73/2.02 tff(5730,plain,
% 1.73/2.02 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1789, 5729, 5666])).
% 1.73/2.02 tff(5731,plain,
% 1.73/2.02 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5320, 5730, 5648])).
% 1.73/2.02 tff(5732,plain,
% 1.73/2.02 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1001, 5731])).
% 1.73/2.02 tff(5733,plain,
% 1.73/2.02 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[5732, 5658])).
% 1.73/2.02 tff(5734,plain,
% 1.73/2.02 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[5656])).
% 1.73/2.02 tff(5735,plain,
% 1.73/2.02 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/2.02 inference(symmetry,[status(thm)],[5734])).
% 1.73/2.02 tff(5736,plain,
% 1.73/2.02 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[5660])).
% 1.73/2.02 tff(5737,plain,
% 1.73/2.02 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[5736, 5735])).
% 1.73/2.02 tff(5738,plain,
% 1.73/2.02 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[5652, 5660])).
% 1.73/2.02 tff(5739,plain,
% 1.73/2.02 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/2.02 inference(symmetry,[status(thm)],[5738])).
% 1.73/2.02 tff(5740,plain,
% 1.73/2.02 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[5649, 5739])).
% 1.73/2.02 tff(5741,plain,
% 1.73/2.02 (((~![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(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(5742,plain,
% 1.73/2.02 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(5743,plain,
% 1.73/2.02 (((~![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(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(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[5742])).
% 1.73/2.02 tff(5744,plain,
% 1.73/2.02 (((~![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(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(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[5743, 5741])).
% 1.73/2.02 tff(5745,plain,
% 1.73/2.02 ((~![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(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(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(5746,plain,
% 1.73/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[5745, 5744])).
% 1.73/2.02 tff(5747,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5746, 65, 1718, 3850, 1004])).
% 1.73/2.02 tff(5748,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(5749,plain,
% 1.73/2.02 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5748, 5730, 5740])).
% 1.73/2.02 tff(5750,plain,
% 1.73/2.02 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[1731, 5749, 5665])).
% 1.73/2.02 tff(5751,plain,
% 1.73/2.02 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[5750, 5737])).
% 1.73/2.02 tff(5752,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2910, 162, 5588, 5586, 5751, 5733, 5655])).
% 1.73/2.02 tff(5753,plain,((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(5754,plain,
% 1.73/2.02 (~r(z, s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5753, 194, 384, 2])).
% 1.73/2.02 tff(5755,plain,
% 1.73/2.02 (b(z, s(z))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[117, 5754])).
% 1.73/2.02 tff(5756,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[4590, 162, 121, 177, 151, 120, 363, 600])).
% 1.73/2.02 tff(5757,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(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(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(5758,plain,
% 1.73/2.02 (~b(z, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5757, 363, 177, 151, 121, 600])).
% 1.73/2.02 tff(5759,plain,
% 1.73/2.02 (r(z, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[83, 5758])).
% 1.73/2.02 tff(5760,plain,
% 1.73/2.02 (~r(z, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2507, 5759, 5625])).
% 1.73/2.02 tff(5761,plain,
% 1.73/2.02 (b(z, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[295, 5760])).
% 1.73/2.02 tff(5762,plain,
% 1.73/2.02 (~r(s(s(s(z))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[3304, 65, 5759, 5625])).
% 1.73/2.02 tff(5763,plain,
% 1.73/2.02 (b(s(s(s(z))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[381, 5762])).
% 1.73/2.02 tff(5764,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(5765,plain,
% 1.73/2.02 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(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(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(5766,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[5765])).
% 1.73/2.02 tff(5767,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[5766, 5764])).
% 1.73/2.02 tff(5768,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(5769,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[5768, 5767])).
% 1.73/2.02 tff(5770,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5769, 162, 121, 5763, 600, 599, 5761])).
% 1.73/2.02 tff(5771,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(5772,plain,
% 1.73/2.02 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5771, 5755, 5588, 5586, 3018, 5584])).
% 1.73/2.02 tff(5773,plain,
% 1.73/2.02 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[360, 5772])).
% 1.73/2.02 tff(5774,plain,
% 1.73/2.02 (~r(z, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[566, 1, 340])).
% 1.73/2.02 tff(5775,plain,
% 1.73/2.02 (b(z, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[83, 5774])).
% 1.73/2.02 tff(5776,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2573, 2719, 5775, 416, 537, 538])).
% 1.73/2.02 tff(5777,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(5778,plain,
% 1.73/2.02 (~r(z, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5777, 5571, 5536, 4602, 5773])).
% 1.73/2.02 tff(5779,plain,
% 1.73/2.02 (b(z, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[295, 5778])).
% 1.73/2.02 tff(5780,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5769, 162, 121, 298, 600, 599, 297])).
% 1.73/2.02 tff(5781,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(5782,plain,
% 1.73/2.02 (~b(s(s(s(z))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5781, 5755, 5588, 5586, 5779])).
% 1.73/2.02 tff(5783,plain,
% 1.73/2.02 (r(s(s(s(z))), z)),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[381, 5782])).
% 1.73/2.02 tff(5784,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(5785,plain,
% 1.73/2.02 (((~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))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(5786,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.73/2.02 inference(monotonicity,[status(thm)],[5785])).
% 1.73/2.02 tff(5787,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.73/2.02 inference(transitivity,[status(thm)],[5786, 5784])).
% 1.73/2.02 tff(5788,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(z))))))),
% 1.73/2.02 inference(quant_inst,[status(thm)],[])).
% 1.73/2.02 tff(5789,plain,
% 1.73/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.73/2.02 inference(modus_ponens,[status(thm)],[5788, 5787])).
% 1.73/2.02 tff(5790,plain,
% 1.73/2.02 ($false),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5789, 162, 121, 177, 151, 122, 362, 599])).
% 1.73/2.02 tff(5791,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.73/2.02 tff(5792,plain,
% 1.73/2.02 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[5791, 122, 177, 151, 121, 599])).
% 1.73/2.02 tff(5793,plain,
% 1.73/2.02 (~b(z, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2573, 122, 416, 537, 538])).
% 1.73/2.02 tff(5794,plain,
% 1.73/2.02 (r(z, s(s(s(s(elem!1)))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[83, 5793])).
% 1.73/2.02 tff(5795,plain,
% 1.73/2.02 (~r(z, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[2507, 5794, 299])).
% 1.73/2.02 tff(5796,plain,
% 1.73/2.02 (b(z, s(s(s(z))))),
% 1.73/2.02 inference(unit_resolution,[status(thm)],[295, 5795])).
% 1.73/2.02 tff(5797,plain,
% 1.73/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.73/2.02 inference(rewrite,[status(thm)],[])).
% 1.73/2.02 tff(5798,plain,
% 1.73/2.02 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(5799,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[5798])).
% 1.86/2.02 tff(5800,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.02 inference(transitivity,[status(thm)],[5799, 5797])).
% 1.86/2.02 tff(5801,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(5802,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[5801, 5800])).
% 1.86/2.02 tff(5803,plain,
% 1.86/2.02 ($false),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[5802, 162, 121, 416, 122, 538, 600, 5796])).
% 1.86/2.02 tff(5804,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.02 tff(5805,plain,
% 1.86/2.02 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[5804, 122, 416, 538, 600, 121, 537])).
% 1.86/2.02 tff(5806,plain,
% 1.86/2.02 ($false),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[338, 5805, 5792])).
% 1.86/2.02 tff(5807,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.02 tff(5808,plain,
% 1.86/2.02 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[5807, 5571, 4602, 5588, 5755, 5536, 3018, 5584, 5586])).
% 1.86/2.02 tff(5809,plain,
% 1.86/2.02 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[95, 5808])).
% 1.86/2.02 tff(5810,plain,
% 1.86/2.02 ($false),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[5533, 65, 5809, 5783, 5773])).
% 1.86/2.02 tff(5811,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.02 tff(5812,plain,
% 1.86/2.02 (~r(s(z), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[5811, 2, 384])).
% 1.86/2.02 tff(5813,plain,
% 1.86/2.02 (b(s(z), z)),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[175, 5812])).
% 1.86/2.02 tff(5814,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(5815,plain,
% 1.86/2.02 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(5816,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[5815])).
% 1.86/2.02 tff(5817,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.02 inference(transitivity,[status(thm)],[5816, 5814])).
% 1.86/2.02 tff(5818,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(5819,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[5818, 5817])).
% 1.86/2.02 tff(5820,plain,
% 1.86/2.02 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[5819, 162, 5813, 5569, 5553, 5538, 297])).
% 1.86/2.03 tff(5821,plain,
% 1.86/2.03 (~b(s(s(z)), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3058, 97, 5536, 385, 384])).
% 1.86/2.03 tff(5822,plain,
% 1.86/2.03 (r(s(s(z)), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[245, 5821])).
% 1.86/2.03 tff(5823,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[554, 65, 97, 5822, 2])).
% 1.86/2.03 tff(5824,plain,((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(5825,plain,
% 1.86/2.03 (~r(z, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5824, 385, 2, 384])).
% 1.86/2.03 tff(5826,plain,
% 1.86/2.03 (b(z, s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[117, 5825])).
% 1.86/2.03 tff(5827,plain,
% 1.86/2.03 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3122, 5826, 3018, 5813, 4606])).
% 1.86/2.03 tff(5828,plain,
% 1.86/2.03 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[95, 5827])).
% 1.86/2.03 tff(5829,plain,
% 1.86/2.03 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4610, 5826, 5813, 3018, 4606])).
% 1.86/2.03 tff(5830,plain,
% 1.86/2.03 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[83, 5829])).
% 1.86/2.03 tff(5831,plain,
% 1.86/2.03 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4634, 5830, 385, 5828, 2, 384])).
% 1.86/2.03 tff(5832,plain,
% 1.86/2.03 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[360, 5831])).
% 1.86/2.03 tff(5833,plain,
% 1.86/2.03 (~r(z, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2601, 5832, 5828])).
% 1.86/2.03 tff(5834,plain,
% 1.86/2.03 (b(z, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[295, 5833])).
% 1.86/2.03 tff(5835,plain,
% 1.86/2.03 (~b(s(s(z)), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1465, 5834, 5536, 578, 588])).
% 1.86/2.03 tff(5836,plain,
% 1.86/2.03 (r(s(s(z)), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[245, 5835])).
% 1.86/2.03 tff(5837,plain,
% 1.86/2.03 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[4631, 65, 5828, 5836])).
% 1.86/2.03 tff(5838,plain,
% 1.86/2.03 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[214, 47, 5837, 209])).
% 1.86/2.03 tff(5839,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5840,plain,
% 1.86/2.03 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5841,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5840])).
% 1.86/2.03 tff(5842,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[5841, 5839])).
% 1.86/2.03 tff(5843,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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)))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(5844,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5843, 5842])).
% 1.86/2.03 tff(5845,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5844, 162, 416, 444, 362, 445, 526])).
% 1.86/2.03 tff(5846,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(5847,plain,
% 1.86/2.03 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5846, 588, 4602, 578, 5838])).
% 1.86/2.03 tff(5848,plain,
% 1.86/2.03 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[338, 5847])).
% 1.86/2.03 tff(5849,plain,
% 1.86/2.03 (~r(s(s(s(z))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3304, 65, 5830, 5848])).
% 1.86/2.03 tff(5850,plain,
% 1.86/2.03 (b(s(s(s(z))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[381, 5849])).
% 1.86/2.03 tff(5851,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5852,plain,
% 1.86/2.03 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, 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(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5853,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5852])).
% 1.86/2.03 tff(5854,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[5853, 5851])).
% 1.86/2.03 tff(5855,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(5856,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5855, 5854])).
% 1.86/2.03 tff(5857,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5856, 162, 5536, 588, 578, 5850, 5834])).
% 1.86/2.03 tff(5858,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(5859,plain,
% 1.86/2.03 (~r(s(s(s(z))), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5858, 2, 384])).
% 1.86/2.03 tff(5860,plain,
% 1.86/2.03 (b(s(s(s(z))), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[595, 5859])).
% 1.86/2.03 tff(5861,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5862,plain,
% 1.86/2.03 (((~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(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(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))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5863,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5862])).
% 1.86/2.03 tff(5864,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[5863, 5861])).
% 1.86/2.03 tff(5865,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), 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))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(5866,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5865, 5864])).
% 1.86/2.03 tff(5867,plain,
% 1.86/2.03 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5866, 162, 5813, 5569, 5860, 5538, 297])).
% 1.86/2.03 tff(5868,plain,
% 1.86/2.03 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[360, 5867])).
% 1.86/2.03 tff(5869,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5870,plain,
% 1.86/2.03 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5871,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5870])).
% 1.86/2.03 tff(5872,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[5871, 5869])).
% 1.86/2.03 tff(5873,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(5874,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5873, 5872])).
% 1.86/2.03 tff(5875,plain,
% 1.86/2.03 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5874, 162, 5813, 5860, 5553, 5538, 297])).
% 1.86/2.03 tff(5876,plain,
% 1.86/2.03 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1001, 5875])).
% 1.86/2.03 tff(5877,plain,
% 1.86/2.03 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5320, 5876, 5868])).
% 1.86/2.03 tff(5878,plain,
% 1.86/2.03 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1789, 5877, 5820])).
% 1.86/2.03 tff(5879,plain,
% 1.86/2.03 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5878])).
% 1.86/2.03 tff(5880,plain,
% 1.86/2.03 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.03 inference(symmetry,[status(thm)],[5879])).
% 1.86/2.03 tff(5881,plain,
% 1.86/2.03 ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5880])).
% 1.86/2.03 tff(5882,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5883,plain,
% 1.86/2.03 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5884,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[5883])).
% 1.86/2.03 tff(5885,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[5884, 5882])).
% 1.86/2.03 tff(5886,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(5887,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[5886, 5885])).
% 1.86/2.03 tff(5888,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5887, 162, 152, 298, 600, 599, 297])).
% 1.86/2.03 tff(5889,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(5890,plain,
% 1.86/2.03 (~b(s(s(s(z))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[5889, 5538, 5860, 5813, 297])).
% 1.86/2.03 tff(5891,plain,
% 1.86/2.03 (r(s(s(s(z))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[381, 5890])).
% 1.86/2.03 tff(5892,plain,
% 1.86/2.03 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[886, 5876, 5891])).
% 1.86/2.03 tff(5893,plain,
% 1.86/2.03 (b(s(s(s(s(s(elem!1))))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[894, 5892])).
% 1.86/2.03 tff(5894,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(5895,plain,
% 1.86/2.03 (((~b(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(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(5896,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[5895])).
% 1.86/2.04 tff(5897,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[5896, 5894])).
% 1.86/2.04 tff(5898,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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)))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(5899,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[5898, 5897])).
% 1.86/2.04 tff(5900,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5899, 162, 177, 151, 362, 600, 599])).
% 1.86/2.04 tff(5901,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(5902,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5901, 5538, 3018, 5860, 5569])).
% 1.86/2.04 tff(5903,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[338, 5902])).
% 1.86/2.04 tff(5904,plain,
% 1.86/2.04 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1508])).
% 1.86/2.04 tff(5905,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1508])).
% 1.86/2.04 tff(5906,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[299, 5905])).
% 1.86/2.04 tff(5907,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), 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(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(5908,plain,
% 1.86/2.04 (((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(5909,plain,
% 1.86/2.04 (((~![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(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~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(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[5908])).
% 1.86/2.04 tff(5910,plain,
% 1.86/2.04 (((~![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(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~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(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[5909, 5907])).
% 1.86/2.04 tff(5911,plain,
% 1.86/2.04 ((~![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(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(5912,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 1.86/2.04 tff(5913,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5912, 65, 946, 5906])).
% 1.86/2.04 tff(5914,plain,
% 1.86/2.04 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[459, 5913])).
% 1.86/2.04 tff(5915,plain,
% 1.86/2.04 (((~![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(elem!1))))))) | (~r(s(s(s(z))), 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(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(5916,plain,
% 1.86/2.04 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(5917,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[5916])).
% 1.86/2.04 tff(5918,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[5917, 5915])).
% 1.86/2.04 tff(5919,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(5920,plain,
% 1.86/2.04 ((~![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(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 1.86/2.04 tff(5921,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5920, 65, 946, 5906])).
% 1.86/2.04 tff(5922,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[442, 5921])).
% 1.86/2.04 tff(5923,plain,
% 1.86/2.04 (~b(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1465, 5922, 2565, 3044, 5914])).
% 1.86/2.04 tff(5924,plain,
% 1.86/2.04 (r(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[295, 5923])).
% 1.86/2.04 tff(5925,plain,
% 1.86/2.04 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2507, 5924, 299])).
% 1.86/2.04 tff(5926,plain,
% 1.86/2.04 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[83, 5925])).
% 1.86/2.04 tff(5927,plain,
% 1.86/2.04 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2577, 5926, 2, 97, 416])).
% 1.86/2.04 tff(5928,plain,
% 1.86/2.04 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[95, 5927])).
% 1.86/2.04 tff(5929,plain,
% 1.86/2.04 (r(s(s(s(s(s(elem!1))))), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[5928, 5904])).
% 1.86/2.04 tff(5930,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5912, 65, 946, 867])).
% 1.86/2.04 tff(5931,plain,
% 1.86/2.04 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[459, 5930])).
% 1.86/2.04 tff(5932,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5920, 65, 946, 867])).
% 1.86/2.04 tff(5933,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[442, 5932])).
% 1.86/2.04 tff(5934,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3150, 5933, 5931, 538, 298, 537])).
% 1.86/2.04 tff(5935,plain,((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(5936,plain,
% 1.86/2.04 (~b(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5935, 946, 3044, 2565, 5906])).
% 1.86/2.04 tff(5937,plain,
% 1.86/2.04 (r(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[381, 5936])).
% 1.86/2.04 tff(5938,plain,
% 1.86/2.04 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[886, 5937, 5906])).
% 1.86/2.04 tff(5939,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5938, 5929])).
% 1.86/2.04 tff(5940,plain,((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(5941,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5940, 5878, 2, 4602, 97, 5903])).
% 1.86/2.04 tff(5942,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[943, 5941])).
% 1.86/2.04 tff(5943,plain,
% 1.86/2.04 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[935, 5942, 5536, 5893, 3044])).
% 1.86/2.04 tff(5944,plain,
% 1.86/2.04 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[5943, 5881])).
% 1.86/2.04 tff(5945,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[4602, 5944])).
% 1.86/2.04 tff(5946,plain,((~b(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(5947,plain,
% 1.86/2.04 (~b(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5946, 97, 2, 384])).
% 1.86/2.04 tff(5948,plain,
% 1.86/2.04 (r(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[295, 5947])).
% 1.86/2.04 tff(5949,plain,
% 1.86/2.04 (~r(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3102, 5948, 97])).
% 1.86/2.04 tff(5950,plain,
% 1.86/2.04 (b(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[493, 5949])).
% 1.86/2.04 tff(5951,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5901, 5950, 3018, 5860, 5569])).
% 1.86/2.04 tff(5952,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[338, 5951])).
% 1.86/2.04 tff(5953,plain,
% 1.86/2.04 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2601, 1, 2252])).
% 1.86/2.04 tff(5954,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[360, 5953])).
% 1.86/2.04 tff(5955,plain,
% 1.86/2.04 (~r(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3102, 1, 97])).
% 1.86/2.04 tff(5956,plain,
% 1.86/2.04 (b(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[493, 5955])).
% 1.86/2.04 tff(5957,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5901, 5956, 177, 600, 151])).
% 1.86/2.04 tff(5958,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[338, 5957])).
% 1.86/2.04 tff(5959,plain,
% 1.86/2.04 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2507, 5958, 1])).
% 1.86/2.04 tff(5960,plain,
% 1.86/2.04 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[83, 5959])).
% 1.86/2.04 tff(5961,plain,
% 1.86/2.04 (((~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(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(5962,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[5961])).
% 1.86/2.04 tff(5963,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[5962, 4543])).
% 1.86/2.04 tff(5964,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(5965,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[5964, 5963])).
% 1.86/2.04 tff(5966,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5965, 162, 152, 177, 151, 5960, 5954, 600])).
% 1.86/2.04 tff(5967,plain,((~r(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(5968,plain,
% 1.86/2.04 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5967, 5948, 3018, 5569, 5860, 5813, 97])).
% 1.86/2.04 tff(5969,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[95, 5968])).
% 1.86/2.04 tff(5970,plain,
% 1.86/2.04 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2573, 5969, 4602, 5536, 3044])).
% 1.86/2.04 tff(5971,plain,
% 1.86/2.04 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[83, 5970])).
% 1.86/2.04 tff(5972,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2507, 5971, 5952, 5948])).
% 1.86/2.04 tff(5973,plain,((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(5974,plain,
% 1.86/2.04 (~r(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5973, 2, 384])).
% 1.86/2.04 tff(5975,plain,
% 1.86/2.04 (b(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[117, 5974])).
% 1.86/2.04 tff(5976,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5499, 443, 3018, 5813, 5860, 4602, 5975, 123, 2])).
% 1.86/2.04 tff(5977,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[459, 5976])).
% 1.86/2.04 tff(5978,plain,
% 1.86/2.04 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5481, 395, 123])).
% 1.86/2.04 tff(5979,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[360, 5978])).
% 1.86/2.04 tff(5980,plain,
% 1.86/2.04 (~b(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2976, 5979, 712, 5975, 5860, 443])).
% 1.86/2.04 tff(5981,plain,
% 1.86/2.04 (r(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[381, 5980])).
% 1.86/2.04 tff(5982,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2028, 5981, 5977, 230])).
% 1.86/2.04 tff(5983,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(5984,plain,
% 1.86/2.04 (~r(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5983, 230, 123, 2, 384])).
% 1.86/2.04 tff(5985,plain,
% 1.86/2.04 (b(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[493, 5984])).
% 1.86/2.04 tff(5986,plain,
% 1.86/2.04 (~b(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2039, 5985, 5813, 5860, 5975])).
% 1.86/2.04 tff(5987,plain,
% 1.86/2.04 (r(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[295, 5986])).
% 1.86/2.04 tff(5988,plain,
% 1.86/2.04 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3010, 363, 4602, 5975, 712, 5860, 5985, 384])).
% 1.86/2.04 tff(5989,plain,
% 1.86/2.04 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[83, 5988])).
% 1.86/2.04 tff(5990,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2507, 5989, 5987])).
% 1.86/2.04 tff(5991,plain,
% 1.86/2.04 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[338, 5990])).
% 1.86/2.04 tff(5992,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[620, 5991, 4602, 712, 363])).
% 1.86/2.04 tff(5993,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[459, 5992])).
% 1.86/2.04 tff(5994,plain,
% 1.86/2.04 (~r(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2028, 5993, 230])).
% 1.86/2.04 tff(5995,plain,
% 1.86/2.04 (b(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[381, 5994])).
% 1.86/2.04 tff(5996,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[704, 5993, 5985, 5860, 384])).
% 1.86/2.04 tff(5997,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[709, 5996, 635])).
% 1.86/2.04 tff(5998,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[851, 5997, 5995, 5975, 5987, 363, 123, 5813, 5989, 384, 4602, 5991, 2])).
% 1.86/2.04 tff(5999,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(6000,plain,
% 1.86/2.04 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5999, 230, 384, 2, 123])).
% 1.86/2.04 tff(6001,plain,
% 1.86/2.04 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[360, 6000])).
% 1.86/2.04 tff(6002,plain,
% 1.86/2.04 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2601, 6001, 5987])).
% 1.86/2.04 tff(6003,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[95, 6002])).
% 1.86/2.04 tff(6004,plain,
% 1.86/2.04 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[566, 6001, 5987])).
% 1.86/2.04 tff(6005,plain,
% 1.86/2.04 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[83, 6004])).
% 1.86/2.04 tff(6006,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5497, 6005, 6003, 3018, 5813, 5975])).
% 1.86/2.04 tff(6007,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(6008,plain,
% 1.86/2.04 (~r(s(s(z)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6007, 123, 2, 384])).
% 1.86/2.04 tff(6009,plain,
% 1.86/2.04 (b(s(s(z)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[245, 6008])).
% 1.86/2.04 tff(6010,plain,
% 1.86/2.04 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[546, 6009, 4602, 5536, 712])).
% 1.86/2.04 tff(6011,plain,
% 1.86/2.04 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[83, 6010])).
% 1.86/2.04 tff(6012,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5517, 6011, 5813, 5860, 5975])).
% 1.86/2.04 tff(6013,plain,
% 1.86/2.04 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[338, 6012])).
% 1.86/2.04 tff(6014,plain,
% 1.86/2.04 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[468, 395, 416, 362, 384])).
% 1.86/2.04 tff(6015,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[360, 6014, 5978])).
% 1.86/2.04 tff(6016,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(6017,plain,
% 1.86/2.04 (~r(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[6016, 6013, 4602, 384, 123])).
% 1.86/2.04 tff(6018,plain,
% 1.86/2.04 (b(s(z), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[493, 6017])).
% 1.86/2.04 tff(6019,plain,
% 1.86/2.04 (~b(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2039, 6018, 5813, 5860, 5975])).
% 1.86/2.04 tff(6020,plain,
% 1.86/2.04 (r(z, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[295, 6019])).
% 1.86/2.04 tff(6021,plain,
% 1.86/2.04 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[5777, 6020, 5536, 4602, 6009])).
% 1.86/2.04 tff(6022,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[360, 6021])).
% 1.86/2.04 tff(6023,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[620, 6022, 4602, 712, 6013])).
% 1.86/2.04 tff(6024,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[459, 6023])).
% 1.86/2.04 tff(6025,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[704, 6024, 6018, 5860, 384])).
% 1.86/2.04 tff(6026,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[709, 6025, 635])).
% 1.86/2.04 tff(6027,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1098, 6026, 6020, 6011, 6009, 5536])).
% 1.86/2.04 tff(6028,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[690, 6027, 679])).
% 1.86/2.04 tff(6029,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(6030,plain,
% 1.86/2.04 (((~b(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(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6031,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6030])).
% 1.86/2.05 tff(6032,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6031, 6029])).
% 1.86/2.05 tff(6033,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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)))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6034,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6033, 6032])).
% 1.86/2.05 tff(6035,plain,
% 1.86/2.05 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6034, 162, 3018, 6013, 5860, 6018, 6028])).
% 1.86/2.05 tff(6036,plain,
% 1.86/2.05 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5439, 6035, 3018])).
% 1.86/2.05 tff(6037,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6038,plain,
% 1.86/2.05 (((~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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6039,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6038])).
% 1.86/2.05 tff(6040,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6039, 6037])).
% 1.86/2.05 tff(6041,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6042,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6041, 6040])).
% 1.86/2.05 tff(6043,plain,
% 1.86/2.05 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6042, 162, 4602, 3018, 6013, 5860, 6026])).
% 1.86/2.05 tff(6044,plain,
% 1.86/2.05 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[763, 47, 6043, 6036])).
% 1.86/2.05 tff(6045,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6046,plain,
% 1.86/2.05 (((~b(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(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(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6047,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6046])).
% 1.86/2.05 tff(6048,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6047, 6045])).
% 1.86/2.05 tff(6049,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(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))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6050,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6049, 6048])).
% 1.86/2.05 tff(6051,plain,
% 1.86/2.05 (~b(s(s(s(s(z)))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6050, 162, 3018, 6013, 5860, 6018, 6028])).
% 1.86/2.05 tff(6052,plain,
% 1.86/2.05 (r(s(s(s(s(z)))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[775, 6051, 642])).
% 1.86/2.05 tff(6053,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[782, 65, 123, 6052, 6044])).
% 1.86/2.05 tff(6054,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6055,plain,
% 1.86/2.05 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6054, 2, 384])).
% 1.86/2.05 tff(6056,plain,
% 1.86/2.05 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[149, 6055])).
% 1.86/2.05 tff(6057,plain,
% 1.86/2.05 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4610, 6056, 5813, 3018, 5975])).
% 1.86/2.05 tff(6058,plain,
% 1.86/2.05 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[83, 6057])).
% 1.86/2.05 tff(6059,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5517, 6058, 5813, 5860, 5975])).
% 1.86/2.05 tff(6060,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[338, 6059])).
% 1.86/2.05 tff(6061,plain,
% 1.86/2.05 (~b(s(z), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5901, 6060, 3018, 5860, 6056])).
% 1.86/2.05 tff(6062,plain,
% 1.86/2.05 (r(s(z), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[493, 6061])).
% 1.86/2.05 tff(6063,plain,
% 1.86/2.05 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[425, 6062, 384])).
% 1.86/2.05 tff(6064,plain,
% 1.86/2.05 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[442, 6063])).
% 1.86/2.05 tff(6065,plain,
% 1.86/2.05 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3122, 6056, 3018, 5813, 5975])).
% 1.86/2.05 tff(6066,plain,
% 1.86/2.05 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[95, 6065])).
% 1.86/2.05 tff(6067,plain,
% 1.86/2.05 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[468, 6062, 4602, 6060, 384])).
% 1.86/2.05 tff(6068,plain,
% 1.86/2.05 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[360, 6067])).
% 1.86/2.05 tff(6069,plain,
% 1.86/2.05 (~r(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2601, 6068, 6066])).
% 1.86/2.05 tff(6070,plain,
% 1.86/2.05 (b(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[295, 6069])).
% 1.86/2.05 tff(6071,plain,
% 1.86/2.05 (~b(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5513, 6070, 5813, 5860, 5975])).
% 1.86/2.05 tff(6072,plain,
% 1.86/2.05 (r(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[381, 6071])).
% 1.86/2.05 tff(6073,plain,
% 1.86/2.05 (~b(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3066, 6070, 5536, 6062, 384])).
% 1.86/2.05 tff(6074,plain,
% 1.86/2.05 (r(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[245, 6073])).
% 1.86/2.05 tff(6075,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2028, 6074, 6072])).
% 1.86/2.05 tff(6076,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[459, 6075])).
% 1.86/2.05 tff(6077,plain,
% 1.86/2.05 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5846, 6076, 4602, 6060, 6064])).
% 1.86/2.05 tff(6078,plain,
% 1.86/2.05 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[4631, 65, 6066, 6074])).
% 1.86/2.05 tff(6079,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[214, 47, 6078, 6077, 209])).
% 1.86/2.05 tff(6080,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6081,plain,
% 1.86/2.05 (~r(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6080, 384])).
% 1.86/2.05 tff(6082,plain,
% 1.86/2.05 (b(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[271, 6081])).
% 1.86/2.05 tff(6083,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2537, 65, 194, 384, 230])).
% 1.86/2.05 tff(6084,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6085,plain,
% 1.86/2.05 (~r(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6084, 194, 384])).
% 1.86/2.05 tff(6086,plain,
% 1.86/2.05 (b(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[245, 6085])).
% 1.86/2.05 tff(6087,plain,
% 1.86/2.05 (~r(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3058, 6086, 385, 537, 384])).
% 1.86/2.05 tff(6088,plain,
% 1.86/2.05 (b(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[117, 6087])).
% 1.86/2.05 tff(6089,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6090,plain,
% 1.86/2.05 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6091,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6090])).
% 1.86/2.05 tff(6092,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6091, 6089])).
% 1.86/2.05 tff(6093,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6094,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6093, 6092])).
% 1.86/2.05 tff(6095,plain,
% 1.86/2.05 (~b(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6094, 162, 6088, 6086, 537, 578, 6082])).
% 1.86/2.05 tff(6096,plain,
% 1.86/2.05 (r(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[381, 6095])).
% 1.86/2.05 tff(6097,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1389, 65, 194, 385, 6096])).
% 1.86/2.05 tff(6098,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6099,plain,
% 1.86/2.05 (~b(z, s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6098, 194, 385, 384])).
% 1.86/2.05 tff(6100,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[524, 6099, 394])).
% 1.86/2.05 tff(6101,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6102,plain,
% 1.86/2.05 (~r(s(z), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6101, 385, 384])).
% 1.86/2.05 tff(6103,plain,
% 1.86/2.05 (b(s(z), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[175, 6102])).
% 1.86/2.05 tff(6104,plain,
% 1.86/2.05 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[216, 513])).
% 1.86/2.05 tff(6105,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2517, 193, 385])).
% 1.86/2.05 tff(6106,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[338, 6105])).
% 1.86/2.05 tff(6107,plain,
% 1.86/2.05 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[403, 54, 384])).
% 1.86/2.05 tff(6108,plain,
% 1.86/2.05 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[191, 6107])).
% 1.86/2.05 tff(6109,plain,
% 1.86/2.05 (~r(z, s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3350, 6108, 54, 384])).
% 1.86/2.05 tff(6110,plain,
% 1.86/2.05 (b(z, s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[524, 6109])).
% 1.86/2.05 tff(6111,plain,
% 1.86/2.05 (~r(s(z), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6098, 6110, 385, 384])).
% 1.86/2.05 tff(6112,plain,
% 1.86/2.05 (b(s(z), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[175, 6111])).
% 1.86/2.05 tff(6113,plain,
% 1.86/2.05 (~r(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2611, 97, 385])).
% 1.86/2.05 tff(6114,plain,
% 1.86/2.05 (b(z, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[295, 6113])).
% 1.86/2.05 tff(6115,plain,
% 1.86/2.05 (~r(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1377, 97, 385])).
% 1.86/2.05 tff(6116,plain,
% 1.86/2.05 (b(s(s(s(z))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[381, 6115])).
% 1.86/2.05 tff(6117,plain,
% 1.86/2.05 (~r(s(z), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6098, 537, 385, 384])).
% 1.86/2.05 tff(6118,plain,
% 1.86/2.05 (b(s(z), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[175, 6117])).
% 1.86/2.05 tff(6119,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6120,plain,
% 1.86/2.05 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(6121,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[6120])).
% 1.86/2.05 tff(6122,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[6121, 6119])).
% 1.86/2.05 tff(6123,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(6124,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6123, 6122])).
% 1.86/2.05 tff(6125,plain,
% 1.86/2.05 (~b(s(z), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6124, 162, 6118, 537, 578, 6116, 6114])).
% 1.86/2.05 tff(6126,plain,
% 1.86/2.05 (r(s(z), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[493, 6125])).
% 1.86/2.05 tff(6127,plain,
% 1.86/2.05 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[425, 6126, 384])).
% 1.86/2.05 tff(6128,plain,
% 1.86/2.05 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[442, 6127])).
% 1.86/2.05 tff(6129,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[5856, 162, 537, 6128, 578, 6116, 6114])).
% 1.86/2.05 tff(6130,plain,((~r(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6131,plain,
% 1.86/2.05 (~r(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6130, 6110, 384, 385])).
% 1.86/2.05 tff(6132,plain,
% 1.86/2.05 (b(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[117, 6131])).
% 1.86/2.05 tff(6133,plain,
% 1.86/2.05 (~b(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1402, 6132, 6082, 6112, 6110])).
% 1.86/2.05 tff(6134,plain,
% 1.86/2.05 (r(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[245, 6133])).
% 1.86/2.05 tff(6135,plain,
% 1.86/2.05 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3122, 6132, 6108, 3042, 6112])).
% 1.86/2.05 tff(6136,plain,
% 1.86/2.05 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[95, 6135])).
% 1.86/2.05 tff(6137,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3138, 65, 54, 6136, 6134])).
% 1.86/2.05 tff(6138,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(6139,plain,
% 1.86/2.05 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6138, 385, 384])).
% 1.86/2.05 tff(6140,plain,
% 1.86/2.05 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[52, 6139])).
% 1.86/2.05 tff(6141,plain,
% 1.86/2.05 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[620, 6104, 578, 6140, 6106])).
% 1.86/2.05 tff(6142,plain,
% 1.86/2.05 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[360, 6141])).
% 1.86/2.06 tff(6143,plain,
% 1.86/2.06 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2549, 6142, 385])).
% 1.86/2.06 tff(6144,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[149, 6143])).
% 1.86/2.06 tff(6145,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6146,plain,
% 1.86/2.06 (((~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(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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6147,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6146])).
% 1.86/2.06 tff(6148,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6147, 6145])).
% 1.86/2.06 tff(6149,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), 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)))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6150,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6149, 6148])).
% 1.86/2.06 tff(6151,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6150, 162, 6140, 6144, 6106, 578, 6104, 6082])).
% 1.86/2.06 tff(6152,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(6153,plain,
% 1.86/2.06 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6152, 385, 384])).
% 1.86/2.06 tff(6154,plain,
% 1.86/2.06 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[191, 6153])).
% 1.86/2.06 tff(6155,plain,
% 1.86/2.06 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[4643, 55, 384])).
% 1.86/2.06 tff(6156,plain,
% 1.86/2.06 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[709, 6155, 635])).
% 1.86/2.06 tff(6157,plain,
% 1.86/2.06 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[4610, 151, 177, 121, 152])).
% 1.86/2.06 tff(6158,plain,
% 1.86/2.06 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[83, 6157])).
% 1.86/2.06 tff(6159,plain,
% 1.86/2.06 (((~![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(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)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6160,plain,
% 1.86/2.06 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6161,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6160])).
% 1.86/2.06 tff(6162,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6161, 6159])).
% 1.86/2.06 tff(6163,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6164,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6163, 6162])).
% 1.86/2.06 tff(6165,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6164, 65, 495, 119, 55])).
% 1.86/2.06 tff(6166,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(6167,plain,
% 1.86/2.06 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6166, 6158, 55])).
% 1.86/2.06 tff(6168,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[216, 6167])).
% 1.86/2.06 tff(6169,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6170,plain,
% 1.86/2.06 (((~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(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(s(s(elem!1)))), s(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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6171,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6170])).
% 1.86/2.06 tff(6172,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6171, 6169])).
% 1.86/2.06 tff(6173,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6174,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(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(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6173, 6172])).
% 1.86/2.06 tff(6175,plain,
% 1.86/2.06 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6174, 162, 416, 151, 445, 383])).
% 1.86/2.06 tff(6176,plain,
% 1.86/2.06 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6175, 6168])).
% 1.86/2.06 tff(6177,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6178,plain,
% 1.86/2.06 (((~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(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(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6179,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6178])).
% 1.86/2.06 tff(6180,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6179, 6177])).
% 1.86/2.06 tff(6181,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6182,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 1.86/2.06 tff(6183,plain,
% 1.86/2.06 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6182, 162, 151, 445, 383, 825])).
% 1.86/2.06 tff(6184,plain,
% 1.86/2.06 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6183, 526])).
% 1.86/2.06 tff(6185,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[690, 6184, 679])).
% 1.86/2.06 tff(6186,plain,
% 1.86/2.06 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[4706, 65, 2252, 6185, 340])).
% 1.86/2.06 tff(6187,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6188,plain,
% 1.86/2.06 (((~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)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6189,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6188])).
% 1.86/2.06 tff(6190,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[6189, 6187])).
% 1.86/2.06 tff(6191,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(6192,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6191, 6190])).
% 1.86/2.06 tff(6193,plain,
% 1.86/2.06 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6192, 162, 416, 151, 383, 825])).
% 1.86/2.06 tff(6194,plain,
% 1.86/2.06 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6193, 526])).
% 1.86/2.06 tff(6195,plain,
% 1.86/2.06 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[4710, 47, 6194, 6186])).
% 1.86/2.06 tff(6196,plain,
% 1.86/2.06 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6195])).
% 1.86/2.06 tff(6197,plain,
% 1.86/2.06 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[631, 6196, 19])).
% 1.86/2.06 tff(6198,plain,
% 1.86/2.06 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6197])).
% 1.86/2.06 tff(6199,plain,
% 1.86/2.06 (s(s(z)) = s(s(elem!1))),
% 1.86/2.06 inference(transitivity,[status(thm)],[313, 6198, 24])).
% 1.86/2.06 tff(6200,plain,
% 1.86/2.06 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6199])).
% 1.86/2.06 tff(6201,plain,
% 1.86/2.06 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6200])).
% 1.86/2.06 tff(6202,plain,
% 1.86/2.06 (s(elem!1) = s(z)),
% 1.86/2.06 inference(transitivity,[status(thm)],[325, 6201, 15])).
% 1.86/2.06 tff(6203,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6202])).
% 1.86/2.06 tff(6204,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6203])).
% 1.86/2.06 tff(6205,plain,
% 1.86/2.06 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6199])).
% 1.86/2.06 tff(6206,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[383, 6205])).
% 1.86/2.06 tff(6207,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6206, 6204])).
% 1.86/2.06 tff(6208,plain,
% 1.86/2.06 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6198])).
% 1.86/2.06 tff(6209,plain,
% 1.86/2.06 (s(s(elem!1)) = s(s(z))),
% 1.86/2.06 inference(transitivity,[status(thm)],[25, 6208, 312])).
% 1.86/2.06 tff(6210,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6209])).
% 1.86/2.06 tff(6211,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6210])).
% 1.86/2.06 tff(6212,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[416, 6211])).
% 1.86/2.06 tff(6213,plain,
% 1.86/2.06 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6202])).
% 1.86/2.06 tff(6214,plain,
% 1.86/2.06 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6213])).
% 1.86/2.06 tff(6215,plain,
% 1.86/2.06 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[177, 6214])).
% 1.86/2.06 tff(6216,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6202])).
% 1.86/2.06 tff(6217,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6216])).
% 1.86/2.06 tff(6218,plain,
% 1.86/2.06 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[151, 6217])).
% 1.86/2.06 tff(6219,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6209])).
% 1.86/2.06 tff(6220,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[6219])).
% 1.86/2.06 tff(6221,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[526, 6220])).
% 1.86/2.06 tff(6222,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6223,plain,
% 1.86/2.06 (((~b(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(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(6224,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[6223])).
% 1.86/2.06 tff(6225,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6224, 6222])).
% 1.86/2.07 tff(6226,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6227,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6226, 6225])).
% 1.86/2.07 tff(6228,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6227, 162, 6221, 6218, 6215, 6212, 6207])).
% 1.86/2.07 tff(6229,plain,((~b(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(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(6230,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6229, 6168, 177, 383, 416, 4675, 151, 445, 825])).
% 1.86/2.07 tff(6231,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[360, 6230, 6176])).
% 1.86/2.07 tff(6232,plain,((~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(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(6233,plain,
% 1.86/2.07 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6232, 6156, 6082, 6140, 578, 6154, 55, 4639, 6103])).
% 1.86/2.07 tff(6234,plain,
% 1.86/2.07 (r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[149, 6233])).
% 1.86/2.07 tff(6235,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2549, 6234, 385])).
% 1.86/2.07 tff(6236,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[360, 6235])).
% 1.86/2.07 tff(6237,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6238,plain,
% 1.86/2.07 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6239,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6238])).
% 1.86/2.07 tff(6240,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6239, 6237])).
% 1.86/2.07 tff(6241,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6242,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6241, 6240])).
% 1.86/2.07 tff(6243,plain,
% 1.86/2.07 ((~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6242, 162, 4639, 6140, 578, 6082])).
% 1.86/2.07 tff(6244,plain,
% 1.86/2.07 (~b(s(s(z)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6243, 6236])).
% 1.86/2.07 tff(6245,plain,
% 1.86/2.07 (r(s(s(z)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[245, 6244])).
% 1.86/2.07 tff(6246,plain,
% 1.86/2.07 (((~![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(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6247,plain,
% 1.86/2.07 (((~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(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6248,plain,
% 1.86/2.07 (((~![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(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6247])).
% 1.86/2.07 tff(6249,plain,
% 1.86/2.07 (((~![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(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6248, 6246])).
% 1.86/2.07 tff(6250,plain,
% 1.86/2.07 ((~![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)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6251,plain,
% 1.86/2.07 ((~![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(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6250, 6249])).
% 1.86/2.07 tff(6252,plain,
% 1.86/2.07 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6251, 65, 6234, 385])).
% 1.86/2.07 tff(6253,plain,
% 1.86/2.07 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[338, 6252])).
% 1.86/2.07 tff(6254,plain,
% 1.86/2.07 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[620, 6253, 578, 6140, 6236])).
% 1.86/2.07 tff(6255,plain,
% 1.86/2.07 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[216, 6254])).
% 1.86/2.07 tff(6256,plain,
% 1.86/2.07 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[453, 6253, 578, 6140, 6236])).
% 1.86/2.07 tff(6257,plain,
% 1.86/2.07 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[442, 6256])).
% 1.86/2.07 tff(6258,plain,
% 1.86/2.07 (~r(z, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[833, 6257, 55])).
% 1.86/2.07 tff(6259,plain,
% 1.86/2.07 (b(z, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[295, 6258])).
% 1.86/2.07 tff(6260,plain,
% 1.86/2.07 (~r(s(s(s(z))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1353, 6257, 385, 6245])).
% 1.86/2.07 tff(6261,plain,
% 1.86/2.07 (b(s(s(s(z))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[381, 6260])).
% 1.86/2.07 tff(6262,plain,
% 1.86/2.07 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6166, 6255, 55])).
% 1.86/2.07 tff(6263,plain,
% 1.86/2.07 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[83, 6262])).
% 1.86/2.07 tff(6264,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6265,plain,
% 1.86/2.07 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6266,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6265])).
% 1.86/2.07 tff(6267,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6266, 6264])).
% 1.86/2.07 tff(6268,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, 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)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6269,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6268, 6267])).
% 1.86/2.07 tff(6270,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6269, 162, 122, 120, 362, 298, 297])).
% 1.86/2.07 tff(6271,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(6272,plain,
% 1.86/2.07 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6271, 6263, 6253, 6261, 6259])).
% 1.86/2.07 tff(6273,plain,
% 1.86/2.07 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[95, 6272])).
% 1.86/2.07 tff(6274,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4631, 65, 6273, 6255, 6245])).
% 1.86/2.07 tff(6275,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(6276,plain,
% 1.86/2.07 (~r(z, s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6275, 385, 384])).
% 1.86/2.07 tff(6277,plain,
% 1.86/2.07 (b(z, s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[524, 6276])).
% 1.86/2.07 tff(6278,plain,
% 1.86/2.07 (~r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6130, 6277, 384, 385])).
% 1.86/2.07 tff(6279,plain,
% 1.86/2.07 (b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[117, 6278])).
% 1.86/2.07 tff(6280,plain,
% 1.86/2.07 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6251, 65, 123, 385])).
% 1.86/2.07 tff(6281,plain,
% 1.86/2.07 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[338, 6280])).
% 1.86/2.07 tff(6282,plain,
% 1.86/2.07 (~r(s(z), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6016, 6281, 6140, 384, 123])).
% 1.86/2.07 tff(6283,plain,
% 1.86/2.07 (b(s(z), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[493, 6282])).
% 1.86/2.07 tff(6284,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2549, 123, 385])).
% 1.86/2.07 tff(6285,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[360, 6284])).
% 1.86/2.07 tff(6286,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6287,plain,
% 1.86/2.07 (((~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(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(6288,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[6287])).
% 1.86/2.07 tff(6289,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[6288, 6286])).
% 1.86/2.07 tff(6290,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(z))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(6291,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[6290, 6289])).
% 1.86/2.07 tff(6292,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6291, 162, 6140, 6154, 6285, 6281, 578, 6283])).
% 1.86/2.07 tff(6293,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(6294,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[6293, 385, 384])).
% 1.86/2.07 tff(6295,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[149, 6294])).
% 1.86/2.07 tff(6296,plain,
% 1.86/2.07 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4610, 6295, 6154, 6279, 6103])).
% 1.86/2.07 tff(6297,plain,
% 1.86/2.07 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[83, 6296])).
% 1.86/2.07 tff(6298,plain,
% 1.86/2.07 (~b(s(s(z)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1402, 6279, 6082, 6103, 6277])).
% 1.86/2.07 tff(6299,plain,
% 1.86/2.07 (r(s(s(z)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[245, 6298])).
% 1.86/2.07 tff(6300,plain,
% 1.86/2.07 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3122, 6295, 6154, 6279, 6103])).
% 1.86/2.07 tff(6301,plain,
% 1.86/2.07 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[95, 6300])).
% 1.86/2.07 tff(6302,plain,
% 1.86/2.07 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4631, 65, 6301, 6299])).
% 1.86/2.07 tff(6303,plain,
% 1.86/2.07 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[216, 6302])).
% 1.86/2.07 tff(6304,plain,
% 1.86/2.07 (((~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)))), 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(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6305,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6304])).
% 1.86/2.08 tff(6306,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6305, 6145])).
% 1.86/2.08 tff(6307,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6308,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6307, 6306])).
% 1.86/2.08 tff(6309,plain,
% 1.86/2.08 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6308, 162, 6140, 6295, 578, 6082])).
% 1.86/2.08 tff(6310,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6309, 6303])).
% 1.86/2.08 tff(6311,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[338, 6310])).
% 1.86/2.08 tff(6312,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6313,plain,
% 1.86/2.08 (((~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(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6314,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6313])).
% 1.86/2.08 tff(6315,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6314, 6312])).
% 1.86/2.08 tff(6316,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6317,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 1.86/2.08 tff(6318,plain,
% 1.86/2.08 ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6317, 162, 6295, 6277, 578, 6082])).
% 1.86/2.08 tff(6319,plain,
% 1.86/2.08 (~b(z, s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6318, 6303])).
% 1.86/2.08 tff(6320,plain,
% 1.86/2.08 (r(z, s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[295, 6319])).
% 1.86/2.08 tff(6321,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2507, 6320, 6311, 6297])).
% 1.86/2.08 tff(6322,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6323,plain,
% 1.86/2.08 (~r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6322, 384])).
% 1.86/2.08 tff(6324,plain,
% 1.86/2.08 (b(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[595, 6323])).
% 1.86/2.08 tff(6325,plain,
% 1.86/2.08 (~b(s(z), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3288, 273, 6324, 54, 3042])).
% 1.86/2.08 tff(6326,plain,
% 1.86/2.08 (r(s(z), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[493, 6325])).
% 1.86/2.08 tff(6327,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[466, 65, 384, 6326, 273])).
% 1.86/2.08 tff(6328,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6329,plain,
% 1.86/2.08 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6328, 54, 384])).
% 1.86/2.08 tff(6330,plain,
% 1.86/2.08 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[459, 6329])).
% 1.86/2.08 tff(6331,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6332,plain,
% 1.86/2.08 (((~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(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6333,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6332])).
% 1.86/2.08 tff(6334,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6333, 6331])).
% 1.86/2.08 tff(6335,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6336,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6335, 6334])).
% 1.86/2.08 tff(6337,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6336, 162, 444, 445, 383, 600, 599])).
% 1.86/2.08 tff(6338,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6339,plain,
% 1.86/2.08 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6338, 599, 383, 600, 445])).
% 1.86/2.08 tff(6340,plain,
% 1.86/2.08 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[442, 6339])).
% 1.86/2.08 tff(6341,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5901, 599, 600, 177, 151])).
% 1.86/2.08 tff(6342,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[338, 6341])).
% 1.86/2.08 tff(6343,plain,
% 1.86/2.08 (((~![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(s(z)), s(s(s(s(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(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6344,plain,
% 1.86/2.08 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6345,plain,
% 1.86/2.08 (((~![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(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(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(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6344])).
% 1.86/2.08 tff(6346,plain,
% 1.86/2.08 (((~![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(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(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(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6345, 6343])).
% 1.86/2.08 tff(6347,plain,
% 1.86/2.08 ((~![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(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6348,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6347, 6346])).
% 1.86/2.08 tff(6349,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6348, 65, 119, 299, 417])).
% 1.86/2.08 tff(6350,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6351,plain,
% 1.86/2.08 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6350, 6342, 6340])).
% 1.86/2.08 tff(6352,plain,
% 1.86/2.08 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[216, 6351])).
% 1.86/2.08 tff(6353,plain,
% 1.86/2.08 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3094, 6340, 54])).
% 1.86/2.08 tff(6354,plain,
% 1.86/2.08 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[360, 6353])).
% 1.86/2.08 tff(6355,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6356,plain,
% 1.86/2.08 (((~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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(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(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6357,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6356])).
% 1.86/2.08 tff(6358,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[6357, 6355])).
% 1.86/2.08 tff(6359,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(6360,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[6359, 6358])).
% 1.86/2.08 tff(6361,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6360, 162, 177, 151, 6354, 6352, 383, 600])).
% 1.86/2.08 tff(6362,plain,((~b(s(z), s(s(s(z))))) | (~b(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(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(6363,plain,
% 1.86/2.08 (~b(s(z), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[6362, 6108, 3042, 6082, 6324, 54, 6330])).
% 1.86/2.08 tff(6364,plain,
% 1.86/2.08 (r(s(z), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[493, 6363])).
% 1.86/2.08 tff(6365,plain,
% 1.86/2.08 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[425, 6364, 384])).
% 1.86/2.08 tff(6366,plain,
% 1.86/2.08 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[442, 6365])).
% 1.86/2.08 tff(6367,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6368,plain,
% 1.86/2.08 (((~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(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(6369,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[6368])).
% 1.86/2.08 tff(6370,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6369, 6367])).
% 1.86/2.09 tff(6371,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6372,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6371, 6370])).
% 1.86/2.09 tff(6373,plain,
% 1.86/2.09 ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6372, 162, 6110, 6330, 6082, 6324])).
% 1.86/2.09 tff(6374,plain,
% 1.86/2.09 (~b(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6373, 6366])).
% 1.86/2.09 tff(6375,plain,
% 1.86/2.09 (r(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[295, 6374])).
% 1.86/2.09 tff(6376,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6377,plain,
% 1.86/2.09 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6378,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6377])).
% 1.86/2.09 tff(6379,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6378, 6376])).
% 1.86/2.09 tff(6380,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6381,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6380, 6379])).
% 1.86/2.09 tff(6382,plain,
% 1.86/2.09 ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6381, 162, 6110, 6330, 6082, 6324])).
% 1.86/2.09 tff(6383,plain,
% 1.86/2.09 (~b(s(s(s(z))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6382, 6366])).
% 1.86/2.09 tff(6384,plain,
% 1.86/2.09 (r(s(s(s(z))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[381, 6383])).
% 1.86/2.09 tff(6385,plain,
% 1.86/2.09 (~r(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2271, 6384, 6364])).
% 1.86/2.09 tff(6386,plain,
% 1.86/2.09 (b(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[175, 6385])).
% 1.86/2.09 tff(6387,plain,
% 1.86/2.09 (~r(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3102, 6375, 6364])).
% 1.86/2.09 tff(6388,plain,
% 1.86/2.09 (b(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[117, 6387])).
% 1.86/2.09 tff(6389,plain,
% 1.86/2.09 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4610, 6388, 6108, 3042, 6386])).
% 1.86/2.09 tff(6390,plain,
% 1.86/2.09 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[83, 6389])).
% 1.86/2.09 tff(6391,plain,
% 1.86/2.09 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2507, 6390, 6375])).
% 1.86/2.09 tff(6392,plain,
% 1.86/2.09 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[338, 6391])).
% 1.86/2.09 tff(6393,plain,
% 1.86/2.09 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3122, 6388, 6108, 3042, 6386])).
% 1.86/2.09 tff(6394,plain,
% 1.86/2.09 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[95, 6393])).
% 1.86/2.09 tff(6395,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2601, 6394, 6375])).
% 1.86/2.09 tff(6396,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[360, 6395])).
% 1.86/2.09 tff(6397,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3328, 162, 6108, 3042, 6396, 6392, 6324])).
% 1.86/2.09 tff(6398,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6399,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6398, 384])).
% 1.86/2.09 tff(6400,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[52, 6399])).
% 1.86/2.09 tff(6401,plain,
% 1.86/2.09 (~r(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[466, 65, 384, 273])).
% 1.86/2.09 tff(6402,plain,
% 1.86/2.09 (b(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[493, 6401])).
% 1.86/2.09 tff(6403,plain,
% 1.86/2.09 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[704, 6402, 273, 6324, 384])).
% 1.86/2.09 tff(6404,plain,
% 1.86/2.09 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[709, 6403, 635])).
% 1.86/2.09 tff(6405,plain,
% 1.86/2.09 (~r(z, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5461, 273, 384, 6324])).
% 1.86/2.09 tff(6406,plain,
% 1.86/2.09 (b(z, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[524, 6405])).
% 1.86/2.09 tff(6407,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5561, 97, 123])).
% 1.86/2.09 tff(6408,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[95, 6407])).
% 1.86/2.09 tff(6409,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2637, 6408, 536, 416, 537, 526])).
% 1.86/2.09 tff(6410,plain,((~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6411,plain,
% 1.86/2.09 (~r(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6410, 123, 6406, 6104, 6400, 193])).
% 1.86/2.09 tff(6412,plain,
% 1.86/2.09 (b(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[117, 6411])).
% 1.86/2.09 tff(6413,plain,
% 1.86/2.09 (~r(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2539, 120, 6400, 526, 384])).
% 1.86/2.09 tff(6414,plain,
% 1.86/2.09 (b(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[175, 6413])).
% 1.86/2.09 tff(6415,plain,
% 1.86/2.09 (~b(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2039, 6414, 6324, 599, 121])).
% 1.86/2.09 tff(6416,plain,
% 1.86/2.09 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2637, 120, 6400, 537, 526])).
% 1.86/2.09 tff(6417,plain,
% 1.86/2.09 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[95, 6416])).
% 1.86/2.09 tff(6418,plain,
% 1.86/2.09 (~r(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2601, 6417, 340])).
% 1.86/2.09 tff(6419,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[295, 6418, 6415])).
% 1.86/2.09 tff(6420,plain,((~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6421,plain,
% 1.86/2.09 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6420, 340, 599, 121, 537, 6104, 384])).
% 1.86/2.09 tff(6422,plain,
% 1.86/2.09 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[83, 6421])).
% 1.86/2.09 tff(6423,plain,
% 1.86/2.09 (~r(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[503, 6422, 193])).
% 1.86/2.09 tff(6424,plain,
% 1.86/2.09 (b(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[175, 6423])).
% 1.86/2.09 tff(6425,plain,
% 1.86/2.09 (~r(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[566, 6422, 340])).
% 1.86/2.09 tff(6426,plain,
% 1.86/2.09 (b(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[295, 6425])).
% 1.86/2.09 tff(6427,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2039, 6426, 6424, 6324, 599, 121])).
% 1.86/2.09 tff(6428,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6429,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6428, 6412, 6402, 193, 6406, 384])).
% 1.86/2.09 tff(6430,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[360, 6429])).
% 1.86/2.09 tff(6431,plain,
% 1.86/2.09 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3010, 6430, 6400, 6104, 6412, 6324, 6402, 384])).
% 1.86/2.09 tff(6432,plain,
% 1.86/2.09 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[83, 6431])).
% 1.86/2.09 tff(6433,plain,
% 1.86/2.09 (~r(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[503, 6432, 193])).
% 1.86/2.09 tff(6434,plain,
% 1.86/2.09 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3010, 363, 6400, 6104, 6412, 6324, 6402, 384])).
% 1.86/2.09 tff(6435,plain,
% 1.86/2.09 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[83, 6434])).
% 1.86/2.09 tff(6436,plain,
% 1.86/2.09 (~r(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[503, 6435, 193])).
% 1.86/2.09 tff(6437,plain,
% 1.86/2.09 (b(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[175, 6436])).
% 1.86/2.09 tff(6438,plain,
% 1.86/2.09 (~b(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2039, 6437, 6324, 6402, 6412])).
% 1.86/2.09 tff(6439,plain,
% 1.86/2.09 (r(z, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[295, 6438])).
% 1.86/2.09 tff(6440,plain,
% 1.86/2.09 (~b(s(s(z)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1402, 6437, 6082, 6412, 6406])).
% 1.86/2.09 tff(6441,plain,
% 1.86/2.09 (r(s(s(z)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[245, 6440])).
% 1.86/2.09 tff(6442,plain,
% 1.86/2.09 (~r(s(s(s(z))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2028, 6441, 273])).
% 1.86/2.09 tff(6443,plain,
% 1.86/2.09 (b(s(s(s(z))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[381, 6442])).
% 1.86/2.09 tff(6444,plain,
% 1.86/2.09 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[751, 6443, 6324, 6437, 6412, 6402])).
% 1.86/2.09 tff(6445,plain,
% 1.86/2.09 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[784, 6444, 6412, 123, 363, 6443, 6324, 6402])).
% 1.86/2.09 tff(6446,plain,
% 1.86/2.09 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[690, 6445, 679])).
% 1.86/2.09 tff(6447,plain,
% 1.86/2.09 (~b(s(s(s(s(z)))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2762, 6446, 6439, 6437, 6412])).
% 1.86/2.09 tff(6448,plain,
% 1.86/2.09 (r(s(s(s(s(z)))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[775, 6447, 642])).
% 1.86/2.09 tff(6449,plain,
% 1.86/2.09 (((~![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(z))) | (~r(s(s(s(s(z)))), 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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6450,plain,
% 1.86/2.09 (((~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(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6451,plain,
% 1.86/2.09 (((~![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(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(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6450])).
% 1.86/2.09 tff(6452,plain,
% 1.86/2.09 (((~![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(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(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6451, 6449])).
% 1.86/2.09 tff(6453,plain,
% 1.86/2.09 ((~![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(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)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6454,plain,
% 1.86/2.09 ((~![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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6453, 6452])).
% 1.86/2.09 tff(6455,plain,
% 1.86/2.09 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6454, 65, 123, 6448])).
% 1.86/2.09 tff(6456,plain,
% 1.86/2.09 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[720, 363, 6400, 6104, 362])).
% 1.86/2.09 tff(6457,plain,
% 1.86/2.09 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[442, 6456])).
% 1.86/2.09 tff(6458,plain,
% 1.86/2.09 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[796, 6446, 6457])).
% 1.86/2.09 tff(6459,plain,
% 1.86/2.09 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[801, 6458, 634])).
% 1.86/2.09 tff(6460,plain,
% 1.86/2.09 (~r(z, s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[811, 6446, 6439])).
% 1.86/2.09 tff(6461,plain,
% 1.86/2.09 (b(z, s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[823, 6460])).
% 1.86/2.09 tff(6462,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6463,plain,
% 1.86/2.09 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6464,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6463])).
% 1.86/2.09 tff(6465,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6464, 6462])).
% 1.86/2.09 tff(6466,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6467,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6466, 6465])).
% 1.86/2.09 tff(6468,plain,
% 1.86/2.09 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6467, 162, 6400, 6406, 6404, 6461, 6459])).
% 1.86/2.09 tff(6469,plain,
% 1.86/2.09 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[4710, 47, 6468, 6455])).
% 1.86/2.09 tff(6470,plain,
% 1.86/2.09 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[6469])).
% 1.86/2.09 tff(6471,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6444, 6470])).
% 1.86/2.09 tff(6472,plain,((~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(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6473,plain,
% 1.86/2.09 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6472, 6430, 273, 193, 384, 123])).
% 1.86/2.09 tff(6474,plain,
% 1.86/2.09 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[338, 6473])).
% 1.86/2.09 tff(6475,plain,
% 1.86/2.09 (~b(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5517, 6474, 6324, 6432, 6412])).
% 1.86/2.09 tff(6476,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[175, 6475, 6433])).
% 1.86/2.09 tff(6477,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6478,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6477, 193, 273, 384])).
% 1.86/2.09 tff(6479,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[149, 6478])).
% 1.86/2.09 tff(6480,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6481,plain,
% 1.86/2.09 (((~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)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6482,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6481])).
% 1.86/2.09 tff(6483,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~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(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6482, 6480])).
% 1.86/2.09 tff(6484,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6485,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6484, 6483])).
% 1.86/2.09 tff(6486,plain,
% 1.86/2.09 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6485, 162, 6400, 6479, 6406, 6104, 6082])).
% 1.86/2.09 tff(6487,plain,
% 1.86/2.09 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[83, 6486])).
% 1.86/2.09 tff(6488,plain,
% 1.86/2.09 (~r(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[534, 6487, 193])).
% 1.86/2.09 tff(6489,plain,
% 1.86/2.09 (b(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[117, 6488])).
% 1.86/2.09 tff(6490,plain,
% 1.86/2.09 (~r(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[503, 6487, 193])).
% 1.86/2.09 tff(6491,plain,
% 1.86/2.09 (b(s(z), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[175, 6490])).
% 1.86/2.09 tff(6492,plain,
% 1.86/2.09 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5517, 6491, 6324, 6487, 6489])).
% 1.86/2.09 tff(6493,plain,
% 1.86/2.09 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[338, 6492])).
% 1.86/2.09 tff(6494,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6428, 6489, 6402, 193, 6406, 384])).
% 1.86/2.09 tff(6495,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[360, 6494])).
% 1.86/2.09 tff(6496,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[608, 6495, 6493, 6324, 6402, 6479])).
% 1.86/2.09 tff(6497,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6498,plain,
% 1.86/2.09 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6497, 273, 384])).
% 1.86/2.09 tff(6499,plain,
% 1.86/2.09 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[191, 6498])).
% 1.86/2.09 tff(6500,plain,
% 1.86/2.09 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[5901, 151, 600, 599, 177])).
% 1.86/2.09 tff(6501,plain,
% 1.86/2.09 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[338, 6500])).
% 1.86/2.09 tff(6502,plain,
% 1.86/2.09 (((~![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(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6503,plain,
% 1.86/2.09 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(6504,plain,
% 1.86/2.09 (((~![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(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[6503])).
% 1.86/2.09 tff(6505,plain,
% 1.86/2.09 (((~![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(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[6504, 6502])).
% 1.86/2.09 tff(6506,plain,
% 1.86/2.09 ((~![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(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(6507,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[6506, 6505])).
% 1.86/2.09 tff(6508,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6507, 65, 119, 299, 273])).
% 1.86/2.09 tff(6509,plain,((~r(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(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(6510,plain,
% 1.86/2.09 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[6509, 6501, 273])).
% 1.86/2.09 tff(6511,plain,
% 1.86/2.09 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[216, 6510])).
% 1.86/2.09 tff(6512,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6513,plain,
% 1.86/2.10 (((~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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6514,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6513])).
% 1.86/2.10 tff(6515,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6514, 6512])).
% 1.86/2.10 tff(6516,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6517,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6516, 6515])).
% 1.86/2.10 tff(6518,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6517, 162, 151, 537, 6511, 383, 825])).
% 1.86/2.10 tff(6519,plain,
% 1.86/2.10 (r(s(s(s(s(z)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1089, 6518])).
% 1.86/2.10 tff(6520,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6521,plain,
% 1.86/2.10 (((~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(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6522,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6521])).
% 1.86/2.10 tff(6523,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6522, 6520])).
% 1.86/2.10 tff(6524,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6525,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6524, 6523])).
% 1.86/2.10 tff(6526,plain,
% 1.86/2.10 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6525, 162, 416, 151, 537, 6511, 383])).
% 1.86/2.10 tff(6527,plain,
% 1.86/2.10 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[95, 6526])).
% 1.86/2.10 tff(6528,plain,
% 1.86/2.10 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6529,plain,
% 1.86/2.10 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6530,plain,
% 1.86/2.10 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), 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)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6529])).
% 1.86/2.10 tff(6531,plain,
% 1.86/2.10 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), 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)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6530, 6528])).
% 1.86/2.10 tff(6532,plain,
% 1.86/2.10 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6533,plain,
% 1.86/2.10 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6532, 6531])).
% 1.86/2.10 tff(6534,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6533, 65, 6527, 6519])).
% 1.86/2.10 tff(6535,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6192, 162, 416, 151, 6511, 383, 825])).
% 1.86/2.10 tff(6536,plain,
% 1.86/2.10 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4710, 47, 6535, 6534])).
% 1.86/2.10 tff(6537,plain,
% 1.86/2.10 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6536])).
% 1.86/2.10 tff(6538,plain,
% 1.86/2.10 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.10 inference(transitivity,[status(thm)],[631, 6537, 19])).
% 1.86/2.10 tff(6539,plain,
% 1.86/2.10 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6538])).
% 1.86/2.10 tff(6540,plain,
% 1.86/2.10 (s(s(z)) = s(s(elem!1))),
% 1.86/2.10 inference(transitivity,[status(thm)],[313, 6539, 24])).
% 1.86/2.10 tff(6541,plain,
% 1.86/2.10 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6540])).
% 1.86/2.10 tff(6542,plain,
% 1.86/2.10 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6541])).
% 1.86/2.10 tff(6543,plain,
% 1.86/2.10 (s(elem!1) = s(z)),
% 1.86/2.10 inference(transitivity,[status(thm)],[325, 6542, 15])).
% 1.86/2.10 tff(6544,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6543])).
% 1.86/2.10 tff(6545,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6544])).
% 1.86/2.10 tff(6546,plain,
% 1.86/2.10 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6540])).
% 1.86/2.10 tff(6547,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(z))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[383, 6546])).
% 1.86/2.10 tff(6548,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6547, 6545])).
% 1.86/2.10 tff(6549,plain,
% 1.86/2.10 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6539])).
% 1.86/2.10 tff(6550,plain,
% 1.86/2.10 (s(s(elem!1)) = s(s(z))),
% 1.86/2.10 inference(transitivity,[status(thm)],[25, 6549, 312])).
% 1.86/2.10 tff(6551,plain,
% 1.86/2.10 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6550])).
% 1.86/2.10 tff(6552,plain,
% 1.86/2.10 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6551])).
% 1.86/2.10 tff(6553,plain,
% 1.86/2.10 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[416, 6552])).
% 1.86/2.10 tff(6554,plain,
% 1.86/2.10 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6543])).
% 1.86/2.10 tff(6555,plain,
% 1.86/2.10 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6554])).
% 1.86/2.10 tff(6556,plain,
% 1.86/2.10 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[177, 6555])).
% 1.86/2.10 tff(6557,plain,
% 1.86/2.10 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6543])).
% 1.86/2.10 tff(6558,plain,
% 1.86/2.10 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6557])).
% 1.86/2.10 tff(6559,plain,
% 1.86/2.10 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[151, 6558])).
% 1.86/2.10 tff(6560,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6550])).
% 1.86/2.10 tff(6561,plain,
% 1.86/2.10 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(symmetry,[status(thm)],[6560])).
% 1.86/2.10 tff(6562,plain,
% 1.86/2.10 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6511, 6561])).
% 1.86/2.10 tff(6563,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6227, 162, 6562, 6559, 6556, 6553, 6548])).
% 1.86/2.10 tff(6564,plain,((~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(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(6565,plain,
% 1.86/2.10 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6564, 6499, 6082, 6400, 6406, 6404, 273, 6324, 6402])).
% 1.86/2.10 tff(6566,plain,
% 1.86/2.10 (r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[149, 6565])).
% 1.86/2.10 tff(6567,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6568,plain,
% 1.86/2.10 (((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6569,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6568])).
% 1.86/2.10 tff(6570,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6569, 6567])).
% 1.86/2.10 tff(6571,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(z))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6572,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6571, 6570])).
% 1.86/2.10 tff(6573,plain,
% 1.86/2.10 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6572, 162, 416, 177, 537, 362, 600])).
% 1.86/2.10 tff(6574,plain,
% 1.86/2.10 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[95, 6573])).
% 1.86/2.10 tff(6575,plain,
% 1.86/2.10 (~r(z, s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5561, 6574, 123])).
% 1.86/2.10 tff(6576,plain,
% 1.86/2.10 (b(z, s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[117, 6575])).
% 1.86/2.10 tff(6577,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6578,plain,
% 1.86/2.10 (((~b(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(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(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(6579,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[6578])).
% 1.86/2.10 tff(6580,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[6579, 6577])).
% 1.86/2.10 tff(6581,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(6582,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[6581, 6580])).
% 1.86/2.10 tff(6583,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[6582, 162, 6576, 177, 537, 362, 383, 599])).
% 1.86/2.11 tff(6584,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6585,plain,
% 1.86/2.11 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6584, 6499, 6406, 6082, 6402, 6566, 6400, 6324])).
% 1.86/2.11 tff(6586,plain,
% 1.86/2.11 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[338, 6585])).
% 1.86/2.11 tff(6587,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6509, 6586, 273])).
% 1.86/2.11 tff(6588,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[216, 6587])).
% 1.86/2.11 tff(6589,plain,
% 1.86/2.11 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1431, 97, 123])).
% 1.86/2.11 tff(6590,plain,
% 1.86/2.11 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[83, 6589])).
% 1.86/2.11 tff(6591,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2637, 6408, 6590, 416, 537, 526])).
% 1.86/2.11 tff(6592,plain,((~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6593,plain,
% 1.86/2.11 (~r(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6592, 6406, 6400, 6588, 6566])).
% 1.86/2.11 tff(6594,plain,
% 1.86/2.11 (b(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[117, 6593])).
% 1.86/2.11 tff(6595,plain,
% 1.86/2.11 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2260, 194, 123])).
% 1.86/2.11 tff(6596,plain,
% 1.86/2.11 (b(s(s(s(s(elem!1)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[95, 6595])).
% 1.86/2.11 tff(6597,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5804, 6596, 6086, 6400, 121, 6324, 299, 537])).
% 1.86/2.11 tff(6598,plain,((~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6599,plain,
% 1.86/2.11 (~r(s(z), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6598, 6594, 6586, 6406, 6566, 384])).
% 1.86/2.11 tff(6600,plain,
% 1.86/2.11 (b(s(z), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[175, 6599])).
% 1.86/2.11 tff(6601,plain,
% 1.86/2.11 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5517, 6600, 6324, 6586, 6594])).
% 1.86/2.11 tff(6602,plain,
% 1.86/2.11 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[83, 6601])).
% 1.86/2.11 tff(6603,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(6604,plain,
% 1.86/2.11 (((~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(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(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(6605,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[6604])).
% 1.86/2.11 tff(6606,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[6605, 6603])).
% 1.86/2.11 tff(6607,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(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)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(6608,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[6607, 6606])).
% 1.86/2.11 tff(6609,plain,
% 1.86/2.11 ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6608, 162, 6400, 6406, 6082, 6324])).
% 1.86/2.11 tff(6610,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6609, 6602])).
% 1.86/2.11 tff(6611,plain,
% 1.86/2.11 (~b(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2039, 6600, 6324, 6402, 6594])).
% 1.86/2.11 tff(6612,plain,
% 1.86/2.11 (r(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[295, 6611])).
% 1.86/2.11 tff(6613,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2677, 6602, 6400, 6588, 6612])).
% 1.86/2.11 tff(6614,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[442, 6613, 6610])).
% 1.86/2.11 tff(6615,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6616,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6615, 384])).
% 1.86/2.11 tff(6617,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[459, 6616])).
% 1.86/2.11 tff(6618,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5469, 55, 384, 6324])).
% 1.86/2.11 tff(6619,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[442, 6618])).
% 1.86/2.11 tff(6620,plain,
% 1.86/2.11 (~b(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6338, 6619, 6082, 6324, 6617])).
% 1.86/2.11 tff(6621,plain,
% 1.86/2.11 (r(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[493, 6620])).
% 1.86/2.11 tff(6622,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[478, 6621, 384])).
% 1.86/2.11 tff(6623,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[191, 6622])).
% 1.86/2.11 tff(6624,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(6625,plain,
% 1.86/2.11 (((~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(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(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(6626,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[6625])).
% 1.86/2.11 tff(6627,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))) | (~b(s(s(z)), s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[6626, 6624])).
% 1.86/2.11 tff(6628,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~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))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(6629,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[6628, 6627])).
% 1.86/2.11 tff(6630,plain,
% 1.86/2.11 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6629, 162, 6400, 6617, 6082, 6324])).
% 1.86/2.11 tff(6631,plain,
% 1.86/2.11 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6630, 6619])).
% 1.86/2.11 tff(6632,plain,
% 1.86/2.11 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[360, 6631])).
% 1.86/2.11 tff(6633,plain,
% 1.86/2.11 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5481, 6632, 6621])).
% 1.86/2.11 tff(6634,plain,
% 1.86/2.11 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[149, 6633])).
% 1.86/2.11 tff(6635,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6232, 6634, 6623, 6082, 6400, 6617, 55, 6156, 4639, 3114])).
% 1.86/2.11 tff(6636,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6637,plain,
% 1.86/2.11 (~r(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6636, 384])).
% 1.86/2.11 tff(6638,plain,
% 1.86/2.11 (b(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[524, 6637])).
% 1.86/2.11 tff(6639,plain,
% 1.86/2.11 ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6372, 162, 537, 445, 383, 600])).
% 1.86/2.11 tff(6640,plain,
% 1.86/2.11 (~b(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6639, 444])).
% 1.86/2.11 tff(6641,plain,
% 1.86/2.11 (r(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[295, 6640])).
% 1.86/2.11 tff(6642,plain,
% 1.86/2.11 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6629, 162, 416, 445, 383, 600])).
% 1.86/2.11 tff(6643,plain,
% 1.86/2.11 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6642, 444])).
% 1.86/2.11 tff(6644,plain,
% 1.86/2.11 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[360, 6643])).
% 1.86/2.11 tff(6645,plain,
% 1.86/2.11 ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6608, 162, 416, 537, 383, 600])).
% 1.86/2.11 tff(6646,plain,
% 1.86/2.11 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6645, 444])).
% 1.86/2.11 tff(6647,plain,
% 1.86/2.11 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[83, 6646])).
% 1.86/2.11 tff(6648,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[566, 6647, 6644, 6641])).
% 1.86/2.11 tff(6649,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6650,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6649, 6638, 6617, 6082, 6324, 6400])).
% 1.86/2.11 tff(6651,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[442, 6650])).
% 1.86/2.11 tff(6652,plain,
% 1.86/2.11 (~r(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[425, 6651, 384])).
% 1.86/2.11 tff(6653,plain,
% 1.86/2.11 (b(s(z), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[493, 6652])).
% 1.86/2.11 tff(6654,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[534, 495, 97])).
% 1.86/2.11 tff(6655,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[191, 6654])).
% 1.86/2.11 tff(6656,plain,
% 1.86/2.11 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5901, 6655, 600, 599, 151])).
% 1.86/2.11 tff(6657,plain,
% 1.86/2.11 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[338, 6656])).
% 1.86/2.11 tff(6658,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6350, 6657, 417])).
% 1.86/2.11 tff(6659,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[216, 6658])).
% 1.86/2.11 tff(6660,plain,
% 1.86/2.11 (~r(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2507, 6657, 495])).
% 1.86/2.11 tff(6661,plain,
% 1.86/2.11 (b(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[295, 6660])).
% 1.86/2.11 tff(6662,plain,
% 1.86/2.11 ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6317, 162, 151, 537, 445, 383])).
% 1.86/2.11 tff(6663,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6662, 6661, 6659])).
% 1.86/2.11 tff(6664,plain,((~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6665,plain,
% 1.86/2.11 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6664, 151, 6638, 6617, 6082, 6651, 6324, 6653, 97])).
% 1.86/2.11 tff(6666,plain,
% 1.86/2.11 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[83, 6665])).
% 1.86/2.11 tff(6667,plain,
% 1.86/2.11 ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6485, 162, 6400, 151, 6638, 6082])).
% 1.86/2.11 tff(6668,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6667, 6666])).
% 1.86/2.11 tff(6669,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[216, 6668])).
% 1.86/2.11 tff(6670,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[512, 6669, 384])).
% 1.86/2.11 tff(6671,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[191, 6670])).
% 1.86/2.11 tff(6672,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6350, 6669, 6651])).
% 1.86/2.11 tff(6673,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[338, 6672])).
% 1.86/2.11 tff(6674,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5901, 6673, 6671, 6324, 6653, 151])).
% 1.86/2.11 tff(6675,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6676,plain,
% 1.86/2.11 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6675, 97, 384])).
% 1.86/2.11 tff(6677,plain,
% 1.86/2.11 (r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[149, 6676])).
% 1.86/2.11 tff(6678,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6592, 6677, 6400, 6638, 97])).
% 1.86/2.11 tff(6679,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[216, 6678])).
% 1.86/2.11 tff(6680,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[512, 6679, 384])).
% 1.86/2.11 tff(6681,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[191, 6680])).
% 1.86/2.11 tff(6682,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6350, 6679, 6651])).
% 1.86/2.11 tff(6683,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[338, 6682])).
% 1.86/2.11 tff(6684,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6584, 6683, 6681, 6638, 6082, 6653, 6677, 6400, 6324])).
% 1.86/2.11 tff(6685,plain,((~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6686,plain,
% 1.86/2.11 (~r(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6685, 384])).
% 1.86/2.11 tff(6687,plain,
% 1.86/2.11 (b(z, s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[117, 6686])).
% 1.86/2.11 tff(6688,plain,
% 1.86/2.11 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[512, 119, 384])).
% 1.86/2.11 tff(6689,plain,
% 1.86/2.11 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[191, 6688])).
% 1.86/2.11 tff(6690,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6350, 119, 6651])).
% 1.86/2.11 tff(6691,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[338, 6690])).
% 1.86/2.11 tff(6692,plain,
% 1.86/2.11 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5901, 6691, 6324, 6653, 6689])).
% 1.86/2.11 tff(6693,plain,
% 1.86/2.11 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6584, 6691, 6638, 6082, 6653, 6689, 6400, 6324])).
% 1.86/2.11 tff(6694,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[149, 6693, 6692])).
% 1.86/2.11 tff(6695,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6696,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6695, 384])).
% 1.86/2.11 tff(6697,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[216, 6696])).
% 1.86/2.11 tff(6698,plain,
% 1.86/2.11 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6485, 162, 416, 151, 537, 526, 383])).
% 1.86/2.11 tff(6699,plain,
% 1.86/2.11 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[83, 6698])).
% 1.86/2.11 tff(6700,plain,
% 1.86/2.11 (~b(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6317, 162, 151, 537, 445, 526, 383])).
% 1.86/2.11 tff(6701,plain,
% 1.86/2.11 (r(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[295, 6700])).
% 1.86/2.11 tff(6702,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2507, 6701, 6699, 299])).
% 1.86/2.11 tff(6703,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6704,plain,
% 1.86/2.11 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6703, 299, 6638, 6617, 6697, 6082, 6400])).
% 1.86/2.11 tff(6705,plain,
% 1.86/2.11 (r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[149, 6704])).
% 1.86/2.11 tff(6706,plain,
% 1.86/2.11 (~r(s(z), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6598, 6705, 6687, 6638, 299, 384])).
% 1.86/2.11 tff(6707,plain,
% 1.86/2.11 (b(s(z), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[175, 6706])).
% 1.86/2.11 tff(6708,plain,
% 1.86/2.11 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[5517, 6707, 6324, 6687, 299])).
% 1.86/2.11 tff(6709,plain,
% 1.86/2.11 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[83, 6708])).
% 1.86/2.11 tff(6710,plain,
% 1.86/2.11 (~b(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2039, 6707, 6324, 6653, 6687])).
% 1.86/2.11 tff(6711,plain,
% 1.86/2.11 (r(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[295, 6710])).
% 1.86/2.11 tff(6712,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2677, 6711, 6709, 6400, 6651, 6697])).
% 1.86/2.11 tff(6713,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(6714,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6713, 384])).
% 1.86/2.11 tff(6715,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[338, 6714])).
% 1.86/2.11 tff(6716,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(6717,plain,
% 1.86/2.11 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(z, s(z))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(6718,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[6717])).
% 1.86/2.11 tff(6719,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[6718, 6716])).
% 1.86/2.11 tff(6720,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), 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)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(6721,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[6720, 6719])).
% 1.86/2.11 tff(6722,plain,
% 1.86/2.11 ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6721, 162, 6687, 6400, 6617, 6082])).
% 1.86/2.11 tff(6723,plain,
% 1.86/2.11 (~b(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6722, 6715])).
% 1.86/2.11 tff(6724,plain,
% 1.86/2.11 (r(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[245, 6723])).
% 1.86/2.11 tff(6725,plain,
% 1.86/2.11 (~r(s(z), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6084, 6724, 384])).
% 1.86/2.11 tff(6726,plain,
% 1.86/2.11 (b(s(z), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[175, 6725])).
% 1.86/2.11 tff(6727,plain,
% 1.86/2.11 (~b(z, s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2039, 6726, 6324, 6653, 6687])).
% 1.86/2.11 tff(6728,plain,
% 1.86/2.11 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[620, 6715, 6400, 6617, 6697])).
% 1.86/2.11 tff(6729,plain,
% 1.86/2.11 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[360, 6728])).
% 1.86/2.11 tff(6730,plain,
% 1.86/2.11 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[6420, 6729, 6653, 6687, 6638, 6697, 384])).
% 1.86/2.11 tff(6731,plain,
% 1.86/2.11 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[83, 6730])).
% 1.86/2.11 tff(6732,plain,
% 1.86/2.12 (~r(z, s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[566, 6731, 6729])).
% 1.86/2.12 tff(6733,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[295, 6732, 6727])).
% 1.86/2.12 tff(6734,plain,(~r(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6735,plain,
% 1.86/2.12 (b(s(z), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3713, 6734])).
% 1.86/2.12 tff(6736,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6737,plain,
% 1.86/2.12 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6738,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[6737])).
% 1.86/2.12 tff(6739,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[6738, 6736])).
% 1.86/2.12 tff(6740,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(6741,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[6740, 6739])).
% 1.86/2.12 tff(6742,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6741, 162, 121, 538, 537, 383, 4039])).
% 1.86/2.12 tff(6743,plain,((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6744,plain,
% 1.86/2.12 (~b(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6743, 2030, 121, 383, 4039])).
% 1.86/2.12 tff(6745,plain,
% 1.86/2.12 (r(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[524, 6744])).
% 1.86/2.12 tff(6746,plain,
% 1.86/2.12 (((~![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(s(z)))) | (~r(s(s(s(z))), 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))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6747,plain,
% 1.86/2.12 (((~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))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6748,plain,
% 1.86/2.12 (((~![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))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[6747])).
% 1.86/2.12 tff(6749,plain,
% 1.86/2.12 (((~![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))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[6748, 6746])).
% 1.86/2.12 tff(6750,plain,
% 1.86/2.12 ((~![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)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(6751,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[6750, 6749])).
% 1.86/2.12 tff(6752,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6751, 65, 273, 6745, 866])).
% 1.86/2.12 tff(6753,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6754,plain,
% 1.86/2.12 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6753, 6735])).
% 1.86/2.12 tff(6755,plain,
% 1.86/2.12 (~r(s(s(s(z))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6754, 273, 383, 121])).
% 1.86/2.12 tff(6756,plain,
% 1.86/2.12 (b(s(s(s(z))), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[381, 6755])).
% 1.86/2.12 tff(6757,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[373, 6756, 296, 54, 96, 273])).
% 1.86/2.12 tff(6758,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6759,plain,
% 1.86/2.12 (~b(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6758, 273, 272, 54, 55])).
% 1.86/2.12 tff(6760,plain,
% 1.86/2.12 (r(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[117, 6759])).
% 1.86/2.12 tff(6761,plain,
% 1.86/2.12 (((~![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(s(z)))) | (~r(s(s(s(z))), 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(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6762,plain,
% 1.86/2.12 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6763,plain,
% 1.86/2.12 (((~![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(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))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[6762])).
% 1.86/2.12 tff(6764,plain,
% 1.86/2.12 (((~![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(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))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[6763, 6761])).
% 1.86/2.12 tff(6765,plain,
% 1.86/2.12 ((~![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(z))) | (~r(s(s(s(z))), z)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(6766,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[6765, 6764])).
% 1.86/2.12 tff(6767,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6766, 65, 6760, 273, 55, 382])).
% 1.86/2.12 tff(6768,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6769,plain,
% 1.86/2.12 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6768, 55, 54])).
% 1.86/2.12 tff(6770,plain,
% 1.86/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[459, 6769])).
% 1.86/2.12 tff(6771,plain,
% 1.86/2.12 (~r(s(s(s(z))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2611, 97, 1])).
% 1.86/2.12 tff(6772,plain,
% 1.86/2.12 (b(s(s(s(z))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[595, 6771])).
% 1.86/2.12 tff(6773,plain,
% 1.86/2.12 (~r(s(z), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3102, 97, 1])).
% 1.86/2.12 tff(6774,plain,
% 1.86/2.12 (b(s(z), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[493, 6773])).
% 1.86/2.12 tff(6775,plain,
% 1.86/2.12 (~r(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[105, 55, 97])).
% 1.86/2.12 tff(6776,plain,
% 1.86/2.12 (b(s(s(z)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[271, 6775])).
% 1.86/2.12 tff(6777,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[833, 55, 1])).
% 1.86/2.12 tff(6778,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[442, 6777])).
% 1.86/2.12 tff(6779,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4145, 6778, 6776, 4039, 6774, 6772])).
% 1.86/2.12 tff(6780,plain,((~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6781,plain,
% 1.86/2.12 ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6780, 6735])).
% 1.86/2.12 tff(6782,plain,
% 1.86/2.12 (~r(z, s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6781, 97, 55])).
% 1.86/2.12 tff(6783,plain,
% 1.86/2.12 (b(z, s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[295, 6782])).
% 1.86/2.12 tff(6784,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[371, 6116, 6783, 122, 362, 363])).
% 1.86/2.12 tff(6785,plain,((~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6786,plain,
% 1.86/2.12 (~r(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6785, 6281, 96, 6285, 385, 55])).
% 1.86/2.12 tff(6787,plain,
% 1.86/2.12 (b(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[117, 6786])).
% 1.86/2.12 tff(6788,plain,
% 1.86/2.12 (~r(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1966, 1, 395])).
% 1.86/2.12 tff(6789,plain,
% 1.86/2.12 (b(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[175, 6788])).
% 1.86/2.12 tff(6790,plain,
% 1.86/2.12 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[5497, 6789, 96, 84, 121])).
% 1.86/2.12 tff(6791,plain,
% 1.86/2.12 (r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[191, 6790])).
% 1.86/2.12 tff(6792,plain,
% 1.86/2.12 (~b(s(s(s(s(z)))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2762, 787, 1, 6789, 121])).
% 1.86/2.12 tff(6793,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[775, 642])).
% 1.86/2.12 tff(6794,plain,
% 1.86/2.12 (r(s(s(s(s(z)))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6793, 6792])).
% 1.86/2.12 tff(6795,plain,
% 1.86/2.12 (((~![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), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6796,plain,
% 1.86/2.12 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6797,plain,
% 1.86/2.12 (((~![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(elem!1)))))) | (~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), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[6796])).
% 1.86/2.12 tff(6798,plain,
% 1.86/2.12 (((~![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(elem!1)))))) | (~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), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[6797, 6795])).
% 1.86/2.12 tff(6799,plain,
% 1.86/2.12 ((~![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(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(6800,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[6799, 6798])).
% 1.86/2.12 tff(6801,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6800, 65, 193, 395, 787, 6794])).
% 1.86/2.12 tff(6802,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(6803,plain,
% 1.86/2.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6802, 6791, 395, 1, 121])).
% 1.86/2.12 tff(6804,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[690, 679])).
% 1.86/2.12 tff(6805,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6804, 6803])).
% 1.86/2.12 tff(6806,plain,
% 1.86/2.12 (((~![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(z)), 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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6807,plain,
% 1.86/2.12 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6808,plain,
% 1.86/2.12 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), 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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[6807])).
% 1.86/2.12 tff(6809,plain,
% 1.86/2.12 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), 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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[6808, 6806])).
% 1.86/2.12 tff(6810,plain,
% 1.86/2.12 ((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(6811,plain,
% 1.86/2.12 ((~![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(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[6810, 6809])).
% 1.86/2.12 tff(6812,plain,
% 1.86/2.12 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6811, 65, 385, 2])).
% 1.86/2.12 tff(6813,plain,
% 1.86/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[459, 6812])).
% 1.86/2.12 tff(6814,plain,
% 1.86/2.12 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[185, 151, 122, 121, 120])).
% 1.86/2.12 tff(6815,plain,
% 1.86/2.12 (r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[191, 6814])).
% 1.86/2.12 tff(6816,plain,
% 1.86/2.12 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[413, 6815, 395])).
% 1.86/2.12 tff(6817,plain,
% 1.86/2.12 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[360, 6816])).
% 1.86/2.12 tff(6818,plain,
% 1.86/2.12 (~b(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[170, 120, 122, 151, 121])).
% 1.86/2.12 tff(6819,plain,
% 1.86/2.12 (r(s(z), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[175, 6818])).
% 1.86/2.12 tff(6820,plain,
% 1.86/2.12 (~r(s(z), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2271, 6819, 866])).
% 1.86/2.12 tff(6821,plain,
% 1.86/2.12 (b(s(z), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[493, 6820])).
% 1.86/2.12 tff(6822,plain,
% 1.86/2.12 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[185, 120, 151, 121, 122])).
% 1.86/2.12 tff(6823,plain,
% 1.86/2.12 (r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[191, 6822])).
% 1.86/2.12 tff(6824,plain,
% 1.86/2.12 (~r(s(z), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[403, 6823, 54])).
% 1.86/2.12 tff(6825,plain,
% 1.86/2.12 (b(s(z), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3713, 6824])).
% 1.86/2.12 tff(6826,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(6827,plain,
% 1.86/2.12 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(6828,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 1.96/2.12 inference(monotonicity,[status(thm)],[6827])).
% 1.96/2.12 tff(6829,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.96/2.12 inference(transitivity,[status(thm)],[6828, 6826])).
% 1.96/2.12 tff(6830,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.96/2.12 inference(quant_inst,[status(thm)],[])).
% 1.96/2.12 tff(6831,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.96/2.12 inference(modus_ponens,[status(thm)],[6830, 6829])).
% 1.96/2.12 tff(6832,plain,
% 1.96/2.12 ($false),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[6831, 162, 121, 151, 122, 445, 6825, 6821])).
% 1.96/2.12 tff(6833,plain,((~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)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.12 tff(6834,plain,
% 1.96/2.12 (~r(s(s(s(z))), z)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[6833, 151, 54, 122, 121, 120, 445])).
% 1.96/2.12 tff(6835,plain,
% 1.96/2.12 (b(s(s(s(z))), z)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[381, 6834])).
% 1.96/2.12 tff(6836,plain,
% 1.96/2.12 (~b(s(z), z)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[170, 151, 122, 121, 120])).
% 1.96/2.12 tff(6837,plain,
% 1.96/2.12 (r(s(z), z)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[175, 6836])).
% 1.96/2.12 tff(6838,plain,
% 1.96/2.12 (~r(z, s(s(s(z))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[1966, 6837, 395])).
% 1.96/2.12 tff(6839,plain,
% 1.96/2.12 (b(z, s(s(s(z))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[295, 6838])).
% 1.96/2.12 tff(6840,plain,
% 1.96/2.12 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[2517, 6815, 385])).
% 1.96/2.12 tff(6841,plain,
% 1.96/2.12 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[338, 6840])).
% 1.96/2.12 tff(6842,plain,
% 1.96/2.12 ($false),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[371, 6841, 6839, 122, 6835, 6817])).
% 1.96/2.12 tff(6843,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.12 tff(6844,plain,
% 1.96/2.12 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[6843, 118, 385, 395, 54, 96, 84, 6813])).
% 1.96/2.13 tff(6845,plain,
% 1.96/2.13 (r(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[149, 6844])).
% 1.96/2.13 tff(6846,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[223, 65, 54, 6845, 2])).
% 1.96/2.13 tff(6847,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6848,plain,
% 1.96/2.13 (~r(s(s(z)), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6847, 395, 385, 54, 55])).
% 1.96/2.13 tff(6849,plain,
% 1.96/2.13 (b(s(s(z)), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[271, 6848])).
% 1.96/2.13 tff(6850,plain,
% 1.96/2.13 (~r(s(s(s(z))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6758, 121, 6849, 54, 55])).
% 1.96/2.13 tff(6851,plain,
% 1.96/2.13 (b(s(s(s(z))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[459, 6850])).
% 1.96/2.13 tff(6852,plain,
% 1.96/2.13 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[833, 1, 55])).
% 1.96/2.13 tff(6853,plain,
% 1.96/2.13 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[442, 6852])).
% 1.96/2.13 tff(6854,plain,
% 1.96/2.13 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3162, 162, 444, 445, 825, 692])).
% 1.96/2.13 tff(6855,plain,
% 1.96/2.13 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[675, 664])).
% 1.96/2.13 tff(6856,plain,
% 1.96/2.13 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6855, 6854])).
% 1.96/2.13 tff(6857,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4659, 65, 385, 1131, 5623])).
% 1.96/2.13 tff(6858,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6859,plain,
% 1.96/2.13 (~r(s(s(s(s(z)))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6858, 6856, 385])).
% 1.96/2.13 tff(6860,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6793, 6859])).
% 1.96/2.13 tff(6861,plain,
% 1.96/2.13 (~b(s(z), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3720, 162, 383, 6735, 825, 6860])).
% 1.96/2.13 tff(6862,plain,
% 1.96/2.13 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[658, 643])).
% 1.96/2.13 tff(6863,plain,
% 1.96/2.13 (r(s(z), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6862, 6861])).
% 1.96/2.13 tff(6864,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6865,plain,
% 1.96/2.13 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6866,plain,
% 1.96/2.13 (((~![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(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6865])).
% 1.96/2.13 tff(6867,plain,
% 1.96/2.13 (((~![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(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6866, 6864])).
% 1.96/2.13 tff(6868,plain,
% 1.96/2.13 ((~![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))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(6869,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[6868, 6867])).
% 1.96/2.13 tff(6870,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6869, 65, 385, 6856, 6863])).
% 1.96/2.13 tff(6871,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(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(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6872,plain,
% 1.96/2.13 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6871, 6853, 6849, 385, 6851, 6805])).
% 1.96/2.13 tff(6873,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[709, 635])).
% 1.96/2.13 tff(6874,plain,
% 1.96/2.13 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6873, 6872])).
% 1.96/2.13 tff(6875,plain,
% 1.96/2.13 (~r(z, s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2647, 6874, 55])).
% 1.96/2.13 tff(6876,plain,
% 1.96/2.13 (b(z, s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[823, 6875])).
% 1.96/2.13 tff(6877,plain,
% 1.96/2.13 (((~![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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6878,plain,
% 1.96/2.13 (((~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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6879,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6878])).
% 1.96/2.13 tff(6880,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6879, 6877])).
% 1.96/2.13 tff(6881,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(6882,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[6881, 6880])).
% 1.96/2.13 tff(6883,plain,
% 1.96/2.13 (~r(s(s(s(s(z)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6882, 65, 1, 55, 6874])).
% 1.96/2.13 tff(6884,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1089, 6883])).
% 1.96/2.13 tff(6885,plain,
% 1.96/2.13 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3209, 644, 54])).
% 1.96/2.13 tff(6886,plain,
% 1.96/2.13 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[763, 47, 753, 6885])).
% 1.96/2.13 tff(6887,plain,
% 1.96/2.13 (~r(s(s(s(s(z)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6882, 65, 1, 55, 644])).
% 1.96/2.13 tff(6888,plain,
% 1.96/2.13 (b(s(s(s(s(z)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1089, 6887])).
% 1.96/2.13 tff(6889,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2725, 162, 96, 84, 6888, 2649, 6886])).
% 1.96/2.13 tff(6890,plain,((~r(s(s(s(s(z)))), 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(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6891,plain,
% 1.96/2.13 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6890, 6874, 1, 55, 54])).
% 1.96/2.13 tff(6892,plain,
% 1.96/2.13 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6891])).
% 1.96/2.13 tff(6893,plain,
% 1.96/2.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[362, 6892])).
% 1.96/2.13 tff(6894,plain,
% 1.96/2.13 (~b(s(s(s(z))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4462, 6893, 6884, 6876, 6805])).
% 1.96/2.13 tff(6895,plain,
% 1.96/2.13 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6891])).
% 1.96/2.13 tff(6896,plain,
% 1.96/2.13 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.96/2.13 inference(transitivity,[status(thm)],[20, 6895, 630])).
% 1.96/2.13 tff(6897,plain,
% 1.96/2.13 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6896])).
% 1.96/2.13 tff(6898,plain,
% 1.96/2.13 (s(s(elem!1)) = s(s(z))),
% 1.96/2.13 inference(transitivity,[status(thm)],[25, 6897, 312])).
% 1.96/2.13 tff(6899,plain,
% 1.96/2.13 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6898])).
% 1.96/2.13 tff(6900,plain,
% 1.96/2.13 (s(elem!1) = s(z)),
% 1.96/2.13 inference(transitivity,[status(thm)],[325, 6899, 15])).
% 1.96/2.13 tff(6901,plain,
% 1.96/2.13 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6900])).
% 1.96/2.13 tff(6902,plain,
% 1.96/2.13 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.96/2.13 inference(symmetry,[status(thm)],[6901])).
% 1.96/2.13 tff(6903,plain,
% 1.96/2.13 (z = elem!1),
% 1.96/2.13 inference(transitivity,[status(thm)],[1182, 6902, 1170])).
% 1.96/2.13 tff(6904,plain,
% 1.96/2.13 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6903])).
% 1.96/2.13 tff(6905,plain,
% 1.96/2.13 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6904, 1179])).
% 1.96/2.13 tff(6906,plain,
% 1.96/2.13 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.96/2.13 inference(transitivity,[status(thm)],[6905, 1180])).
% 1.96/2.13 tff(6907,plain,
% 1.96/2.13 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6906])).
% 1.96/2.13 tff(6908,plain,
% 1.96/2.13 (~(s(z) = elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[111, 6907])).
% 1.96/2.13 tff(6909,plain,
% 1.96/2.13 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6898])).
% 1.96/2.13 tff(6910,plain,
% 1.96/2.13 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.96/2.13 inference(symmetry,[status(thm)],[6909])).
% 1.96/2.13 tff(6911,plain,
% 1.96/2.13 ((~b(s(s(z)), z)) <=> (~b(s(s(elem!1)), z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6910])).
% 1.96/2.13 tff(6912,plain,
% 1.96/2.13 ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[5089, 6735])).
% 1.96/2.13 tff(6913,plain,
% 1.96/2.13 (~b(s(s(z)), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6912, 6789, 6849, 121])).
% 1.96/2.13 tff(6914,plain,
% 1.96/2.13 (~b(s(s(elem!1)), z)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[6913, 6911])).
% 1.96/2.13 tff(6915,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.96/2.13 tff(6916,plain,
% 1.96/2.13 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.96/2.13 inference(commutativity,[status(thm)],[])).
% 1.96/2.13 tff(6917,plain,
% 1.96/2.13 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.96/2.13 inference(symmetry,[status(thm)],[6916])).
% 1.96/2.13 tff(6918,plain,
% 1.96/2.13 (r(s(s(elem!1)), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2783, 1604])).
% 1.96/2.13 tff(6919,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.96/2.13 tff(6920,plain,
% 1.96/2.13 (r(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1682, 6919, 1247])).
% 1.96/2.13 tff(6921,plain,
% 1.96/2.13 (~r(s(s(s(z))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1663, 6920, 385])).
% 1.96/2.13 tff(6922,plain,
% 1.96/2.13 (s(s(s(z))) = elem!1),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3664, 6921, 6915])).
% 1.96/2.13 tff(6923,plain,
% 1.96/2.13 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6922])).
% 1.96/2.13 tff(6924,plain,
% 1.96/2.13 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.96/2.13 inference(transitivity,[status(thm)],[6923, 1202])).
% 1.96/2.13 tff(6925,plain,
% 1.96/2.13 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6924])).
% 1.96/2.13 tff(6926,plain,
% 1.96/2.13 (~(z = elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[286, 6925])).
% 1.96/2.13 tff(6927,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.96/2.13 tff(6928,plain,
% 1.96/2.13 (s(z) = s(elem!1)),
% 1.96/2.13 inference(symmetry,[status(thm)],[6927])).
% 1.96/2.13 tff(6929,plain,
% 1.96/2.13 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6928])).
% 1.96/2.13 tff(6930,plain,
% 1.96/2.13 (z = elem!1),
% 1.96/2.13 inference(transitivity,[status(thm)],[1182, 6929, 1170])).
% 1.96/2.13 tff(6931,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1234, 6930])).
% 1.96/2.13 tff(6932,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6933,plain,
% 1.96/2.13 (~(s(elem!1) = s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6932, 6926])).
% 1.96/2.13 tff(6934,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 1.96/2.13 tff(6935,plain,
% 1.96/2.13 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6934])).
% 1.96/2.13 tff(6936,plain,
% 1.96/2.13 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.96/2.13 inference(symmetry,[status(thm)],[6935])).
% 1.96/2.13 tff(6937,plain,
% 1.96/2.13 (s(elem!1) = s(z)),
% 1.96/2.13 inference(transitivity,[status(thm)],[325, 6936, 15])).
% 1.96/2.13 tff(6938,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.96/2.13 tff(6939,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6938, 6937])).
% 1.96/2.13 tff(6940,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6941,plain,
% 1.96/2.13 (~(s(s(z)) = s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6940, 6933])).
% 1.96/2.13 tff(6942,plain,
% 1.96/2.13 (~b(s(s(z)), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[5089, 383, 121, 152, 4039])).
% 1.96/2.13 tff(6943,plain,
% 1.96/2.13 (r(s(s(z)), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[245, 6942])).
% 1.96/2.13 tff(6944,plain,
% 1.96/2.13 (((~![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(s(z)), z)) | (~r(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)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6945,plain,
% 1.96/2.13 (((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6946,plain,
% 1.96/2.13 (((~![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(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(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)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6945])).
% 1.96/2.13 tff(6947,plain,
% 1.96/2.13 (((~![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(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(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)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6946, 6944])).
% 1.96/2.13 tff(6948,plain,
% 1.96/2.13 ((~![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(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(6949,plain,
% 1.96/2.13 ((~![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(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[6948, 6947])).
% 1.96/2.13 tff(6950,plain,
% 1.96/2.13 (~r(s(s(z)), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6949, 65, 3375, 6943])).
% 1.96/2.13 tff(6951,plain,
% 1.96/2.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6952,plain,
% 1.96/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(6953,plain,
% 1.96/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[6952, 6951])).
% 1.96/2.13 tff(6954,plain,
% 1.96/2.13 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6953, 47, 6950])).
% 1.96/2.13 tff(6955,plain,
% 1.96/2.13 (b(s(s(z)), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6954, 6941])).
% 1.96/2.13 tff(6956,plain,
% 1.96/2.13 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3447])).
% 1.96/2.13 tff(6957,plain,
% 1.96/2.13 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6956])).
% 1.96/2.13 tff(6958,plain,
% 1.96/2.13 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6957])).
% 1.96/2.13 tff(6959,plain,
% 1.96/2.13 ((elem!1 = s(z)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3447])).
% 1.96/2.13 tff(6960,plain,
% 1.96/2.13 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6959, 133])).
% 1.96/2.13 tff(6961,plain,
% 1.96/2.13 ((s(z) = s(s(s(s(elem!1))))) <=> (elem!1 = s(z))),
% 1.96/2.13 inference(symmetry,[status(thm)],[6960])).
% 1.96/2.13 tff(6962,plain,
% 1.96/2.13 ((s(z) = s(s(s(s(elem!1))))) <=> (s(z) = elem!1)),
% 1.96/2.13 inference(transitivity,[status(thm)],[6961, 1180])).
% 1.96/2.13 tff(6963,plain,
% 1.96/2.13 ((~(s(z) = s(s(s(s(elem!1)))))) <=> (~(s(z) = elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6962])).
% 1.96/2.13 tff(6964,plain,
% 1.96/2.13 (~(s(z) = elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[143, 6963])).
% 1.96/2.13 tff(6965,plain,
% 1.96/2.13 (r(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1682, 6964, 6919])).
% 1.96/2.13 tff(6966,plain,
% 1.96/2.13 (~r(s(s(s(z))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1663, 6965, 385])).
% 1.96/2.13 tff(6967,plain,
% 1.96/2.13 (s(s(s(z))) = elem!1),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3664, 6966, 6915])).
% 1.96/2.13 tff(6968,plain,
% 1.96/2.13 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6967, 3447])).
% 1.96/2.13 tff(6969,plain,
% 1.96/2.13 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6968])).
% 1.96/2.13 tff(6970,plain,
% 1.96/2.13 (s(s(z)) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[313, 6969, 19, 6958])).
% 1.96/2.13 tff(6971,plain,
% 1.96/2.13 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6970])).
% 1.96/2.13 tff(6972,plain,
% 1.96/2.13 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(z)))),
% 1.96/2.13 inference(symmetry,[status(thm)],[6971])).
% 1.96/2.13 tff(6973,plain,
% 1.96/2.13 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(6974,plain,
% 1.96/2.13 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6973, 11])).
% 1.96/2.13 tff(6975,plain,
% 1.96/2.13 (s(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(symmetry,[status(thm)],[6974])).
% 1.96/2.13 tff(6976,plain,
% 1.96/2.13 (s(s(elem!1)) = s(z)),
% 1.96/2.13 inference(transitivity,[status(thm)],[6957, 6975, 6972, 15])).
% 1.96/2.13 tff(6977,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[331, 6976])).
% 1.96/2.13 tff(6978,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6979,plain,
% 1.96/2.13 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6978, 6919, 385, 6915])).
% 1.96/2.13 tff(6980,plain,
% 1.96/2.13 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1540, 6979])).
% 1.96/2.13 tff(6981,plain,
% 1.96/2.13 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1493, 6980, 1489])).
% 1.96/2.13 tff(6982,plain,
% 1.96/2.13 (((~![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(z, 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(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6983,plain,
% 1.96/2.13 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6984,plain,
% 1.96/2.13 (((~![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(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(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)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6983])).
% 1.96/2.13 tff(6985,plain,
% 1.96/2.13 (((~![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(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(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)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6984, 6982])).
% 1.96/2.13 tff(6986,plain,
% 1.96/2.13 ((~![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(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(6987,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[6986, 6985])).
% 1.96/2.13 tff(6988,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6987, 65, 3375, 1495, 495])).
% 1.96/2.13 tff(6989,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(6990,plain,
% 1.96/2.13 (~r(z, s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6989, 6981, 3375])).
% 1.96/2.13 tff(6991,plain,
% 1.96/2.13 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[83, 6990])).
% 1.96/2.13 tff(6992,plain,
% 1.96/2.13 (((~![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(s(s(s(elem!1)))), 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)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6993,plain,
% 1.96/2.13 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(6994,plain,
% 1.96/2.13 (((~![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(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), 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)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[6993])).
% 1.96/2.13 tff(6995,plain,
% 1.96/2.13 (((~![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(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), 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)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[6994, 6992])).
% 1.96/2.13 tff(6996,plain,
% 1.96/2.13 ((~![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(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(6997,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[6996, 6995])).
% 1.96/2.13 tff(6998,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6997, 65, 3375, 1495, 2252])).
% 1.96/2.13 tff(6999,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(7000,plain,
% 1.96/2.13 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6999, 1495, 3375])).
% 1.96/2.13 tff(7001,plain,
% 1.96/2.13 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[95, 7000])).
% 1.96/2.13 tff(7002,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[5497, 7001, 4952, 152, 120, 121])).
% 1.96/2.13 tff(7003,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(7004,plain,
% 1.96/2.13 (~r(s(z), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[7003, 6991, 152, 121, 3375, 6981])).
% 1.96/2.13 tff(7005,plain,
% 1.96/2.13 (b(s(z), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3591, 7004])).
% 1.96/2.13 tff(7006,plain,
% 1.96/2.13 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[6999, 6981, 3375])).
% 1.96/2.13 tff(7007,plain,
% 1.96/2.13 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[95, 7006])).
% 1.96/2.13 tff(7008,plain,
% 1.96/2.13 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[5497, 7007, 152, 6991, 121])).
% 1.96/2.13 tff(7009,plain,
% 1.96/2.13 (r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[191, 7008])).
% 1.96/2.13 tff(7010,plain,
% 1.96/2.13 (~r(s(s(elem!1)), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4116, 7009, 6981])).
% 1.96/2.13 tff(7011,plain,
% 1.96/2.13 (b(s(s(elem!1)), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3824, 7010])).
% 1.96/2.13 tff(7012,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(7013,plain,
% 1.96/2.13 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(7014,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7013])).
% 1.96/2.14 tff(7015,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[7014, 7012])).
% 1.96/2.14 tff(7016,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(7017,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7016, 7015])).
% 1.96/2.14 tff(7018,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7017, 162, 7011, 7005, 383, 4039, 6955])).
% 1.96/2.14 tff(7019,plain,(b(s(z), elem!1) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), z)) | b(s(s(s(z))), elem!1) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(7020,plain,
% 1.96/2.14 (b(s(z), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7019, 1489, 4039, 152, 121, 6918, 6915, 383, 385, 1247])).
% 1.96/2.14 tff(7021,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7022,plain,
% 1.96/2.14 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7023,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7022])).
% 1.96/2.14 tff(7024,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[7023, 7021])).
% 1.96/2.14 tff(7025,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(7026,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7025, 7024])).
% 1.96/2.14 tff(7027,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7026, 162, 152, 121, 537, 383, 4039])).
% 1.96/2.14 tff(7028,plain,((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(7029,plain,
% 1.96/2.14 (~b(z, s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7028, 383, 121, 152, 4039])).
% 1.96/2.14 tff(7030,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.96/2.14 tff(7031,plain,
% 1.96/2.14 ((z = elem!1) <=> (z = s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[2398])).
% 1.96/2.14 tff(7032,plain,
% 1.96/2.14 ((z = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 1.96/2.14 inference(transitivity,[status(thm)],[7031, 73])).
% 1.96/2.14 tff(7033,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = z) <=> (z = elem!1)),
% 1.96/2.14 inference(symmetry,[status(thm)],[7032])).
% 1.96/2.14 tff(7034,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = z)),
% 1.96/2.14 inference(transitivity,[status(thm)],[7033, 1203])).
% 1.96/2.14 tff(7035,plain,
% 1.96/2.14 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = z))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7034])).
% 1.96/2.14 tff(7036,plain,
% 1.96/2.14 (~(elem!1 = z)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[77, 7035])).
% 1.96/2.14 tff(7037,plain,
% 1.96/2.14 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1533])).
% 1.96/2.14 tff(7038,plain,
% 1.96/2.14 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(elem!1)))),
% 1.96/2.14 inference(symmetry,[status(thm)],[7037])).
% 1.96/2.14 tff(7039,plain,
% 1.96/2.14 (elem!1 = s(s(elem!1))),
% 1.96/2.14 inference(transitivity,[status(thm)],[2398, 2404])).
% 1.96/2.14 tff(7040,plain,
% 1.96/2.14 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7039])).
% 1.96/2.14 tff(7041,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[7040])).
% 1.96/2.14 tff(7042,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(elem!1)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[7041, 7038])).
% 1.96/2.14 tff(7043,plain,
% 1.96/2.14 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7042])).
% 1.96/2.14 tff(7044,plain,
% 1.96/2.14 (~b(elem!1, s(s(elem!1)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[1489, 7043])).
% 1.96/2.14 tff(7045,plain,
% 1.96/2.14 (~(z = elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1208, 1206])).
% 1.96/2.14 tff(7046,plain,
% 1.96/2.14 (((~![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(elem!1, 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(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7047,plain,
% 1.96/2.14 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7048,plain,
% 1.96/2.14 (((~![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(elem!1, z)) | (~r(s(s(elem!1)), 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(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7047])).
% 1.96/2.14 tff(7049,plain,
% 1.96/2.14 (((~![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(elem!1, z)) | (~r(s(s(elem!1)), 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(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[7048, 7046])).
% 1.96/2.14 tff(7050,plain,
% 1.96/2.14 ((~![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(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(7051,plain,
% 1.96/2.14 ((~![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(elem!1, s(s(elem!1)))) | (~r(elem!1, z))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7050, 7049])).
% 1.96/2.14 tff(7052,plain,
% 1.96/2.14 (~r(elem!1, s(s(elem!1)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7051, 65, 3473, 3375])).
% 1.96/2.14 tff(7053,plain,
% 1.96/2.14 (elem!1 = s(s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3637, 7052, 3632])).
% 1.96/2.14 tff(7054,plain,
% 1.96/2.14 (s(s(elem!1)) = elem!1),
% 1.96/2.14 inference(symmetry,[status(thm)],[7053])).
% 1.96/2.14 tff(7055,plain,
% 1.96/2.14 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7054])).
% 1.96/2.14 tff(7056,plain,
% 1.96/2.14 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.96/2.14 inference(symmetry,[status(thm)],[7055])).
% 1.96/2.14 tff(7057,plain,
% 1.96/2.14 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.96/2.14 inference(commutativity,[status(thm)],[])).
% 1.96/2.14 tff(7058,plain,
% 1.96/2.14 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7054])).
% 1.96/2.14 tff(7059,plain,
% 1.96/2.14 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.96/2.14 inference(transitivity,[status(thm)],[7058, 7057])).
% 1.96/2.14 tff(7060,plain,
% 1.96/2.14 (elem!1 = s(s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1555, 7053])).
% 1.96/2.14 tff(7061,plain,
% 1.96/2.14 (s(s(s(s(elem!1)))) = elem!1),
% 1.96/2.14 inference(symmetry,[status(thm)],[7060])).
% 1.96/2.14 tff(7062,plain,
% 1.96/2.14 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.96/2.14 inference(transitivity,[status(thm)],[7061, 7053])).
% 1.96/2.14 tff(7063,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7062])).
% 1.96/2.14 tff(7064,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.96/2.14 inference(transitivity,[status(thm)],[7063, 7059])).
% 1.96/2.14 tff(7065,plain,
% 1.96/2.14 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7064])).
% 1.96/2.14 tff(7066,plain,
% 1.96/2.14 (~(s(s(z)) = elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[37, 7065])).
% 1.96/2.14 tff(7067,plain,
% 1.96/2.14 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7054])).
% 1.96/2.14 tff(7068,plain,
% 1.96/2.14 ((~r(s(s(z)), s(s(elem!1)))) <=> (~r(s(s(z)), elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7067])).
% 1.96/2.14 tff(7069,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7054])).
% 1.96/2.14 tff(7070,plain,
% 1.96/2.14 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.96/2.14 inference(symmetry,[status(thm)],[7069])).
% 1.96/2.14 tff(7071,plain,
% 1.96/2.14 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7061])).
% 1.96/2.14 tff(7072,plain,
% 1.96/2.14 (~r(elem!1, s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[5049, 3473, 55])).
% 1.96/2.14 tff(7073,plain,
% 1.96/2.14 (r(elem!1, s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3447])).
% 1.96/2.14 tff(7074,plain,
% 1.96/2.14 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.96/2.14 inference(symmetry,[status(thm)],[7073])).
% 1.96/2.14 tff(7075,plain,
% 1.96/2.14 (r(elem!1, s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[54, 7074])).
% 1.96/2.14 tff(7076,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[5055, 7075])).
% 1.96/2.14 tff(7077,plain,(r(elem!1, s(s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~(elem!1 = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(7078,plain,
% 1.96/2.14 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7077, 7060, 7072])).
% 1.96/2.14 tff(7079,plain,
% 1.96/2.14 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[52, 7078])).
% 1.96/2.14 tff(7080,plain,
% 1.96/2.14 (b(elem!1, s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7079, 7071])).
% 1.96/2.14 tff(7081,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7080, 7070])).
% 1.96/2.14 tff(7082,plain,
% 1.96/2.14 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1544])).
% 1.96/2.14 tff(7083,plain,
% 1.96/2.14 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.96/2.14 inference(symmetry,[status(thm)],[7082])).
% 1.96/2.14 tff(7084,plain,
% 1.96/2.14 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7083])).
% 1.96/2.14 tff(7085,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.96/2.14 tff(7086,plain,
% 1.96/2.14 (~b(s(z), elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7085, 7084])).
% 1.96/2.14 tff(7087,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4935, 7086])).
% 1.96/2.14 tff(7088,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(z), elem!1)) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(7089,plain,
% 1.96/2.14 (b(s(z), s(s(elem!1)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7088, 7053, 4935])).
% 1.96/2.14 tff(7090,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7091,plain,
% 1.96/2.14 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7092,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7091])).
% 1.96/2.14 tff(7093,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[7092, 7090])).
% 1.96/2.14 tff(7094,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(7095,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7094, 7093])).
% 1.96/2.14 tff(7096,plain,
% 1.96/2.14 ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7095, 162, 7089, 121, 383, 4039])).
% 1.96/2.14 tff(7097,plain,
% 1.96/2.14 (~b(s(s(z)), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7096, 7081])).
% 1.96/2.14 tff(7098,plain,
% 1.96/2.14 (r(s(s(z)), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[245, 7097])).
% 1.96/2.14 tff(7099,plain,
% 1.96/2.14 (~r(s(s(z)), s(s(elem!1)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[6949, 65, 3375, 7098])).
% 1.96/2.14 tff(7100,plain,
% 1.96/2.14 (~r(s(s(z)), elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7099, 7068])).
% 1.96/2.14 tff(7101,plain,
% 1.96/2.14 (b(s(s(z)), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[5002, 7100, 7066])).
% 1.96/2.14 tff(7102,plain,
% 1.96/2.14 (b(s(s(z)), s(s(elem!1)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7101, 7056])).
% 1.96/2.14 tff(7103,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7104,plain,
% 1.96/2.14 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(7105,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7104])).
% 1.96/2.14 tff(7106,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[7105, 7103])).
% 1.96/2.14 tff(7107,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(7108,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[7107, 7106])).
% 1.96/2.14 tff(7109,plain,
% 1.96/2.14 (~b(s(s(z)), s(s(elem!1)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7108, 162, 7089, 383, 4039, 7081])).
% 1.96/2.14 tff(7110,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7109, 7102])).
% 1.96/2.14 tff(7111,plain,((~r(elem!1, z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | b(elem!1, s(s(elem!1))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7112,plain,
% 1.96/2.15 (~r(elem!1, z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7111, 3632, 4039, 6918, 121, 4935, 383, 3020])).
% 1.96/2.15 tff(7113,plain,
% 1.96/2.15 (b(elem!1, z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3486, 7112, 1206])).
% 1.96/2.15 tff(7114,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.96/2.15 tff(7115,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7116,plain,
% 1.96/2.15 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7117,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7116])).
% 1.96/2.15 tff(7118,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[7117, 7115])).
% 1.96/2.15 tff(7119,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(7120,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7119, 7118])).
% 1.96/2.15 tff(7121,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7120, 162, 4882, 7114, 152, 121, 4935])).
% 1.96/2.15 tff(7122,plain,((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7123,plain,
% 1.96/2.15 (~b(z, elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7122, 7113, 152, 121, 4935])).
% 1.96/2.15 tff(7124,plain,
% 1.96/2.15 (r(z, elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4889, 7123, 7045])).
% 1.96/2.15 tff(7125,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7126,plain,
% 1.96/2.15 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7127,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7126])).
% 1.96/2.15 tff(7128,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[7127, 7125])).
% 1.96/2.15 tff(7129,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(7130,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7129, 7128])).
% 1.96/2.15 tff(7131,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7130, 162, 7114, 152, 121, 4119, 4935])).
% 1.96/2.15 tff(7132,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7133,plain,
% 1.96/2.15 (~b(elem!1, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7132, 7113, 121, 4935, 152])).
% 1.96/2.15 tff(7134,plain,
% 1.96/2.15 (r(elem!1, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1651, 7133, 7030])).
% 1.96/2.15 tff(7135,plain,
% 1.96/2.15 (~(elem!1 = s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7088, 7085, 4935])).
% 1.96/2.15 tff(7136,plain,
% 1.96/2.15 (r(elem!1, s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3637, 7135, 3632])).
% 1.96/2.15 tff(7137,plain,
% 1.96/2.15 (r(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3591, 7085])).
% 1.96/2.15 tff(7138,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4760, 65, 7137, 1616, 7136])).
% 1.96/2.15 tff(7139,plain,(b(s(z), s(s(elem!1))) | (~r(elem!1, s(z))) | b(elem!1, s(s(elem!1))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7140,plain,
% 1.96/2.15 (b(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7139, 7134, 3632, 4935])).
% 1.96/2.15 tff(7141,plain,
% 1.96/2.15 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[6917])).
% 1.96/2.15 tff(7142,plain,
% 1.96/2.15 (~(s(s(z)) = s(s(elem!1)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[1314, 7141])).
% 1.96/2.15 tff(7143,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7144,plain,
% 1.96/2.15 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7145,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7144])).
% 1.96/2.15 tff(7146,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[7145, 7143])).
% 1.96/2.15 tff(7147,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(7148,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7147, 7146])).
% 1.96/2.15 tff(7149,plain,
% 1.96/2.15 (~b(s(s(z)), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7148, 162, 1149, 3576, 152, 121, 383])).
% 1.96/2.15 tff(7150,plain,
% 1.96/2.15 (r(s(s(z)), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[245, 7149])).
% 1.96/2.15 tff(7151,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7152,plain,
% 1.96/2.15 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7153,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7152])).
% 1.96/2.15 tff(7154,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[7153, 7151])).
% 1.96/2.15 tff(7155,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(7156,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 1.96/2.15 tff(7157,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7156, 162, 3577, 1149, 3576, 152, 121])).
% 1.96/2.15 tff(7158,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7159,plain,
% 1.96/2.15 (~b(s(s(elem!1)), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7158, 1149, 121, 152, 3576])).
% 1.96/2.15 tff(7160,plain,
% 1.96/2.15 (r(s(s(elem!1)), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3824, 7159])).
% 1.96/2.15 tff(7161,plain,
% 1.96/2.15 (((~![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)), z)) | (~r(s(s(z)), z)) | (~r(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(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7162,plain,
% 1.96/2.15 (((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7163,plain,
% 1.96/2.15 (((~![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(s(z)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(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(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7162])).
% 1.96/2.15 tff(7164,plain,
% 1.96/2.15 (((~![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(s(z)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(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(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[7163, 7161])).
% 1.96/2.15 tff(7165,plain,
% 1.96/2.15 ((~![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(s(z)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(7166,plain,
% 1.96/2.15 ((~![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)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7165, 7164])).
% 1.96/2.15 tff(7167,plain,
% 1.96/2.15 (~r(s(s(z)), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7166, 65, 7160, 3375, 7150])).
% 1.96/2.15 tff(7168,plain,
% 1.96/2.15 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6953, 47, 7167])).
% 1.96/2.15 tff(7169,plain,
% 1.96/2.15 (b(s(s(z)), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7168, 7142])).
% 1.96/2.15 tff(7170,plain,
% 1.96/2.15 (((~![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(s(z)), z)) | (~r(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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7171,plain,
% 1.96/2.15 (((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7172,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7171])).
% 1.96/2.15 tff(7173,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[7172, 7170])).
% 1.96/2.15 tff(7174,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(7175,plain,
% 1.96/2.15 ((~![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(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7174, 7173])).
% 1.96/2.15 tff(7176,plain,
% 1.96/2.15 (~r(s(s(elem!1)), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7175, 65, 3375, 7150])).
% 1.96/2.15 tff(7177,plain,
% 1.96/2.15 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(7178,plain,
% 1.96/2.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(7179,plain,
% 1.96/2.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7178, 7177])).
% 1.96/2.15 tff(7180,plain,
% 1.96/2.15 (b(s(s(elem!1)), s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7179, 47, 1314, 7176])).
% 1.96/2.15 tff(7181,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7108, 162, 3576, 383, 4039, 7180, 7169])).
% 1.96/2.15 tff(7182,plain,((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7183,plain,
% 1.96/2.15 (s(s(elem!1)) = s(s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7182, 1149, 383, 4039, 3576, 3375, 152, 121])).
% 1.96/2.15 tff(7184,plain,
% 1.96/2.15 (s(s(z)) = s(s(elem!1))),
% 1.96/2.15 inference(symmetry,[status(thm)],[7183])).
% 1.96/2.15 tff(7185,plain,
% 1.96/2.15 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7184])).
% 1.96/2.15 tff(7186,plain,
% 1.96/2.15 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.96/2.15 inference(symmetry,[status(thm)],[7185])).
% 1.96/2.15 tff(7187,plain,
% 1.96/2.15 (b(z, s(s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[1149, 7186])).
% 1.96/2.15 tff(7188,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3019, 7187])).
% 1.96/2.15 tff(7189,plain,((~b(z, s(s(elem!1)))) | b(z, s(s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7190,plain,
% 1.96/2.15 (~b(z, s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7189, 7140, 383, 4039, 3019, 6918, 152, 121])).
% 1.96/2.15 tff(7191,plain,
% 1.96/2.15 (r(z, s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3401, 7190])).
% 1.96/2.15 tff(7192,plain,
% 1.96/2.15 (~r(elem!1, s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4899, 7191, 7124])).
% 1.96/2.15 tff(7193,plain,
% 1.96/2.15 (elem!1 = s(s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3637, 7192, 3632])).
% 1.96/2.15 tff(7194,plain,
% 1.96/2.15 (s(s(elem!1)) = elem!1),
% 1.96/2.15 inference(symmetry,[status(thm)],[7193])).
% 1.96/2.15 tff(7195,plain,
% 1.96/2.15 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.96/2.15 inference(monotonicity,[status(thm)],[7194])).
% 1.96/2.15 tff(7196,plain,
% 1.96/2.15 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.96/2.15 inference(symmetry,[status(thm)],[7195])).
% 1.96/2.15 tff(7197,plain,
% 1.96/2.15 (b(s(s(elem!1)), z)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[7113, 7196])).
% 1.96/2.15 tff(7198,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1604, 7197])).
% 1.96/2.15 tff(7199,plain,(b(elem!1, s(s(elem!1))) | b(s(s(elem!1)), z) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | b(z, s(s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (elem!1 = s(z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7200,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7199, 7044, 7036, 383, 4039, 7029, 152, 121, 1604, 7030, 4935])).
% 1.96/2.15 tff(7201,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | b(s(s(elem!1)), z) | (elem!1 = s(z)) | (~b(s(z), elem!1)) | b(s(s(elem!1)), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(7202,plain,
% 1.96/2.15 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7201, 7020, 4039, 152, 121, 1604, 1615, 383, 1489])).
% 1.96/2.15 tff(7203,plain,
% 1.96/2.15 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1493, 7202, 1489])).
% 1.96/2.15 tff(7204,plain,
% 1.96/2.15 (~r(z, s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6989, 7203, 6918])).
% 1.96/2.15 tff(7205,plain,
% 1.96/2.15 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[83, 7204])).
% 1.96/2.15 tff(7206,plain,
% 1.96/2.15 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6999, 7203, 6918])).
% 1.96/2.15 tff(7207,plain,
% 1.96/2.15 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[95, 7206])).
% 1.96/2.15 tff(7208,plain,
% 1.96/2.15 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[5497, 7207, 152, 7205, 121])).
% 1.96/2.15 tff(7209,plain,
% 1.96/2.15 (r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[191, 7208])).
% 1.96/2.15 tff(7210,plain,
% 1.96/2.15 (~r(s(s(elem!1)), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4116, 7209, 7203])).
% 1.96/2.15 tff(7211,plain,
% 1.96/2.15 (b(s(s(elem!1)), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3824, 7210])).
% 1.96/2.15 tff(7212,plain,
% 1.96/2.15 (~r(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7003, 7205, 152, 121, 6918, 7203])).
% 1.96/2.15 tff(7213,plain,
% 1.96/2.15 (b(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3591, 7212])).
% 1.96/2.15 tff(7214,plain,
% 1.96/2.15 (~r(s(s(z)), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6949, 65, 6918, 6943])).
% 1.96/2.15 tff(7215,plain,
% 1.96/2.15 (~b(z, s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[7189, 7213, 383, 4039, 7029, 6918, 152, 121])).
% 1.96/2.15 tff(7216,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.96/2.15 tff(7217,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7218,plain,
% 1.96/2.16 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7219,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7218])).
% 1.96/2.16 tff(7220,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7219, 7217])).
% 1.96/2.16 tff(7221,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(7222,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7221, 7220])).
% 1.96/2.16 tff(7223,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7222, 162, 3577, 3576, 4935, 1248, 383, 7216])).
% 1.96/2.16 tff(7224,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(7225,plain,
% 1.96/2.16 (~b(s(s(z)), s(s(elem!1)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7224, 1248, 3576, 4935, 3577, 383])).
% 1.96/2.16 tff(7226,assumption,(~r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.96/2.16 tff(7227,plain,
% 1.96/2.16 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[6953, 47, 7226])).
% 1.96/2.16 tff(7228,plain,
% 1.96/2.16 (s(s(z)) = s(s(elem!1))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7227, 7225])).
% 1.96/2.16 tff(7229,plain,
% 1.96/2.16 (s(elem!1) = s(z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[6940, 7228])).
% 1.96/2.16 tff(7230,plain,
% 1.96/2.16 (z = elem!1),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[6932, 7229])).
% 1.96/2.16 tff(7231,plain,
% 1.96/2.16 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7230])).
% 1.96/2.16 tff(7232,plain,
% 1.96/2.16 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7231])).
% 1.96/2.16 tff(7233,plain,
% 1.96/2.16 (b(z, s(s(elem!1)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[1248, 7232])).
% 1.96/2.16 tff(7234,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.96/2.16 tff(7235,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7234, 7233])).
% 1.96/2.16 tff(7236,plain,((~b(elem!1, s(s(elem!1)))) | b(z, s(s(elem!1))) | r(s(s(z)), s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(7237,plain,
% 1.96/2.16 (~b(elem!1, s(s(elem!1)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7236, 7215, 7214, 7213, 7020, 7211, 383])).
% 1.96/2.16 tff(7238,plain,
% 1.96/2.16 (elem!1 = z),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7199, 7237, 383, 4039, 7029, 152, 121, 1604, 1615, 7020])).
% 1.96/2.16 tff(7239,plain,
% 1.96/2.16 (s(s(elem!1)) = s(s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1316, 7238])).
% 1.96/2.16 tff(7240,plain,
% 1.96/2.16 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7239])).
% 1.96/2.16 tff(7241,plain,
% 1.96/2.16 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7240])).
% 1.96/2.16 tff(7242,plain,
% 1.96/2.16 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7241])).
% 1.96/2.16 tff(7243,plain,
% 1.96/2.16 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7242])).
% 1.96/2.16 tff(7244,plain,
% 1.96/2.16 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7243])).
% 1.96/2.16 tff(7245,plain,
% 1.96/2.16 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.96/2.16 inference(symmetry,[status(thm)],[7244])).
% 1.96/2.16 tff(7246,plain,
% 1.96/2.16 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7241])).
% 1.96/2.16 tff(7247,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7246])).
% 1.96/2.16 tff(7248,plain,
% 1.96/2.16 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 1.96/2.16 inference(symmetry,[status(thm)],[7247])).
% 1.96/2.16 tff(7249,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), z)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7207, 7248])).
% 1.96/2.16 tff(7250,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7246])).
% 1.96/2.16 tff(7251,plain,
% 1.96/2.16 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7250])).
% 1.96/2.16 tff(7252,plain,
% 1.96/2.16 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[3525])).
% 1.96/2.16 tff(7253,plain,
% 1.96/2.16 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7240])).
% 1.96/2.16 tff(7254,plain,
% 1.96/2.16 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7253, 3525])).
% 1.96/2.16 tff(7255,plain,
% 1.96/2.16 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7254, 7252])).
% 1.96/2.16 tff(7256,plain,
% 1.96/2.16 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7255])).
% 1.96/2.16 tff(7257,plain,
% 1.96/2.16 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1259, 7202])).
% 1.96/2.16 tff(7258,plain,
% 1.96/2.16 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7257, 7256])).
% 1.96/2.16 tff(7259,plain,
% 1.96/2.16 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[170, 7207, 121, 152, 7205])).
% 1.96/2.16 tff(7260,plain,
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% 1.96/2.16 inference(unit_resolution,[status(thm)],[149, 7259])).
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% 1.96/2.16 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2547, 65, 7260, 385])).
% 1.96/2.16 tff(7262,plain,
% 1.96/2.16 ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[358, 47, 7261])).
% 1.96/2.16 tff(7263,plain,
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% 1.96/2.16 inference(unit_resolution,[status(thm)],[7262, 7258])).
% 1.96/2.16 tff(7264,plain,
% 1.96/2.16 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7238])).
% 1.96/2.16 tff(7265,plain,
% 1.96/2.16 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), z))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7264])).
% 1.96/2.16 tff(7266,plain,
% 1.96/2.16 (~b(s(s(s(z))), z)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[6915, 7265])).
% 1.96/2.16 tff(7267,plain,
% 1.96/2.16 (r(s(s(s(z))), z)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[379, 47, 286, 7266])).
% 1.96/2.16 tff(7268,plain,
% 1.96/2.16 (~r(s(s(s(z))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[6753, 7267, 121, 4039, 383])).
% 1.96/2.16 tff(7269,plain,
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% 1.96/2.16 inference(unit_resolution,[status(thm)],[459, 7268])).
% 1.96/2.16 tff(7270,plain,
% 1.96/2.16 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[6251, 65, 7260, 385])).
% 1.96/2.16 tff(7271,plain,
% 1.96/2.16 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7254])).
% 1.96/2.16 tff(7272,plain,
% 1.96/2.16 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7257, 7271])).
% 1.96/2.16 tff(7273,plain,
% 1.96/2.16 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[337, 7272, 7270])).
% 1.96/2.16 tff(7274,plain,
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% 1.96/2.16 inference(unit_resolution,[status(thm)],[3401, 7215])).
% 1.96/2.16 tff(7275,plain,
% 1.96/2.16 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7241])).
% 1.96/2.16 tff(7276,plain,
% 1.96/2.16 (b(z, s(s(s(s(z)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7205, 7275])).
% 1.96/2.16 tff(7277,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7246])).
% 1.96/2.16 tff(7278,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7277])).
% 1.96/2.16 tff(7279,plain,
% 1.96/2.16 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7239])).
% 1.96/2.16 tff(7280,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7203, 7279])).
% 1.96/2.16 tff(7281,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7280, 7278])).
% 1.96/2.16 tff(7282,plain,
% 1.96/2.16 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4036, 7281, 7249, 7276, 7274, 7257, 7238])).
% 1.96/2.16 tff(7283,plain,
% 1.96/2.16 (b(s(s(z)), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[442, 7282])).
% 1.96/2.16 tff(7284,plain,
% 1.96/2.16 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[453, 7283, 7273, 7269, 7263])).
% 1.96/2.16 tff(7285,plain,
% 1.96/2.16 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[52, 7284])).
% 1.96/2.16 tff(7286,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7285, 7251])).
% 1.96/2.16 tff(7287,plain,
% 1.96/2.16 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1517, 7257])).
% 1.96/2.16 tff(7288,plain,
% 1.96/2.16 (z = elem!1),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1236, 7238])).
% 1.96/2.16 tff(7289,plain,
% 1.96/2.16 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1700, 7288])).
% 1.96/2.16 tff(7290,plain,
% 1.96/2.16 (b(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7239])).
% 1.96/2.16 tff(7291,plain,
% 1.96/2.16 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7290])).
% 1.96/2.16 tff(7292,plain,
% 1.96/2.16 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7243])).
% 1.96/2.16 tff(7293,plain,
% 1.96/2.16 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7292, 7291])).
% 1.96/2.16 tff(7294,plain,
% 1.96/2.16 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7293])).
% 1.96/2.16 tff(7295,plain,
% 1.96/2.16 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1336, 7273, 7238])).
% 1.96/2.16 tff(7296,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7246])).
% 1.96/2.16 tff(7297,plain,
% 1.96/2.16 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7296])).
% 1.96/2.16 tff(7298,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7263, 7297])).
% 1.96/2.16 tff(7299,plain,
% 1.96/2.16 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1524, 7202])).
% 1.96/2.16 tff(7300,plain,
% 1.96/2.16 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[1716])).
% 1.96/2.16 tff(7301,plain,
% 1.96/2.16 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[1714, 7300])).
% 1.96/2.16 tff(7302,plain,
% 1.96/2.16 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7301])).
% 1.96/2.16 tff(7303,plain,
% 1.96/2.16 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.96/2.16 inference(symmetry,[status(thm)],[1830])).
% 1.96/2.16 tff(7304,plain,
% 1.96/2.16 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1713])).
% 1.96/2.16 tff(7305,plain,
% 1.96/2.16 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.96/2.16 inference(transitivity,[status(thm)],[7304, 7303])).
% 1.96/2.16 tff(7306,plain,
% 1.96/2.16 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7305])).
% 1.96/2.16 tff(7307,plain,
% 1.96/2.16 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.96/2.16 inference(symmetry,[status(thm)],[1710])).
% 1.96/2.16 tff(7308,plain,
% 1.96/2.16 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7307])).
% 1.96/2.16 tff(7309,plain,
% 1.96/2.16 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7308, 1475])).
% 1.96/2.16 tff(7310,plain,
% 1.96/2.16 ((~b(z, s(s(s(z))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7309])).
% 1.96/2.16 tff(7311,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4031, 162, 1076, 693, 1075, 297, 692])).
% 1.96/2.16 tff(7312,plain,((~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)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(7313,plain,
% 1.96/2.16 (~b(z, s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7312, 692, 693, 1075, 1076])).
% 1.96/2.16 tff(7314,plain,
% 1.96/2.16 (~b(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7313, 7310])).
% 1.96/2.16 tff(7315,plain,
% 1.96/2.16 (r(elem!1, s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1483, 7314, 1473])).
% 1.96/2.16 tff(7316,plain,
% 1.96/2.16 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1754, 1746, 445, 444, 1691, 866, 7315, 1211])).
% 1.96/2.16 tff(7317,plain,
% 1.96/2.16 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1813, 7316, 1588])).
% 1.96/2.16 tff(7318,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1821, 7317, 1211])).
% 1.96/2.16 tff(7319,plain,
% 1.96/2.16 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1713])).
% 1.96/2.16 tff(7320,plain,
% 1.96/2.16 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7319])).
% 1.96/2.16 tff(7321,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.96/2.16 tff(7322,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1713])).
% 1.96/2.16 tff(7323,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7322])).
% 1.96/2.16 tff(7324,plain,
% 1.96/2.16 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1711])).
% 1.96/2.16 tff(7325,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[2218, 7324])).
% 1.96/2.16 tff(7326,plain,
% 1.96/2.16 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1805, 7325, 692, 693, 1691, 866, 7315, 1211])).
% 1.96/2.16 tff(7327,plain,
% 1.96/2.16 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1813, 7326, 1588])).
% 1.96/2.16 tff(7328,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1821, 7327, 1211])).
% 1.96/2.16 tff(7329,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7328, 7323])).
% 1.96/2.16 tff(7330,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1713])).
% 1.96/2.16 tff(7331,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7330])).
% 1.96/2.16 tff(7332,plain,
% 1.96/2.16 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7324, 7331])).
% 1.96/2.16 tff(7333,plain,
% 1.96/2.16 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[2218, 7332])).
% 1.96/2.16 tff(7334,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7335,plain,
% 1.96/2.16 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(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(z)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7336,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7335])).
% 1.96/2.16 tff(7337,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(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(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7336, 7334])).
% 1.96/2.16 tff(7338,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(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(z))))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(7339,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7338, 7337])).
% 1.96/2.16 tff(7340,plain,
% 1.96/2.16 (~b(z, s(s(s(s(s(z))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7339, 162, 1076, 1075, 7321, 7333])).
% 1.96/2.16 tff(7341,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7340, 7329])).
% 1.96/2.16 tff(7342,plain,((~b(s(s(s(s(elem!1)))), s(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(s(z))))), z)) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(7343,plain,
% 1.96/2.16 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7342, 7321, 1075, 1076, 1211, 692, 693, 1691, 866])).
% 1.96/2.16 tff(7344,plain,
% 1.96/2.16 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1789, 7343, 1692])).
% 1.96/2.16 tff(7345,plain,
% 1.96/2.16 (((~![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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), 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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7346,plain,
% 1.96/2.16 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7347,plain,
% 1.96/2.16 (((~![X0: $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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7346])).
% 1.96/2.16 tff(7348,plain,
% 1.96/2.16 (((~![X0: $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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), 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(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7347, 7345])).
% 1.96/2.16 tff(7349,plain,
% 1.96/2.16 ((~![X0: $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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(7350,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7349, 7348])).
% 1.96/2.16 tff(7351,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7350, 65, 54, 193, 1004, 2860])).
% 1.96/2.16 tff(7352,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(7353,plain,
% 1.96/2.16 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7352, 7344, 193, 54])).
% 1.96/2.16 tff(7354,plain,
% 1.96/2.16 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1049, 7353, 1041])).
% 1.96/2.16 tff(7355,plain,
% 1.96/2.16 (b(s(z), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7354, 7320])).
% 1.96/2.16 tff(7356,plain,
% 1.96/2.16 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1318])).
% 1.96/2.16 tff(7357,plain,
% 1.96/2.16 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7356])).
% 1.96/2.16 tff(7358,plain,
% 1.96/2.16 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7357])).
% 1.96/2.16 tff(7359,plain,
% 1.96/2.16 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7358])).
% 1.96/2.16 tff(7360,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7359])).
% 1.96/2.16 tff(7361,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[7360])).
% 1.96/2.16 tff(7362,plain,
% 1.96/2.16 (b(z, s(s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[971, 7361])).
% 1.96/2.16 tff(7363,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.96/2.16 tff(7364,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7365,plain,
% 1.96/2.16 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(7366,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[7365])).
% 1.96/2.16 tff(7367,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[7366, 7364])).
% 1.96/2.16 tff(7368,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(7369,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[7368, 7367])).
% 1.96/2.16 tff(7370,plain,
% 1.96/2.16 (~b(z, s(s(s(s(s(z))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7369, 162, 152, 121, 7321, 7363])).
% 1.96/2.16 tff(7371,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7370, 7362])).
% 1.96/2.16 tff(7372,plain,((~b(z, s(s(s(s(s(elem!1))))))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(7373,plain,
% 1.96/2.16 (~b(s(z), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7372, 7321, 152, 121, 971, 1317])).
% 1.96/2.16 tff(7374,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[7373, 7355])).
% 1.96/2.16 tff(7375,plain,((~b(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(7376,plain,
% 1.96/2.17 (~b(s(s(s(s(s(z))))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7375, 7318, 54, 1692, 152, 121, 193, 1075, 1076, 1211, 692, 693, 1691, 866])).
% 1.96/2.17 tff(7377,plain,
% 1.96/2.17 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7376, 7306])).
% 1.96/2.17 tff(7378,plain,
% 1.96/2.17 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1858, 7377, 1834])).
% 1.96/2.17 tff(7379,plain,
% 1.96/2.17 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1866, 7378, 866, 1211])).
% 1.96/2.17 tff(7380,plain,
% 1.96/2.17 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1001, 7379])).
% 1.96/2.17 tff(7381,plain,
% 1.96/2.17 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7380, 1735])).
% 1.96/2.17 tff(7382,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1752, 162, 444, 445, 1746, 2904, 1870])).
% 1.96/2.17 tff(7383,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(7384,plain,
% 1.96/2.17 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7383, 7381, 445, 1746, 444])).
% 1.96/2.17 tff(7385,plain,
% 1.96/2.17 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7384, 7302])).
% 1.96/2.17 tff(7386,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[1713, 7307])).
% 1.96/2.17 tff(7387,plain,
% 1.96/2.17 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[7386])).
% 1.96/2.17 tff(7388,plain,
% 1.96/2.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7389,plain,
% 1.96/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(7390,plain,
% 1.96/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7389, 7388])).
% 1.96/2.17 tff(7391,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7390, 47, 2888, 7376])).
% 1.96/2.17 tff(7392,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7393,plain,
% 1.96/2.17 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7394,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(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(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[7393])).
% 1.96/2.17 tff(7395,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(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(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[7394, 7392])).
% 1.96/2.17 tff(7396,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(7397,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7396, 7395])).
% 1.96/2.17 tff(7398,plain,
% 1.96/2.17 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7397, 65, 385, 866, 7391])).
% 1.96/2.17 tff(7399,plain,
% 1.96/2.17 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7398, 7387])).
% 1.96/2.17 tff(7400,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1731, 7399, 7385, 1691])).
% 1.96/2.17 tff(7401,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~(elem!1 = z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(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))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(7402,plain,
% 1.96/2.17 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7401, 7299, 7269, 7283, 385, 7267, 7238, 7285, 7287, 152, 121, 7209, 7276, 7249, 7298, 7295])).
% 1.96/2.17 tff(7403,plain,
% 1.96/2.17 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7402, 7294])).
% 1.96/2.17 tff(7404,plain,
% 1.96/2.17 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1760, 7403, 7289])).
% 1.96/2.17 tff(7405,plain,
% 1.96/2.17 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1768, 7404, 7238])).
% 1.96/2.17 tff(7406,plain,
% 1.96/2.17 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4316, 7405, 7287, 7276, 7238, 7286, 7249])).
% 1.96/2.17 tff(7407,plain,
% 1.96/2.17 (r(s(s(s(s(s(elem!1))))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[894, 7406])).
% 1.96/2.17 tff(7408,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), z)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7407, 7245])).
% 1.96/2.17 tff(7409,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[7243])).
% 1.96/2.17 tff(7410,plain,
% 1.96/2.17 (r(s(s(s(s(s(elem!1))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.17 inference(symmetry,[status(thm)],[7409])).
% 1.96/2.17 tff(7411,plain,
% 1.96/2.17 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7405, 7410])).
% 1.96/2.17 tff(7412,plain,
% 1.96/2.17 (r(z, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[524, 7029])).
% 1.96/2.17 tff(7413,plain,
% 1.96/2.17 (~b(z, s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7312, 7298, 7295, 7276, 7249])).
% 1.96/2.17 tff(7414,plain,
% 1.96/2.17 (r(z, s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[293, 47, 7413, 288])).
% 1.96/2.17 tff(7415,plain,
% 1.96/2.17 (((~![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(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7416,plain,
% 1.96/2.17 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7417,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[7416])).
% 1.96/2.17 tff(7418,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[7417, 7415])).
% 1.96/2.17 tff(7419,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(7420,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7419, 7418])).
% 1.96/2.17 tff(7421,plain,
% 1.96/2.17 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7420, 65, 7414, 7412, 7411])).
% 1.96/2.17 tff(7422,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7421, 7408])).
% 1.96/2.17 tff(7423,plain,(b(s(s(elem!1)), s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | b(s(s(s(z))), elem!1) | b(s(s(elem!1)), z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(7424,plain,
% 1.96/2.17 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7423, 1604, 152, 121, 4039, 383, 6915, 385, 1247])).
% 1.96/2.17 tff(7425,plain,
% 1.96/2.17 (~(s(elem!1) = s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6932, 7045])).
% 1.96/2.17 tff(7426,plain,
% 1.96/2.17 (~(s(s(z)) = s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6940, 7425])).
% 1.96/2.17 tff(7427,plain,
% 1.96/2.17 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6953, 47, 7214])).
% 1.96/2.17 tff(7428,plain,
% 1.96/2.17 (b(s(s(z)), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7427, 7426])).
% 1.96/2.17 tff(7429,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.96/2.17 tff(7430,plain,
% 1.96/2.17 (~(elem!1 = s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1555, 6979])).
% 1.96/2.17 tff(7431,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7108, 162, 3576, 383, 4039, 7216, 7429])).
% 1.96/2.17 tff(7432,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(7433,plain,
% 1.96/2.17 (~b(s(z), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7432, 7429, 4039, 7216, 383])).
% 1.96/2.17 tff(7434,plain,
% 1.96/2.17 (r(s(z), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[3591, 7433])).
% 1.96/2.17 tff(7435,plain,
% 1.96/2.17 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[6922])).
% 1.96/2.17 tff(7436,plain,
% 1.96/2.17 (r(elem!1, s(z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[385, 7435])).
% 1.96/2.17 tff(7437,plain,
% 1.96/2.17 (~r(elem!1, s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4762, 7436, 7434])).
% 1.96/2.17 tff(7438,plain,
% 1.96/2.17 (b(elem!1, s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[3637, 7437, 7430])).
% 1.96/2.17 tff(7439,plain,
% 1.96/2.17 (~(s(s(elem!1)) = elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1561, 7430])).
% 1.96/2.17 tff(7440,plain,
% 1.96/2.17 (((~![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(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(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7441,plain,
% 1.96/2.17 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7442,plain,
% 1.96/2.17 (((~![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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~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(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[7441])).
% 1.96/2.17 tff(7443,plain,
% 1.96/2.17 (((~![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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~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(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.96/2.17 inference(transitivity,[status(thm)],[7442, 7440])).
% 1.96/2.17 tff(7444,plain,
% 1.96/2.17 ((~![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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(7445,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7444, 7443])).
% 1.96/2.17 tff(7446,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7445, 65, 1246, 1655, 1571])).
% 1.96/2.17 tff(7447,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(7448,plain,
% 1.96/2.17 (~r(s(s(elem!1)), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7447, 6920, 7434])).
% 1.96/2.17 tff(7449,plain,
% 1.96/2.17 (b(s(s(elem!1)), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1569, 7448, 7439])).
% 1.96/2.17 tff(7450,plain,
% 1.96/2.17 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4793, 6979])).
% 1.96/2.17 tff(7451,plain,
% 1.96/2.17 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2082, 6980])).
% 1.96/2.17 tff(7452,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7453,plain,
% 1.96/2.17 (((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(elem!1)), s(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(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7454,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[7453])).
% 1.96/2.17 tff(7455,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[7454, 7452])).
% 1.96/2.17 tff(7456,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(7457,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[7456, 7455])).
% 1.96/2.17 tff(7458,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7457, 162, 416, 1147, 1146, 7216, 7429])).
% 1.96/2.17 tff(7459,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(7460,plain,
% 1.96/2.17 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[7459, 416, 1147, 7216, 7429])).
% 1.96/2.17 tff(7461,plain,
% 1.96/2.17 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2101, 7460, 2094])).
% 1.96/2.17 tff(7462,plain,
% 1.96/2.17 (((~![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(elem!1)))) | (~r(s(z), 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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7463,plain,
% 1.96/2.17 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(7464,plain,
% 1.96/2.17 (((~![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(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), 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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[7463])).
% 1.96/2.18 tff(7465,plain,
% 1.96/2.18 (((~![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(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), 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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[7464, 7462])).
% 1.96/2.18 tff(7466,plain,
% 1.96/2.18 ((~![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(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(7467,plain,
% 1.96/2.18 ((~![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(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7466, 7465])).
% 1.96/2.18 tff(7468,plain,
% 1.96/2.18 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7467, 65, 7434, 7461])).
% 1.96/2.18 tff(7469,plain,
% 1.96/2.18 (b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[149, 7468])).
% 1.96/2.18 tff(7470,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7471,plain,
% 1.96/2.18 (((~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(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7472,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[7471])).
% 1.96/2.18 tff(7473,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[7472, 7470])).
% 1.96/2.18 tff(7474,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(7475,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7474, 7473])).
% 1.96/2.18 tff(7476,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7475, 162, 416, 177, 7469, 383, 4039])).
% 1.96/2.18 tff(7477,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7478,plain,
% 1.96/2.18 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7477, 177, 383, 4039, 2094, 1147, 7216, 7429])).
% 1.96/2.18 tff(7479,plain,
% 1.96/2.18 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[52, 7478])).
% 1.96/2.18 tff(7480,plain,
% 1.96/2.18 (~r(z, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[71, 65, 7479, 7412])).
% 1.96/2.18 tff(7481,plain,
% 1.96/2.18 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[83, 7480])).
% 1.96/2.18 tff(7482,plain,
% 1.96/2.18 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[90, 65, 7479, 7412])).
% 1.96/2.18 tff(7483,plain,
% 1.96/2.18 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[95, 7482])).
% 1.96/2.18 tff(7484,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[5497, 7483, 7481, 152, 177, 121])).
% 1.96/2.18 tff(7485,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7486,plain,
% 1.96/2.18 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7485, 7451, 121, 383, 4039, 152, 1147, 7216, 7429])).
% 1.96/2.18 tff(7487,plain,
% 1.96/2.18 (r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[191, 7486])).
% 1.96/2.18 tff(7488,plain,
% 1.96/2.18 (((~![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(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(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7489,plain,
% 1.96/2.18 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7490,plain,
% 1.96/2.18 (((~![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(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), 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), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[7489])).
% 1.96/2.18 tff(7491,plain,
% 1.96/2.18 (((~![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(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), 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), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[7490, 7488])).
% 1.96/2.18 tff(7492,plain,
% 1.96/2.18 ((~![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(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(7493,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7492, 7491])).
% 1.96/2.18 tff(7494,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7493, 65, 1655, 193, 1572])).
% 1.96/2.18 tff(7495,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7496,plain,
% 1.96/2.18 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7495, 7487, 6920])).
% 1.96/2.18 tff(7497,plain,
% 1.96/2.18 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1529, 7496, 7450])).
% 1.96/2.18 tff(7498,plain,
% 1.96/2.18 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3613, 7487, 6920])).
% 1.96/2.18 tff(7499,plain,
% 1.96/2.18 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3975, 7498, 6979])).
% 1.96/2.18 tff(7500,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7501,plain,
% 1.96/2.18 (((~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(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7502,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(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)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[7501])).
% 1.96/2.18 tff(7503,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(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)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[7502, 7500])).
% 1.96/2.18 tff(7504,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(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)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(7505,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7504, 7503])).
% 1.96/2.18 tff(7506,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7505, 162, 1600, 1248, 3990, 1147, 1240])).
% 1.96/2.18 tff(7507,plain,((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7508,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7507, 7499, 7497, 1147, 7449, 7438])).
% 1.96/2.18 tff(7509,plain,(b(s(z), elem!1) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7510,plain,
% 1.96/2.18 (b(s(z), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7509, 7429, 121, 383, 4039, 152, 7428, 7424, 385, 6915, 1247])).
% 1.96/2.18 tff(7511,plain,
% 1.96/2.18 (~b(s(z), s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7432, 7429, 4039, 7428, 383])).
% 1.96/2.18 tff(7512,plain,
% 1.96/2.18 (~(elem!1 = s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7088, 7510, 7511])).
% 1.96/2.18 tff(7513,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1559, 7039])).
% 1.96/2.18 tff(7514,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7515,plain,
% 1.96/2.18 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7514, 7512])).
% 1.96/2.18 tff(7516,plain,
% 1.96/2.18 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2082, 7515])).
% 1.96/2.18 tff(7517,plain,
% 1.96/2.18 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7485, 7516, 121, 383, 4039, 152, 7424, 7428, 7429])).
% 1.96/2.18 tff(7518,plain,
% 1.96/2.18 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[3448])).
% 1.96/2.18 tff(7519,plain,
% 1.96/2.18 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(symmetry,[status(thm)],[7518])).
% 1.96/2.18 tff(7520,plain,
% 1.96/2.18 (b(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4935, 7519])).
% 1.96/2.18 tff(7521,assumption,(~b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.96/2.18 tff(7522,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7521, 7520])).
% 1.96/2.18 tff(7523,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | b(s(z), s(s(s(s(elem!1))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7524,plain,
% 1.96/2.18 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7523, 7517, 7510])).
% 1.96/2.18 tff(7525,plain,
% 1.96/2.18 (~(s(s(elem!1)) = elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1561, 7512])).
% 1.96/2.18 tff(7526,plain,
% 1.96/2.18 (b(elem!1, s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7199, 7510, 383, 4039, 7029, 152, 121, 1604, 1615, 1206])).
% 1.96/2.18 tff(7527,plain,
% 1.96/2.18 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2077, 7515])).
% 1.96/2.18 tff(7528,plain,
% 1.96/2.18 (r(s(z), s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3591, 7511])).
% 1.96/2.18 tff(7529,plain,
% 1.96/2.18 (r(s(z), s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[191, 7517])).
% 1.96/2.18 tff(7530,plain,
% 1.96/2.18 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2092, 7529, 7528])).
% 1.96/2.18 tff(7531,plain,
% 1.96/2.18 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2101, 7530, 7516])).
% 1.96/2.18 tff(7532,plain,
% 1.96/2.18 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1259, 7515])).
% 1.96/2.18 tff(7533,plain,
% 1.96/2.18 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7459, 7531, 7424, 7428, 7429])).
% 1.96/2.18 tff(7534,plain,
% 1.96/2.18 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[52, 7533])).
% 1.96/2.18 tff(7535,plain,
% 1.96/2.18 (~r(z, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[71, 65, 7534, 7412])).
% 1.96/2.18 tff(7536,plain,
% 1.96/2.18 (b(z, s(s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[83, 7535])).
% 1.96/2.18 tff(7537,plain,
% 1.96/2.18 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[90, 65, 7534, 7412])).
% 1.96/2.18 tff(7538,plain,
% 1.96/2.18 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[95, 7537])).
% 1.96/2.18 tff(7539,plain,
% 1.96/2.18 (r(elem!1, z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3486, 3442, 1206])).
% 1.96/2.18 tff(7540,plain,
% 1.96/2.18 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[170, 122, 121, 152, 120])).
% 1.96/2.18 tff(7541,plain,
% 1.96/2.18 (r(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[149, 7540])).
% 1.96/2.18 tff(7542,plain,
% 1.96/2.18 (((~![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(elem!1, z)) | (~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)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7543,plain,
% 1.96/2.18 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7544,plain,
% 1.96/2.18 (((~![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(s(elem!1)), z)) | (~r(elem!1, z)) | (~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)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[7543])).
% 1.96/2.18 tff(7545,plain,
% 1.96/2.18 (((~![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(s(elem!1)), z)) | (~r(elem!1, z)) | (~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)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[7544, 7542])).
% 1.96/2.18 tff(7546,plain,
% 1.96/2.18 ((~![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(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(7547,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7546, 7545])).
% 1.96/2.18 tff(7548,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7547, 65, 3473, 3375, 1571])).
% 1.96/2.18 tff(7549,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7550,plain,
% 1.96/2.18 (~r(s(s(elem!1)), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7549, 7539, 3375])).
% 1.96/2.18 tff(7551,plain,
% 1.96/2.18 (b(s(s(elem!1)), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1569, 7550, 1564])).
% 1.96/2.18 tff(7552,plain,
% 1.96/2.18 (~r(s(s(z)), s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[6949, 65, 3375, 230])).
% 1.96/2.18 tff(7553,plain,
% 1.96/2.18 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[6953, 47, 7552])).
% 1.96/2.18 tff(7554,plain,
% 1.96/2.18 (b(s(s(z)), s(s(elem!1)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7553, 7426])).
% 1.96/2.18 tff(7555,plain,
% 1.96/2.18 (~r(s(s(z)), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4997, 65, 7539, 230])).
% 1.96/2.18 tff(7556,plain,
% 1.96/2.18 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[5051])).
% 1.96/2.18 tff(7557,plain,
% 1.96/2.18 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.18 inference(symmetry,[status(thm)],[7556])).
% 1.96/2.18 tff(7558,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.96/2.18 tff(7559,plain,
% 1.96/2.18 (~(s(s(z)) = elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[5025, 4877])).
% 1.96/2.18 tff(7560,plain,
% 1.96/2.18 (b(s(s(z)), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[5002, 7559, 7558])).
% 1.96/2.18 tff(7561,plain,
% 1.96/2.18 (b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7560, 7557])).
% 1.96/2.18 tff(7562,plain,
% 1.96/2.18 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[5015])).
% 1.96/2.18 tff(7563,plain,
% 1.96/2.18 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7429, 7562])).
% 1.96/2.18 tff(7564,plain,
% 1.96/2.18 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4877, 5015])).
% 1.96/2.18 tff(7565,plain,
% 1.96/2.18 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[1248, 7564])).
% 1.96/2.18 tff(7566,plain,
% 1.96/2.18 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[5015])).
% 1.96/2.18 tff(7567,plain,
% 1.96/2.18 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7216, 7566])).
% 1.96/2.18 tff(7568,plain,
% 1.96/2.18 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[5015])).
% 1.96/2.18 tff(7569,plain,
% 1.96/2.18 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4877])).
% 1.96/2.18 tff(7570,plain,
% 1.96/2.18 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 1.96/2.18 inference(symmetry,[status(thm)],[7569])).
% 1.96/2.18 tff(7571,plain,
% 1.96/2.18 (b(elem!1, z)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[741, 7570])).
% 1.96/2.18 tff(7572,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3442, 7571])).
% 1.96/2.18 tff(7573,plain,((~(elem!1 = s(s(s(elem!1))))) | b(elem!1, z) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7574,plain,
% 1.96/2.18 (~b(s(s(s(elem!1))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7573, 4877, 3442])).
% 1.96/2.18 tff(7575,plain,
% 1.96/2.18 (r(s(s(s(elem!1))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[5193, 7574])).
% 1.96/2.18 tff(7576,plain,
% 1.96/2.18 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4971, 7575, 3375])).
% 1.96/2.18 tff(7577,plain,
% 1.96/2.18 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2116, 7576, 1253])).
% 1.96/2.18 tff(7578,plain,
% 1.96/2.18 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7577, 7568])).
% 1.96/2.18 tff(7579,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7580,plain,
% 1.96/2.18 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7581,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[7580])).
% 1.96/2.18 tff(7582,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[7581, 7579])).
% 1.96/2.18 tff(7583,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(7584,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[7583, 7582])).
% 1.96/2.18 tff(7585,plain,
% 1.96/2.18 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7584, 162, 7578, 7567, 7565, 7563])).
% 1.96/2.18 tff(7586,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7585, 7561])).
% 1.96/2.18 tff(7587,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | r(s(s(z)), elem!1) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7588,plain,
% 1.96/2.18 (~(elem!1 = s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7587, 7555, 7554, 1248, 1253, 3375, 7429, 3442])).
% 1.96/2.18 tff(7589,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.96/2.18 tff(7590,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.96/2.18 tff(7591,plain,
% 1.96/2.18 (elem!1 = s(s(s(elem!1)))),
% 1.96/2.18 inference(symmetry,[status(thm)],[7590])).
% 1.96/2.18 tff(7592,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7589, 7591])).
% 1.96/2.18 tff(7593,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(7594,plain,
% 1.96/2.18 (~(s(s(s(elem!1))) = elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7593, 7589])).
% 1.96/2.18 tff(7595,plain,
% 1.96/2.18 (((~![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(s(s(elem!1))), elem!1)) | (~r(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(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(7596,plain,
% 1.96/2.18 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7597,plain,
% 1.96/2.19 (((~![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(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~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(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7596])).
% 1.96/2.19 tff(7598,plain,
% 1.96/2.19 (((~![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(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~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(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(transitivity,[status(thm)],[7597, 7595])).
% 1.96/2.19 tff(7599,plain,
% 1.96/2.19 ((~![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(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7600,plain,
% 1.96/2.19 ((~![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(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7599, 7598])).
% 1.96/2.19 tff(7601,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7600, 65, 3473, 1261])).
% 1.96/2.19 tff(7602,plain,
% 1.96/2.19 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4971, 1261, 3375])).
% 1.96/2.19 tff(7603,plain,
% 1.96/2.19 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2116, 7602, 1253])).
% 1.96/2.19 tff(7604,plain,
% 1.96/2.19 (~r(elem!1, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4870, 1261, 3473])).
% 1.96/2.19 tff(7605,plain,
% 1.96/2.19 (b(elem!1, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1483, 7604, 7589])).
% 1.96/2.19 tff(7606,plain,
% 1.96/2.19 (~b(s(s(s(elem!1))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3892, 7605, 1248, 7603, 1600])).
% 1.96/2.19 tff(7607,plain,
% 1.96/2.19 (((~![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))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7608,plain,
% 1.96/2.19 ((~![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))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7609,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7608, 7607])).
% 1.96/2.19 tff(7610,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7609, 47, 7606, 7601, 7594])).
% 1.96/2.19 tff(7611,plain,((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(7612,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7611, 7588, 7539, 3375, 7551, 1248, 1253])).
% 1.96/2.19 tff(7613,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[5193, 7612])).
% 1.96/2.19 tff(7614,plain,
% 1.96/2.19 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.96/2.19 inference(commutativity,[status(thm)],[])).
% 1.96/2.19 tff(7615,plain,
% 1.96/2.19 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.96/2.19 inference(symmetry,[status(thm)],[7614])).
% 1.96/2.19 tff(7616,plain,
% 1.96/2.19 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7615])).
% 1.96/2.19 tff(7617,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.96/2.19 tff(7618,plain,
% 1.96/2.19 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7617])).
% 1.96/2.19 tff(7619,plain,
% 1.96/2.19 (s(s(elem!1)) = z),
% 1.96/2.19 inference(transitivity,[status(thm)],[25, 7618, 13])).
% 1.96/2.19 tff(7620,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[35, 7619])).
% 1.96/2.19 tff(7621,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(7622,plain,
% 1.96/2.19 (~(s(z) = s(s(s(elem!1))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7621, 7616])).
% 1.96/2.19 tff(7623,plain,
% 1.96/2.19 (((~![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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(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(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7624,plain,
% 1.96/2.19 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7625,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7624])).
% 1.96/2.19 tff(7626,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[7625, 7623])).
% 1.96/2.19 tff(7627,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7628,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7627, 7626])).
% 1.96/2.19 tff(7629,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7628, 65, 123, 3850, 3743])).
% 1.96/2.19 tff(7630,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(7631,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7630, 3850, 123])).
% 1.96/2.19 tff(7632,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.96/2.19 tff(7633,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.96/2.19 tff(7634,plain,
% 1.96/2.19 (((~![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)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7635,plain,
% 1.96/2.19 ((~![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)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7636,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7635, 7634])).
% 1.96/2.19 tff(7637,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7636, 47, 7633, 7632, 7621])).
% 1.96/2.19 tff(7638,plain,(b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(7639,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7638, 7631])).
% 1.96/2.19 tff(7640,plain,
% 1.96/2.19 (~b(s(z), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[749, 7639, 152, 741, 121])).
% 1.96/2.19 tff(7641,plain,
% 1.96/2.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7642,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7643,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7642, 7641])).
% 1.96/2.19 tff(7644,plain,
% 1.96/2.19 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7643, 47, 7640])).
% 1.96/2.19 tff(7645,plain,
% 1.96/2.19 (r(s(z), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7644, 7622])).
% 1.96/2.19 tff(7646,plain,
% 1.96/2.19 (((~![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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~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(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7647,plain,
% 1.96/2.19 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7648,plain,
% 1.96/2.19 (((~![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(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $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(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7647])).
% 1.96/2.19 tff(7649,plain,
% 1.96/2.19 (((~![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(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $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(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[7648, 7646])).
% 1.96/2.19 tff(7650,plain,
% 1.96/2.19 ((~![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(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7651,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7650, 7649])).
% 1.96/2.19 tff(7652,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7651, 65, 123, 3850, 7645])).
% 1.96/2.19 tff(7653,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(7654,plain,
% 1.96/2.19 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7653, 7613, 152, 7541, 121])).
% 1.96/2.19 tff(7655,plain,
% 1.96/2.19 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1304, 7654, 1275])).
% 1.96/2.19 tff(7656,plain,
% 1.96/2.19 (~b(z, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4190, 7655, 122, 120, 7613])).
% 1.96/2.19 tff(7657,plain,
% 1.96/2.19 (r(z, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2296, 7656])).
% 1.96/2.19 tff(7658,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7659,plain,
% 1.96/2.19 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7660,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7659])).
% 1.96/2.19 tff(7661,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(transitivity,[status(thm)],[7660, 7658])).
% 1.96/2.19 tff(7662,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7663,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7662, 7661])).
% 1.96/2.19 tff(7664,plain,
% 1.96/2.19 (~b(z, s(s(elem!1)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7663, 162, 1147, 7613, 122, 7655, 120])).
% 1.96/2.19 tff(7665,plain,
% 1.96/2.19 (r(z, s(s(elem!1)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3401, 7664])).
% 1.96/2.19 tff(7666,plain,
% 1.96/2.19 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4022, 7665, 7657])).
% 1.96/2.19 tff(7667,plain,
% 1.96/2.19 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7628, 65, 123, 3743])).
% 1.96/2.19 tff(7668,plain,
% 1.96/2.19 (((~![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(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(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(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7669,plain,
% 1.96/2.19 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7670,plain,
% 1.96/2.19 (((~![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(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7669])).
% 1.96/2.19 tff(7671,plain,
% 1.96/2.19 (((~![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(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[7670, 7668])).
% 1.96/2.19 tff(7672,plain,
% 1.96/2.19 ((~![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(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7673,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[7672, 7671])).
% 1.96/2.19 tff(7674,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7673, 65, 123, 3743])).
% 1.96/2.19 tff(7675,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2126, 7674, 7667, 1253, 1146, 2112, 1147])).
% 1.96/2.19 tff(7676,plain,((~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(7677,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7676, 7666, 1147, 1146, 7541, 1253])).
% 1.96/2.19 tff(7678,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7611, 7589, 3473, 3375, 1600, 1248, 1253])).
% 1.96/2.19 tff(7679,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[5193, 7678])).
% 1.96/2.19 tff(7680,plain,
% 1.96/2.19 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7653, 7679, 152, 7541, 121])).
% 1.96/2.19 tff(7681,plain,
% 1.96/2.19 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1304, 7680, 1275])).
% 1.96/2.19 tff(7682,plain,
% 1.96/2.19 (~b(z, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4190, 7681, 122, 120, 7679])).
% 1.96/2.19 tff(7683,plain,
% 1.96/2.19 (b(elem!1, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1483, 7589, 4980])).
% 1.96/2.19 tff(7684,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.96/2.19 tff(7685,plain,
% 1.96/2.19 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[1275, 2104])).
% 1.96/2.19 tff(7686,plain,
% 1.96/2.19 (~r(s(s(s(s(elem!1)))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4809, 3473, 3532])).
% 1.96/2.19 tff(7687,plain,
% 1.96/2.19 (b(s(s(s(s(elem!1)))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[95, 7686])).
% 1.96/2.19 tff(7688,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7689,plain,
% 1.96/2.19 (((~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(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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(7690,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[7689])).
% 1.96/2.19 tff(7691,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(transitivity,[status(thm)],[7690, 7688])).
% 1.96/2.19 tff(7692,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(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)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(7693,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7692, 7691])).
% 2.03/2.20 tff(7694,plain,
% 2.03/2.20 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7693, 162, 1600, 741, 7687, 3884, 3883])).
% 2.03/2.20 tff(7695,plain,
% 2.03/2.20 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2109, 47, 7694])).
% 2.03/2.20 tff(7696,plain,
% 2.03/2.20 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7695, 7685])).
% 2.03/2.20 tff(7697,plain,
% 2.03/2.20 (((~![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(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(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(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7698,plain,
% 2.03/2.20 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7699,plain,
% 2.03/2.20 (((~![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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7698])).
% 2.03/2.20 tff(7700,plain,
% 2.03/2.20 (((~![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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[7699, 7697])).
% 2.03/2.20 tff(7701,plain,
% 2.03/2.20 ((~![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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(7702,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7701, 7700])).
% 2.03/2.20 tff(7703,plain,
% 2.03/2.20 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7702, 65, 3473, 3532, 7696])).
% 2.03/2.20 tff(7704,plain,
% 2.03/2.20 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3892, 3883, 1248, 3884, 1600])).
% 2.03/2.20 tff(7705,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7609, 47, 7704, 7703, 7684])).
% 2.03/2.20 tff(7706,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(7707,plain,
% 2.03/2.20 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7706, 7679, 3473, 1248, 1275, 1600, 3532, 7683, 7594])).
% 2.03/2.20 tff(7708,plain,
% 2.03/2.20 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2116, 7707, 1253])).
% 2.03/2.20 tff(7709,plain,
% 2.03/2.20 (~r(z, s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[4022, 7708, 3998])).
% 2.03/2.20 tff(7710,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2296, 7709, 7682])).
% 2.03/2.20 tff(7711,plain,((elem!1 = s(s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), z)) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(7712,plain,
% 2.03/2.20 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7711, 7665, 122, 120, 1253, 1275, 7539, 1248, 7551, 7588, 152, 121, 3375, 4980])).
% 2.03/2.20 tff(7713,plain,
% 2.03/2.20 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3975, 7712, 1538])).
% 2.03/2.20 tff(7714,plain,
% 2.03/2.20 (b(elem!1, s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1483, 7588, 4980])).
% 2.03/2.20 tff(7715,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7716,plain,
% 2.03/2.20 (((~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(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(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(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7717,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7716])).
% 2.03/2.20 tff(7718,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[7717, 7715])).
% 2.03/2.20 tff(7719,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(7720,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7719, 7718])).
% 2.03/2.20 tff(7721,plain,
% 2.03/2.20 ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7720, 162, 152, 7613, 7655, 7714])).
% 2.03/2.20 tff(7722,plain,
% 2.03/2.20 (~b(s(s(s(elem!1))), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7721, 7713])).
% 2.03/2.20 tff(7723,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7638, 7722, 7677])).
% 2.03/2.20 tff(7724,plain,(b(elem!1, z) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(elem!1)), z)) | r(elem!1, s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(7725,plain,
% 2.03/2.20 (r(elem!1, s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7724, 3442, 1147, 1146, 1253, 152, 122, 120, 1275, 1248, 121, 3375, 1538, 7429, 230, 1564, 1206])).
% 2.03/2.20 tff(7726,plain,
% 2.03/2.20 (~r(s(s(s(elem!1))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[4870, 7725, 7539])).
% 2.03/2.20 tff(7727,plain,
% 2.03/2.20 (b(s(s(s(elem!1))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[5193, 7726])).
% 2.03/2.20 tff(7728,plain,
% 2.03/2.20 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7653, 7727, 152, 7541, 121])).
% 2.03/2.20 tff(7729,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1304, 7728, 1275])).
% 2.03/2.20 tff(7730,plain,
% 2.03/2.20 (~b(z, s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[4190, 7729, 122, 120, 7727])).
% 2.03/2.20 tff(7731,plain,
% 2.03/2.20 (r(z, s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[2296, 7730])).
% 2.03/2.20 tff(7732,plain,
% 2.03/2.20 (((~![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))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7733,plain,
% 2.03/2.20 (((~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))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7734,plain,
% 2.03/2.20 (((~![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(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)))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7733])).
% 2.03/2.20 tff(7735,plain,
% 2.03/2.20 (((~![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(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))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[7734, 7732])).
% 2.03/2.20 tff(7736,plain,
% 2.03/2.20 ((~![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(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(7737,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7736, 7735])).
% 2.03/2.20 tff(7738,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7737, 65, 7539, 7725, 7731])).
% 2.03/2.20 tff(7739,plain,(b(elem!1, z) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(7740,plain,
% 2.03/2.20 (b(elem!1, z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7739, 7538, 7536, 7532, 152, 121, 7424, 7531, 7527, 7526, 6918, 7524, 7429, 6943, 7525, 1206])).
% 2.03/2.20 tff(7741,plain,
% 2.03/2.20 (~b(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7132, 7740, 121, 7510, 152])).
% 2.03/2.20 tff(7742,plain,
% 2.03/2.20 (r(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1651, 7741, 1615])).
% 2.03/2.20 tff(7743,plain,
% 2.03/2.20 (~r(s(s(s(z))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1624, 7742, 385])).
% 2.03/2.20 tff(7744,plain,
% 2.03/2.20 (s(s(s(z))) = elem!1),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3664, 7743, 6915])).
% 2.03/2.20 tff(7745,plain,
% 2.03/2.20 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7744])).
% 2.03/2.20 tff(7746,plain,
% 2.03/2.20 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7745])).
% 2.03/2.20 tff(7747,plain,
% 2.03/2.20 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[170, 7538, 121, 152, 7536])).
% 2.03/2.20 tff(7748,plain,
% 2.03/2.20 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[149, 7747])).
% 2.03/2.20 tff(7749,plain,
% 2.03/2.20 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[6251, 65, 7748, 385])).
% 2.03/2.20 tff(7750,plain,
% 2.03/2.20 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7749, 7746])).
% 2.03/2.20 tff(7751,plain,
% 2.03/2.20 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7744])).
% 2.03/2.20 tff(7752,plain,
% 2.03/2.20 (~b(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7132, 7114, 121, 4935, 152])).
% 2.03/2.20 tff(7753,plain,
% 2.03/2.20 (r(elem!1, s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1651, 7752, 7030])).
% 2.03/2.20 tff(7754,plain,
% 2.03/2.20 (~r(s(s(s(z))), elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1624, 7753, 385])).
% 2.03/2.20 tff(7755,plain,
% 2.03/2.20 (s(s(s(z))) = elem!1),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3664, 7754, 6915])).
% 2.03/2.20 tff(7756,plain,
% 2.03/2.20 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7755])).
% 2.03/2.20 tff(7757,plain,
% 2.03/2.20 (r(s(s(z)), elem!1)),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[417, 7756])).
% 2.03/2.20 tff(7758,plain,
% 2.03/2.20 (~b(z, elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7122, 7114, 152, 121, 4935])).
% 2.03/2.20 tff(7759,plain,
% 2.03/2.20 (r(z, elem!1)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[4889, 7758, 1234])).
% 2.03/2.20 tff(7760,plain,
% 2.03/2.20 (((~![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(s(z)), z)) | (~r(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(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7761,plain,
% 2.03/2.20 (((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7762,plain,
% 2.03/2.20 (((~![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(s(z)), elem!1)) | (~r(z, 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, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7761])).
% 2.03/2.20 tff(7763,plain,
% 2.03/2.20 (((~![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(s(z)), elem!1)) | (~r(z, 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, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.03/2.20 inference(transitivity,[status(thm)],[7762, 7760])).
% 2.03/2.20 tff(7764,plain,
% 2.03/2.20 ((~![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(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(7765,plain,
% 2.03/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7764, 7763])).
% 2.03/2.20 tff(7766,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7765, 65, 7759, 230, 7757])).
% 2.03/2.20 tff(7767,plain,((~b(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z))) | (elem!1 = s(z)) | (z = elem!1) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(7768,plain,
% 2.03/2.20 (~r(s(s(z)), s(s(s(z))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7767, 7740, 6943, 6915, 385, 1615, 7045, 121, 7510, 152])).
% 2.03/2.20 tff(7769,plain,
% 2.03/2.20 (b(s(s(z)), s(s(s(z))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[442, 7768])).
% 2.03/2.20 tff(7770,plain,
% 2.03/2.20 (b(s(s(z)), elem!1)),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7769, 7751])).
% 2.03/2.20 tff(7771,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7772,plain,
% 2.03/2.20 (((~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(7773,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7772])).
% 2.03/2.20 tff(7774,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[7773, 7771])).
% 2.03/2.20 tff(7775,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(7776,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7775, 7774])).
% 2.03/2.20 tff(7777,plain,
% 2.03/2.20 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7776, 162, 7740, 7510, 7538, 7770, 383])).
% 2.03/2.20 tff(7778,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[3975, 7777, 7750, 7524])).
% 2.03/2.20 tff(7779,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (elem!1 = z) | (~b(s(z), s(s(z)))) | b(s(s(elem!1)), z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(7780,plain,
% 2.03/2.20 (~b(s(s(elem!1)), s(s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7779, 1206, 6915, 385, 121, 152, 383, 4039, 1604, 1247])).
% 2.03/2.20 tff(7781,plain,
% 2.03/2.20 (~r(s(s(elem!1)), s(s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7175, 65, 6918, 6943])).
% 2.03/2.20 tff(7782,plain,
% 2.03/2.20 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7179, 47, 7781])).
% 2.03/2.20 tff(7783,plain,
% 2.03/2.20 (s(s(elem!1)) = s(s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7782, 7780])).
% 2.03/2.20 tff(7784,plain,
% 2.03/2.20 (s(s(z)) = s(s(elem!1))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7783, 6917])).
% 2.03/2.20 tff(7785,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7426, 7784])).
% 2.03/2.20 tff(7786,plain,((elem!1 = z) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | b(s(s(elem!1)), z) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(7787,plain,
% 2.03/2.20 (elem!1 = z),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7786, 1604, 385, 121, 152, 383, 4039, 6915, 1247])).
% 2.03/2.20 tff(7788,plain,
% 2.03/2.20 (s(s(elem!1)) = s(s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1316, 7787])).
% 2.03/2.20 tff(7789,plain,
% 2.03/2.20 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7788])).
% 2.03/2.20 tff(7790,plain,
% 2.03/2.20 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7789])).
% 2.03/2.20 tff(7791,plain,
% 2.03/2.20 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.03/2.20 inference(symmetry,[status(thm)],[7790])).
% 2.03/2.20 tff(7792,plain,
% 2.03/2.20 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7791])).
% 2.03/2.20 tff(7793,plain,
% 2.03/2.20 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.20 inference(symmetry,[status(thm)],[7792])).
% 2.03/2.20 tff(7794,plain,
% 2.03/2.20 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7788])).
% 2.03/2.20 tff(7795,plain,
% 2.03/2.20 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7424, 7794])).
% 2.03/2.20 tff(7796,plain,
% 2.03/2.20 (b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[7795, 7793])).
% 2.03/2.20 tff(7797,plain,
% 2.03/2.20 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7791])).
% 2.03/2.20 tff(7798,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.03/2.20 inference(symmetry,[status(thm)],[7797])).
% 2.03/2.20 tff(7799,plain,
% 2.03/2.20 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7787])).
% 2.03/2.20 tff(7800,plain,
% 2.03/2.20 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), z))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[7799])).
% 2.03/2.20 tff(7801,plain,
% 2.03/2.20 (~b(s(s(s(z))), z)),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[6915, 7800])).
% 2.03/2.20 tff(7802,plain,
% 2.03/2.20 (r(s(s(s(z))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[379, 47, 286, 7801])).
% 2.03/2.21 tff(7803,plain,
% 2.03/2.21 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[6753, 7802, 121, 4039, 383])).
% 2.03/2.21 tff(7804,plain,
% 2.03/2.21 (b(s(s(s(z))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[459, 7803])).
% 2.03/2.21 tff(7805,plain,
% 2.03/2.21 (~r(s(s(z)), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1353, 7802, 385, 6943])).
% 2.03/2.21 tff(7806,plain,
% 2.03/2.21 (b(s(s(z)), s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[442, 7805])).
% 2.03/2.21 tff(7807,plain,
% 2.03/2.21 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[1711])).
% 2.03/2.21 tff(7808,plain,
% 2.03/2.21 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7807])).
% 2.03/2.21 tff(7809,plain,
% 2.03/2.21 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7808])).
% 2.03/2.21 tff(7810,plain,
% 2.03/2.21 (b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[526, 7809])).
% 2.03/2.21 tff(7811,plain,
% 2.03/2.21 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7807])).
% 2.03/2.21 tff(7812,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7811])).
% 2.03/2.21 tff(7813,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[1710])).
% 2.03/2.21 tff(7814,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7813, 7812])).
% 2.03/2.21 tff(7815,plain,
% 2.03/2.21 (s(elem!1) = s(z)),
% 2.03/2.21 inference(symmetry,[status(thm)],[1697])).
% 2.03/2.21 tff(7816,plain,
% 2.03/2.21 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[2071])).
% 2.03/2.21 tff(7817,plain,
% 2.03/2.21 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7816])).
% 2.03/2.21 tff(7818,plain,
% 2.03/2.21 (s(s(elem!1)) = s(z)),
% 2.03/2.21 inference(transitivity,[status(thm)],[25, 7817, 324, 7815])).
% 2.03/2.21 tff(7819,assumption,(~(s(s(elem!1)) = s(z))), introduced(assumption)).
% 2.03/2.21 tff(7820,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7819, 7818])).
% 2.03/2.21 tff(7821,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(7822,plain,
% 2.03/2.21 ((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(z = elem!1))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7821, 331])).
% 2.03/2.21 tff(7823,plain,
% 2.03/2.21 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7822, 1237])).
% 2.03/2.21 tff(7824,plain,
% 2.03/2.21 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1255, 7823])).
% 2.03/2.21 tff(7825,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[1710])).
% 2.03/2.21 tff(7826,plain,
% 2.03/2.21 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7825])).
% 2.03/2.21 tff(7827,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[385, 7826])).
% 2.03/2.21 tff(7828,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7630, 123, 7827])).
% 2.03/2.21 tff(7829,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1304, 7828, 7824])).
% 2.03/2.21 tff(7830,plain,
% 2.03/2.21 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7829, 7814])).
% 2.03/2.21 tff(7831,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[1710])).
% 2.03/2.21 tff(7832,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7831, 3525])).
% 2.03/2.21 tff(7833,plain,
% 2.03/2.21 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7832])).
% 2.03/2.21 tff(7834,plain,
% 2.03/2.21 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7824, 7833])).
% 2.03/2.21 tff(7835,plain,
% 2.03/2.21 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7807])).
% 2.03/2.21 tff(7836,plain,
% 2.03/2.21 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7835])).
% 2.03/2.21 tff(7837,plain,
% 2.03/2.21 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7807])).
% 2.03/2.21 tff(7838,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7837])).
% 2.03/2.21 tff(7839,plain,
% 2.03/2.21 (r(s(s(s(s(z)))), s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[123, 7838])).
% 2.03/2.21 tff(7840,plain,
% 2.03/2.21 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4659, 65, 385, 7839])).
% 2.03/2.21 tff(7841,plain,
% 2.03/2.21 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7840, 7836])).
% 2.03/2.21 tff(7842,plain,
% 2.03/2.21 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[337, 7841, 7834])).
% 2.03/2.21 tff(7843,plain,
% 2.03/2.21 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1336, 7842, 1211])).
% 2.03/2.21 tff(7844,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1412, 162, 444, 445, 7843, 7830, 7810])).
% 2.03/2.21 tff(7845,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)))) | (~(elem!1 = z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(7846,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7845, 7806, 7804, 7787, 7795, 385])).
% 2.03/2.21 tff(7847,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[149, 7846])).
% 2.03/2.21 tff(7848,plain,
% 2.03/2.21 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7847, 7798])).
% 2.03/2.21 tff(7849,plain,
% 2.03/2.21 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7791])).
% 2.03/2.21 tff(7850,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7849])).
% 2.03/2.21 tff(7851,plain,
% 2.03/2.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7791])).
% 2.03/2.21 tff(7852,plain,
% 2.03/2.21 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7851])).
% 2.03/2.21 tff(7853,plain,
% 2.03/2.21 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7790])).
% 2.03/2.21 tff(7854,plain,
% 2.03/2.21 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7787])).
% 2.03/2.21 tff(7855,plain,
% 2.03/2.21 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 2.03/2.21 inference(transitivity,[status(thm)],[7854, 73])).
% 2.03/2.21 tff(7856,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7855])).
% 2.03/2.21 tff(7857,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.21 inference(transitivity,[status(thm)],[7856, 1163])).
% 2.03/2.21 tff(7858,plain,
% 2.03/2.21 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7857])).
% 2.03/2.21 tff(7859,plain,
% 2.03/2.21 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[77, 7858])).
% 2.03/2.21 tff(7860,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7789])).
% 2.03/2.21 tff(7861,plain,
% 2.03/2.21 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(symmetry,[status(thm)],[7860])).
% 2.03/2.21 tff(7862,plain,
% 2.03/2.21 ((~b(s(s(s(z))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7861])).
% 2.03/2.21 tff(7863,plain,
% 2.03/2.21 (~b(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7801, 7862])).
% 2.03/2.21 tff(7864,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[5193, 7863])).
% 2.03/2.21 tff(7865,plain,
% 2.03/2.21 (z = elem!1),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1236, 7787])).
% 2.03/2.21 tff(7866,plain,
% 2.03/2.21 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4971, 7864, 6918])).
% 2.03/2.21 tff(7867,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(commutativity,[status(thm)],[])).
% 2.03/2.21 tff(7868,plain,
% 2.03/2.21 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7867])).
% 2.03/2.21 tff(7869,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[1319])).
% 2.03/2.21 tff(7870,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7869, 7867])).
% 2.03/2.21 tff(7871,plain,
% 2.03/2.21 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7870, 7868])).
% 2.03/2.21 tff(7872,plain,
% 2.03/2.21 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7871])).
% 2.03/2.21 tff(7873,plain,
% 2.03/2.21 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[37, 7872])).
% 2.03/2.21 tff(7874,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[1318])).
% 2.03/2.21 tff(7875,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7874])).
% 2.03/2.21 tff(7876,plain,
% 2.03/2.21 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7357])).
% 2.03/2.21 tff(7877,plain,
% 2.03/2.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7876])).
% 2.03/2.21 tff(7878,plain,
% 2.03/2.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7877, 7875])).
% 2.03/2.21 tff(7879,plain,
% 2.03/2.21 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7878])).
% 2.03/2.21 tff(7880,plain,
% 2.03/2.21 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7876])).
% 2.03/2.21 tff(7881,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 2.03/2.21 inference(symmetry,[status(thm)],[7880])).
% 2.03/2.21 tff(7882,plain,
% 2.03/2.21 (r(s(s(s(s(z)))), z)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[1230, 7881])).
% 2.03/2.21 tff(7883,plain,
% 2.03/2.21 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1364, 65, 230])).
% 2.03/2.21 tff(7884,plain,
% 2.03/2.21 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7883, 7882])).
% 2.03/2.21 tff(7885,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7884, 7879])).
% 2.03/2.21 tff(7886,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1243, 1229, 1204])).
% 2.03/2.21 tff(7887,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1529, 7886, 1245])).
% 2.03/2.21 tff(7888,plain,
% 2.03/2.21 (elem!1 = z),
% 2.03/2.21 inference(symmetry,[status(thm)],[1204])).
% 2.03/2.21 tff(7889,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7888])).
% 2.03/2.21 tff(7890,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.03/2.21 inference(symmetry,[status(thm)],[7889])).
% 2.03/2.21 tff(7891,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[1261, 7890])).
% 2.03/2.21 tff(7892,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(7893,plain,
% 2.03/2.21 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(7894,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7893])).
% 2.03/2.21 tff(7895,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7894, 7892])).
% 2.03/2.21 tff(7896,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(7897,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7896, 7895])).
% 2.03/2.21 tff(7898,plain,
% 2.03/2.21 (~r(s(s(s(elem!1))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7897, 65, 1572, 3850])).
% 2.03/2.21 tff(7899,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7898, 7891])).
% 2.03/2.21 tff(7900,plain,((~r(s(s(s(elem!1))), z)) | (~(z = elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(7901,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7900, 7887, 1204, 1261])).
% 2.03/2.21 tff(7902,plain,
% 2.03/2.21 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7822, 1204])).
% 2.03/2.21 tff(7903,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7356])).
% 2.03/2.21 tff(7904,plain,
% 2.03/2.21 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(symmetry,[status(thm)],[7903])).
% 2.03/2.21 tff(7905,plain,
% 2.03/2.21 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7876])).
% 2.03/2.21 tff(7906,plain,
% 2.03/2.21 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7905, 7904])).
% 2.03/2.21 tff(7907,plain,
% 2.03/2.21 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7906])).
% 2.03/2.21 tff(7908,plain,
% 2.03/2.21 (((~![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(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(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(7909,plain,
% 2.03/2.21 (((~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(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(7910,plain,
% 2.03/2.21 (((~![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(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(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7909])).
% 2.03/2.21 tff(7911,plain,
% 2.03/2.21 (((~![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(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(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7910, 7908])).
% 2.03/2.21 tff(7912,plain,
% 2.03/2.21 ((~![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(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)))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(7913,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7912, 7911])).
% 2.03/2.21 tff(7914,plain,
% 2.03/2.21 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7913, 65, 866])).
% 2.03/2.21 tff(7915,plain,
% 2.03/2.21 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7914, 7882])).
% 2.03/2.21 tff(7916,plain,
% 2.03/2.21 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7915, 7907])).
% 2.03/2.21 tff(7917,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2126, 7916, 1147, 2112, 7902, 7901])).
% 2.03/2.21 tff(7918,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2101, 7917, 7885, 7873])).
% 2.03/2.21 tff(7919,plain,(b(s(s(s(s(elem!1)))), z) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(7920,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7919, 7424, 7866, 7788, 6943, 7802, 7865, 7864, 7859])).
% 2.03/2.21 tff(7921,plain,
% 2.03/2.21 (~b(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[170, 7847, 121, 152, 7920])).
% 2.03/2.21 tff(7922,plain,
% 2.03/2.21 (r(z, s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[83, 7921])).
% 2.03/2.21 tff(7923,plain,
% 2.03/2.21 (r(z, s(s(s(s(z)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7922, 7853])).
% 2.03/2.21 tff(7924,plain,
% 2.03/2.21 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2647, 7923, 7412])).
% 2.03/2.21 tff(7925,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7924, 7852])).
% 2.03/2.21 tff(7926,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[52, 7925])).
% 2.03/2.21 tff(7927,plain,
% 2.03/2.21 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7926, 7850])).
% 2.03/2.21 tff(7928,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(7929,plain,
% 2.03/2.21 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), 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)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(7930,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[7929])).
% 2.03/2.21 tff(7931,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[7930, 7928])).
% 2.03/2.21 tff(7932,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(7933,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[7932, 7931])).
% 2.03/2.21 tff(7934,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7933, 162, 383, 4039, 7927, 7848, 7796])).
% 2.03/2.21 tff(7935,plain,(b(s(s(elem!1)), z) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(7936,plain,
% 2.03/2.21 (b(s(s(elem!1)), z) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1) | (s(z) = elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7935, 6735])).
% 2.03/2.21 tff(7937,plain,
% 2.03/2.21 (b(s(s(s(z))), elem!1)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7936, 6914, 121, 385, 6789, 6908, 6849])).
% 2.03/2.21 tff(7938,plain,
% 2.03/2.21 (elem!1 = z),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1208, 6903])).
% 2.03/2.21 tff(7939,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[3761, 7938, 7937, 6894])).
% 2.03/2.21 tff(7940,plain,((~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(7941,plain,
% 2.03/2.21 (~r(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7940, 6787, 385, 6281, 55, 54, 395])).
% 2.03/2.21 tff(7942,plain,
% 2.03/2.21 (b(z, s(s(s(z))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[295, 7941])).
% 2.03/2.21 tff(7943,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~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(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(7944,plain,
% 2.03/2.21 (((~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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~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(elem!1)))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(7945,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~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(elem!1))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[7944])).
% 2.03/2.22 tff(7946,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(elem!1)))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[7945, 7943])).
% 2.03/2.22 tff(7947,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(7948,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[7947, 7946])).
% 2.03/2.22 tff(7949,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7948, 162, 96, 84, 6285, 6281, 7942])).
% 2.03/2.22 tff(7950,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(7951,plain,
% 2.03/2.22 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7950, 395, 55, 54, 385])).
% 2.03/2.22 tff(7952,plain,
% 2.03/2.22 (b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[149, 7951])).
% 2.03/2.22 tff(7953,plain,
% 2.03/2.22 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6271, 6116, 84, 96, 6783])).
% 2.03/2.22 tff(7954,plain,
% 2.03/2.22 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[338, 7953])).
% 2.03/2.22 tff(7955,plain,
% 2.03/2.22 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2517, 385, 299])).
% 2.03/2.22 tff(7956,plain,
% 2.03/2.22 (b(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[191, 7955])).
% 2.03/2.22 tff(7957,plain,
% 2.03/2.22 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3340, 7956, 122, 120, 152])).
% 2.03/2.22 tff(7958,plain,
% 2.03/2.22 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[149, 7957])).
% 2.03/2.22 tff(7959,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6251, 65, 7958, 385, 299])).
% 2.03/2.22 tff(7960,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(7961,plain,
% 2.03/2.22 (~b(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7960, 7954, 96, 84, 385])).
% 2.03/2.22 tff(7962,plain,
% 2.03/2.22 (r(s(z), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[175, 7961])).
% 2.03/2.22 tff(7963,plain,
% 2.03/2.22 (b(s(s(s(s(z)))), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1089, 5601])).
% 2.03/2.22 tff(7964,plain,
% 2.03/2.22 (((~![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(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(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(7965,plain,
% 2.03/2.22 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(7966,plain,
% 2.03/2.22 (((~![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(z, s(s(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(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[7965])).
% 2.03/2.22 tff(7967,plain,
% 2.03/2.22 (((~![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(z, s(s(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(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[7966, 7964])).
% 2.03/2.22 tff(7968,plain,
% 2.03/2.22 ((~![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(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(7969,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[7968, 7967])).
% 2.03/2.22 tff(7970,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7969, 65, 97, 803, 645])).
% 2.03/2.22 tff(7971,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(7972,plain,
% 2.03/2.22 (~r(z, s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7971, 645, 97])).
% 2.03/2.22 tff(7973,plain,
% 2.03/2.22 (b(z, s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[823, 7972])).
% 2.03/2.22 tff(7974,plain,
% 2.03/2.22 (((~![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), s(s(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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(7975,plain,
% 2.03/2.22 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(7976,plain,
% 2.03/2.22 (((~![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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[7975])).
% 2.03/2.22 tff(7977,plain,
% 2.03/2.22 (((~![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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[7976, 7974])).
% 2.03/2.22 tff(7978,plain,
% 2.03/2.22 ((~![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(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)))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(7979,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[7978, 7977])).
% 2.03/2.22 tff(7980,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7979, 65, 395, 787, 645])).
% 2.03/2.22 tff(7981,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,[]))).
% 2.03/2.22 tff(7982,plain,
% 2.03/2.22 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7981, 645, 395])).
% 2.03/2.22 tff(7983,plain,
% 2.03/2.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[690, 7982, 679])).
% 2.03/2.22 tff(7984,plain,
% 2.03/2.22 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7312, 7983, 7973, 297, 7963])).
% 2.03/2.22 tff(7985,plain,
% 2.03/2.22 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[675, 7984, 664])).
% 2.03/2.22 tff(7986,plain,
% 2.03/2.22 (((~![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), 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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(7987,plain,
% 2.03/2.22 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(7988,plain,
% 2.03/2.22 (((~![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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[7987])).
% 2.03/2.22 tff(7989,plain,
% 2.03/2.22 (((~![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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[7988, 7986])).
% 2.03/2.22 tff(7990,plain,
% 2.03/2.22 ((~![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(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))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(7991,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[7990, 7989])).
% 2.03/2.22 tff(7992,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7991, 65, 395, 7985, 645])).
% 2.03/2.22 tff(7993,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(7994,plain,
% 2.03/2.22 (~r(s(z), s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7993, 7962, 97, 6783, 395])).
% 2.03/2.22 tff(7995,plain,
% 2.03/2.22 (b(s(z), s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[6862, 7994])).
% 2.03/2.22 tff(7996,plain,
% 2.03/2.22 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[373, 6116, 54, 96, 6783])).
% 2.03/2.22 tff(7997,plain,
% 2.03/2.22 (b(s(s(s(z))), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[459, 7996])).
% 2.03/2.22 tff(7998,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4099, 162, 538, 444, 445, 298, 297])).
% 2.03/2.22 tff(7999,plain,((~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(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(8000,plain,
% 2.03/2.22 (~b(s(s(z)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[7999, 444, 7997, 6116, 6783])).
% 2.03/2.22 tff(8001,plain,
% 2.03/2.22 (r(s(s(z)), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[245, 8000])).
% 2.03/2.22 tff(8002,plain,
% 2.03/2.22 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2647, 803, 55])).
% 2.03/2.22 tff(8003,plain,
% 2.03/2.22 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[709, 8002, 635])).
% 2.03/2.22 tff(8004,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8005,plain,
% 2.03/2.22 (((~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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(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(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8006,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[8005])).
% 2.03/2.22 tff(8007,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[8006, 8004])).
% 2.03/2.22 tff(8008,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(8009,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[8008, 8007])).
% 2.03/2.22 tff(8010,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8009, 162, 383, 4039, 825, 694, 1369])).
% 2.03/2.22 tff(8011,plain,((~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(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(8012,plain,
% 2.03/2.22 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8011, 8003, 4039, 383, 694])).
% 2.03/2.22 tff(8013,plain,
% 2.03/2.22 (r(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[801, 8012, 634])).
% 2.03/2.22 tff(8014,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(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(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8015,plain,
% 2.03/2.22 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8016,plain,
% 2.03/2.22 (((~![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(z)), s(s(s(s(z)))))) | (~r(z, s(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(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[8015])).
% 2.03/2.22 tff(8017,plain,
% 2.03/2.22 (((~![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(z)), s(s(s(s(z)))))) | (~r(z, s(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(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[8016, 8014])).
% 2.03/2.22 tff(8018,plain,
% 2.03/2.22 ((~![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(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(8019,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[8018, 8017])).
% 2.03/2.22 tff(8020,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8019, 65, 230, 8013, 803])).
% 2.03/2.22 tff(8021,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(8022,plain,
% 2.03/2.22 ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(z))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8021, 6735])).
% 2.03/2.22 tff(8023,plain,
% 2.03/2.22 (~r(z, s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8022, 8001, 6849, 7995, 55])).
% 2.03/2.22 tff(8024,plain,
% 2.03/2.22 (b(z, s(s(s(s(z)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[823, 8023])).
% 2.03/2.22 tff(8025,plain,
% 2.03/2.22 (((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), 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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8026,plain,
% 2.03/2.22 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8027,plain,
% 2.03/2.22 (((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), 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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[8026])).
% 2.03/2.22 tff(8028,plain,
% 2.03/2.22 (((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), 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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[8027, 8025])).
% 2.03/2.22 tff(8029,plain,
% 2.03/2.22 ((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(8030,plain,
% 2.03/2.22 ((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[8029, 8028])).
% 2.03/2.22 tff(8031,plain,
% 2.03/2.22 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8030, 65, 385, 945])).
% 2.03/2.22 tff(8032,plain,
% 2.03/2.22 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1001, 8031])).
% 2.03/2.22 tff(8033,plain,
% 2.03/2.22 (((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8034,plain,
% 2.03/2.22 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(8035,plain,
% 2.03/2.22 (((~![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(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[8034])).
% 2.03/2.22 tff(8036,plain,
% 2.03/2.22 (((~![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(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[8035, 8033])).
% 2.03/2.22 tff(8037,plain,
% 2.03/2.22 ((~![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(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(8038,plain,
% 2.03/2.22 ((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[8037, 8036])).
% 2.03/2.23 tff(8039,plain,
% 2.03/2.23 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8038, 65, 385, 945])).
% 2.03/2.23 tff(8040,plain,
% 2.03/2.23 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2375, 47, 995, 8039])).
% 2.03/2.23 tff(8041,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(s(elem!1))))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8042,plain,
% 2.03/2.23 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(s(elem!1))))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8043,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(s(elem!1)))))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8042])).
% 2.03/2.23 tff(8044,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(s(elem!1))))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[8043, 8041])).
% 2.03/2.23 tff(8045,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(8046,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[8045, 8044])).
% 2.03/2.23 tff(8047,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8046, 162, 8040, 298, 8032, 297, 5546])).
% 2.03/2.23 tff(8048,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(8049,plain,
% 2.03/2.23 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8048, 6783, 385, 97, 6116])).
% 2.03/2.23 tff(8050,plain,
% 2.03/2.23 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[968, 8049])).
% 2.03/2.23 tff(8051,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8052,plain,
% 2.03/2.23 (((~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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8053,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8052])).
% 2.03/2.23 tff(8054,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[8053, 8051])).
% 2.03/2.23 tff(8055,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(8056,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[8055, 8054])).
% 2.03/2.23 tff(8057,plain,
% 2.03/2.23 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8056, 162, 151, 4039, 970, 825, 694])).
% 2.03/2.23 tff(8058,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8059,plain,
% 2.03/2.23 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8060,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8059])).
% 2.03/2.23 tff(8061,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[8060, 8058])).
% 2.03/2.23 tff(8062,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(8063,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[8062, 8061])).
% 2.03/2.23 tff(8064,plain,
% 2.03/2.23 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8063, 162, 383, 4039, 970, 825, 694])).
% 2.03/2.23 tff(8065,plain,
% 2.03/2.23 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[943, 8064])).
% 2.03/2.23 tff(8066,plain,
% 2.03/2.23 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4330, 8065, 54])).
% 2.03/2.23 tff(8067,plain,
% 2.03/2.23 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1789, 8066, 8057])).
% 2.03/2.23 tff(8068,plain,
% 2.03/2.23 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[8067])).
% 2.03/2.23 tff(8069,plain,
% 2.03/2.23 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8068])).
% 2.03/2.23 tff(8070,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[8069])).
% 2.03/2.23 tff(8071,plain,
% 2.03/2.23 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1517, 8067])).
% 2.03/2.23 tff(8072,plain,
% 2.03/2.23 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1259, 8071])).
% 2.03/2.23 tff(8073,plain,
% 2.03/2.23 (elem!1 = s(s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1540, 8072])).
% 2.03/2.23 tff(8074,plain,
% 2.03/2.23 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8073])).
% 2.03/2.23 tff(8075,plain,
% 2.03/2.23 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1255, 8071])).
% 2.03/2.23 tff(8076,plain,
% 2.03/2.23 (~(elem!1 = s(s(s(s(z)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2411, 8075, 8072])).
% 2.03/2.23 tff(8077,plain,
% 2.03/2.23 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8073])).
% 2.03/2.23 tff(8078,plain,
% 2.03/2.23 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[8077])).
% 2.03/2.23 tff(8079,plain,
% 2.03/2.23 ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8078])).
% 2.03/2.23 tff(8080,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(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(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8081,plain,
% 2.03/2.23 (((~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))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8082,plain,
% 2.03/2.23 (((~![X0: $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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8081])).
% 2.03/2.23 tff(8083,plain,
% 2.03/2.23 (((~![X0: $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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.23 inference(transitivity,[status(thm)],[8082, 8080])).
% 2.03/2.23 tff(8084,plain,
% 2.03/2.23 ((~![X0: $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)))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(8085,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[8084, 8083])).
% 2.03/2.23 tff(8086,plain,
% 2.03/2.23 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8085, 65, 230, 1341])).
% 2.03/2.23 tff(8087,plain,
% 2.03/2.23 (b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[801, 8086, 634])).
% 2.03/2.23 tff(8088,plain,
% 2.03/2.23 (((~![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(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)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8089,plain,
% 2.03/2.23 (((~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)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8090,plain,
% 2.03/2.23 (((~![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)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8089])).
% 2.03/2.23 tff(8091,plain,
% 2.03/2.23 (((~![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)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[8090, 8088])).
% 2.03/2.23 tff(8092,plain,
% 2.03/2.23 ((~![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))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(8093,plain,
% 2.03/2.23 ((~![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(s(s(s(z)))), s(z)))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[8092, 8091])).
% 2.03/2.23 tff(8094,plain,
% 2.03/2.23 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8093, 65, 194, 1341])).
% 2.03/2.23 tff(8095,plain,
% 2.03/2.23 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[775, 8094, 642])).
% 2.03/2.23 tff(8096,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8097,plain,
% 2.03/2.23 (((~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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(8098,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[8097])).
% 2.03/2.23 tff(8099,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[8098, 8096])).
% 2.03/2.23 tff(8100,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(8101,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8100, 8099])).
% 2.03/2.24 tff(8102,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8101, 162, 383, 4039, 825, 694, 8095, 8087])).
% 2.03/2.24 tff(8103,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(8104,plain,
% 2.03/2.24 (~r(s(s(s(s(z)))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8103, 825, 4039, 383, 694, 194, 230])).
% 2.03/2.24 tff(8105,plain,
% 2.03/2.24 (b(s(s(s(s(z)))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1089, 8104])).
% 2.03/2.24 tff(8106,plain,
% 2.03/2.24 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[5714, 878, 194])).
% 2.03/2.24 tff(8107,plain,
% 2.03/2.24 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1050, 8106])).
% 2.03/2.24 tff(8108,plain,
% 2.03/2.24 (((~![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(s(s(elem!1))))), z)) | (~r(s(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), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8109,plain,
% 2.03/2.24 (((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8110,plain,
% 2.03/2.24 (((~![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(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(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), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[8109])).
% 2.03/2.24 tff(8111,plain,
% 2.03/2.24 (((~![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(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(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), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[8110, 8108])).
% 2.03/2.24 tff(8112,plain,
% 2.03/2.24 ((~![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(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(8113,plain,
% 2.03/2.24 ((~![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(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8112, 8111])).
% 2.03/2.24 tff(8114,plain,
% 2.03/2.24 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8113, 65, 194, 878])).
% 2.03/2.24 tff(8115,plain,
% 2.03/2.24 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[968, 8114])).
% 2.03/2.24 tff(8116,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8117,plain,
% 2.03/2.24 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8118,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[8117])).
% 2.03/2.24 tff(8119,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[8118, 8116])).
% 2.03/2.24 tff(8120,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(8121,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8120, 8119])).
% 2.03/2.24 tff(8122,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8121, 162, 927, 1029, 4039, 970, 925])).
% 2.03/2.24 tff(8123,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(8124,plain,
% 2.03/2.24 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8123, 8115, 4039, 2937, 8107])).
% 2.03/2.24 tff(8125,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[921, 47, 2928, 8124, 916])).
% 2.03/2.24 tff(8126,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(8127,plain,
% 2.03/2.24 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8126, 194, 230, 4039])).
% 2.03/2.24 tff(8128,plain,
% 2.03/2.24 (b(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[894, 8127])).
% 2.03/2.24 tff(8129,plain,
% 2.03/2.24 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[8067])).
% 2.03/2.24 tff(8130,plain,
% 2.03/2.24 (b(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[120, 8129])).
% 2.03/2.24 tff(8131,plain,
% 2.03/2.24 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[1513])).
% 2.03/2.24 tff(8132,plain,
% 2.03/2.24 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[8131])).
% 2.03/2.24 tff(8133,plain,
% 2.03/2.24 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[3211, 8132])).
% 2.03/2.24 tff(8134,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))), s(s(s(s(z)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8135,plain,
% 2.03/2.24 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))), s(s(s(s(z)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8136,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))), s(s(s(s(z))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[8135])).
% 2.03/2.24 tff(8137,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(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(s(elem!1))))), s(s(s(s(z)))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[8136, 8134])).
% 2.03/2.24 tff(8138,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(8139,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8138, 8137])).
% 2.03/2.24 tff(8140,plain,
% 2.03/2.24 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8139, 162, 971, 1076, 1075, 926])).
% 2.03/2.24 tff(8141,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8140, 8133])).
% 2.03/2.24 tff(8142,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (~b(z, s(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(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(8143,plain,
% 2.03/2.24 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8142, 8130, 8128, 8105, 1075, 8067])).
% 2.03/2.24 tff(8144,plain,
% 2.03/2.24 (~b(elem!1, s(s(s(s(z)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8143, 8079])).
% 2.03/2.24 tff(8145,plain,
% 2.03/2.24 (r(elem!1, s(s(s(s(z)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2445, 8144, 8076])).
% 2.03/2.24 tff(8146,plain,
% 2.03/2.24 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8145, 8074])).
% 2.03/2.24 tff(8147,plain,
% 2.03/2.24 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8146, 8070])).
% 2.03/2.24 tff(8148,plain,
% 2.03/2.24 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8011, 825, 4039, 383, 694])).
% 2.03/2.24 tff(8149,plain,
% 2.03/2.24 (r(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[801, 8148, 634])).
% 2.03/2.24 tff(8150,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(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(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8151,plain,
% 2.03/2.24 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8152,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), 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(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[8151])).
% 2.03/2.24 tff(8153,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), 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(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[8152, 8150])).
% 2.03/2.24 tff(8154,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(8155,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8154, 8153])).
% 2.03/2.24 tff(8156,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8155, 65, 8065, 8149, 8147])).
% 2.03/2.24 tff(8157,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(8158,plain,
% 2.03/2.24 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8157, 6735])).
% 2.03/2.24 tff(8159,plain,
% 2.03/2.24 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8158, 8024, 54, 84, 7952, 8050, 7995, 6849, 7962, 8001])).
% 2.03/2.24 tff(8160,plain,
% 2.03/2.24 (r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[6873, 8159])).
% 2.03/2.24 tff(8161,plain,
% 2.03/2.24 (((~![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(s(s(s(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(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8162,plain,
% 2.03/2.24 (((~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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8163,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[8162])).
% 2.03/2.24 tff(8164,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.24 inference(transitivity,[status(thm)],[8163, 8161])).
% 2.03/2.24 tff(8165,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(8166,plain,
% 2.03/2.24 ((~![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(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8165, 8164])).
% 2.03/2.24 tff(8167,plain,
% 2.03/2.24 (~r(s(s(s(s(z)))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[8166, 65, 97, 55, 8160])).
% 2.03/2.24 tff(8168,plain,
% 2.03/2.24 (b(s(s(s(s(z)))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1089, 8167])).
% 2.03/2.24 tff(8169,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(8170,plain,
% 2.03/2.24 (((~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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8171,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8170])).
% 2.03/2.25 tff(8172,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[8171, 8169])).
% 2.03/2.25 tff(8173,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(8174,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8173, 8172])).
% 2.03/2.25 tff(8175,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8174, 162, 298, 1076, 1075, 297, 692])).
% 2.03/2.25 tff(8176,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(8177,plain,
% 2.03/2.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8176, 8168, 6783, 6116, 8024])).
% 2.03/2.25 tff(8178,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6804, 8177])).
% 2.03/2.25 tff(8179,plain,
% 2.03/2.25 (((~![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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8180,plain,
% 2.03/2.25 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8181,plain,
% 2.03/2.25 (((~![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), 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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8180])).
% 2.03/2.25 tff(8182,plain,
% 2.03/2.25 (((~![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), 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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[8181, 8179])).
% 2.03/2.25 tff(8183,plain,
% 2.03/2.25 ((~![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), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(8184,plain,
% 2.03/2.25 ((~![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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8183, 8182])).
% 2.03/2.25 tff(8185,plain,
% 2.03/2.25 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8184, 65, 7962, 395, 8178])).
% 2.03/2.25 tff(8186,plain,
% 2.03/2.25 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2517, 7954, 385])).
% 2.03/2.25 tff(8187,plain,
% 2.03/2.25 (b(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[191, 8186])).
% 2.03/2.25 tff(8188,plain,
% 2.03/2.25 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3209, 8160, 54])).
% 2.03/2.25 tff(8189,plain,
% 2.03/2.25 (~r(z, s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8022, 230, 6849, 7995, 55])).
% 2.03/2.25 tff(8190,plain,
% 2.03/2.25 (b(z, s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[823, 8189])).
% 2.03/2.25 tff(8191,plain,
% 2.03/2.25 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8158, 8190, 54, 84, 7952, 8050, 7995, 6849, 7962, 230])).
% 2.03/2.25 tff(8192,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6873, 8191])).
% 2.03/2.25 tff(8193,plain,
% 2.03/2.25 (~r(s(s(s(s(z)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8166, 65, 97, 55, 8192])).
% 2.03/2.25 tff(8194,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1089, 8193])).
% 2.03/2.25 tff(8195,plain,
% 2.03/2.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8176, 8194, 6783, 6116, 8190])).
% 2.03/2.25 tff(8196,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6804, 8195])).
% 2.03/2.25 tff(8197,plain,
% 2.03/2.25 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8184, 65, 7962, 395, 8196])).
% 2.03/2.25 tff(8198,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6793, 8197])).
% 2.03/2.25 tff(8199,plain,
% 2.03/2.25 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3219, 8198, 7995, 8187, 7952])).
% 2.03/2.25 tff(8200,plain,
% 2.03/2.25 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3209, 8192, 54])).
% 2.03/2.25 tff(8201,plain,
% 2.03/2.25 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[763, 47, 8200])).
% 2.03/2.25 tff(8202,plain,
% 2.03/2.25 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8201, 8199])).
% 2.03/2.25 tff(8203,plain,
% 2.03/2.25 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8202])).
% 2.03/2.25 tff(8204,plain,
% 2.03/2.25 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8203])).
% 2.03/2.25 tff(8205,plain,
% 2.03/2.25 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8204])).
% 2.03/2.25 tff(8206,plain,
% 2.03/2.25 (b(z, s(s(s(s(s(elem!1)))))) <=> b(z, s(s(s(s(s(z))))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8205])).
% 2.03/2.25 tff(8207,plain,
% 2.03/2.25 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8202])).
% 2.03/2.25 tff(8208,plain,
% 2.03/2.25 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[20, 8207, 630])).
% 2.03/2.25 tff(8209,plain,
% 2.03/2.25 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8208])).
% 2.03/2.25 tff(8210,plain,
% 2.03/2.25 (s(s(elem!1)) = s(s(z))),
% 2.03/2.25 inference(transitivity,[status(thm)],[25, 8209, 312])).
% 2.03/2.25 tff(8211,plain,
% 2.03/2.25 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8210])).
% 2.03/2.25 tff(8212,plain,
% 2.03/2.25 (s(elem!1) = s(z)),
% 2.03/2.25 inference(transitivity,[status(thm)],[325, 8211, 15])).
% 2.03/2.25 tff(8213,plain,
% 2.03/2.25 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8212])).
% 2.03/2.25 tff(8214,plain,
% 2.03/2.25 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8213])).
% 2.03/2.25 tff(8215,plain,
% 2.03/2.25 (z = elem!1),
% 2.03/2.25 inference(transitivity,[status(thm)],[1182, 8214, 1170])).
% 2.03/2.25 tff(8216,plain,
% 2.03/2.25 (elem!1 = z),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1208, 8215])).
% 2.03/2.25 tff(8217,plain,
% 2.03/2.25 (elem!1 = z),
% 2.03/2.25 inference(transitivity,[status(thm)],[1171, 8213, 13])).
% 2.03/2.25 tff(8218,plain,
% 2.03/2.25 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(z))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8217, 8203])).
% 2.03/2.25 tff(8219,plain,
% 2.03/2.25 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.03/2.25 inference(transitivity,[status(thm)],[8218, 2881])).
% 2.03/2.25 tff(8220,plain,
% 2.03/2.25 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8219])).
% 2.03/2.25 tff(8221,plain,
% 2.03/2.25 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8220])).
% 2.03/2.25 tff(8222,plain,
% 2.03/2.25 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[2888, 8221])).
% 2.03/2.25 tff(8223,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8203, 8212])).
% 2.03/2.25 tff(8224,plain,
% 2.03/2.25 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8223])).
% 2.03/2.25 tff(8225,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8203])).
% 2.03/2.25 tff(8226,plain,
% 2.03/2.25 (b(s(s(s(s(s(z))))), s(z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8050, 8225])).
% 2.03/2.25 tff(8227,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8226, 8224])).
% 2.03/2.25 tff(8228,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8202, 8212])).
% 2.03/2.25 tff(8229,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8228])).
% 2.03/2.25 tff(8230,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8198, 8229])).
% 2.03/2.25 tff(8231,plain,
% 2.03/2.25 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8212, 8202])).
% 2.03/2.25 tff(8232,plain,
% 2.03/2.25 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8231])).
% 2.03/2.25 tff(8233,plain,
% 2.03/2.25 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[7995, 8232])).
% 2.03/2.25 tff(8234,plain,
% 2.03/2.25 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8208])).
% 2.03/2.25 tff(8235,plain,
% 2.03/2.25 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[8234, 987])).
% 2.03/2.25 tff(8236,plain,
% 2.03/2.25 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8235])).
% 2.03/2.25 tff(8237,plain,
% 2.03/2.25 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8236])).
% 2.03/2.25 tff(8238,plain,
% 2.03/2.25 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[996, 8237])).
% 2.03/2.25 tff(8239,plain,
% 2.03/2.25 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[2746, 8238])).
% 2.03/2.25 tff(8240,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8202, 8208])).
% 2.03/2.25 tff(8241,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8240])).
% 2.03/2.25 tff(8242,plain,
% 2.03/2.25 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8196, 8241])).
% 2.03/2.25 tff(8243,plain,
% 2.03/2.25 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1781, 1004, 4350, 1211])).
% 2.03/2.25 tff(8244,plain,
% 2.03/2.25 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8243, 2170])).
% 2.03/2.25 tff(8245,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1760, 8244, 1701])).
% 2.03/2.25 tff(8246,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8245, 4291])).
% 2.03/2.25 tff(8247,plain,
% 2.03/2.25 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[4330, 1004, 54])).
% 2.03/2.25 tff(8248,plain,
% 2.03/2.25 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[943, 8247])).
% 2.03/2.25 tff(8249,plain,
% 2.03/2.25 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[5748, 1004, 3850])).
% 2.03/2.25 tff(8250,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1731, 8249, 1691])).
% 2.03/2.25 tff(8251,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8250, 1835])).
% 2.03/2.25 tff(8252,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8253,plain,
% 2.03/2.25 (((~b(s(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(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8254,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8253])).
% 2.03/2.25 tff(8255,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[8254, 8252])).
% 2.03/2.25 tff(8256,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(8257,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8256, 8255])).
% 2.03/2.25 tff(8258,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8257, 162, 444, 8251, 445, 8248, 8246])).
% 2.03/2.25 tff(8259,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~(elem!1 = z)) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(8260,plain,
% 2.03/2.25 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8259, 8216, 54, 7997, 8238, 444, 8242])).
% 2.03/2.25 tff(8261,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1789, 8260, 8239])).
% 2.03/2.25 tff(8262,plain,
% 2.03/2.25 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[5331, 8261, 8233, 8230, 8227])).
% 2.03/2.25 tff(8263,plain,
% 2.03/2.25 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[5338, 8262, 8216])).
% 2.03/2.25 tff(8264,plain,
% 2.03/2.25 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1050, 8263])).
% 2.03/2.25 tff(8265,plain,
% 2.03/2.25 (~r(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[4443, 8264, 97])).
% 2.03/2.25 tff(8266,plain,
% 2.03/2.25 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1741, 8265, 8216])).
% 2.03/2.25 tff(8267,plain,
% 2.03/2.25 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1813, 8266, 8222])).
% 2.03/2.25 tff(8268,plain,
% 2.03/2.25 (b(z, s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1821, 8267, 8216])).
% 2.03/2.25 tff(8269,plain,
% 2.03/2.25 (b(z, s(s(s(s(s(z))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8268, 8206])).
% 2.03/2.25 tff(8270,plain,
% 2.03/2.25 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8204])).
% 2.03/2.25 tff(8271,plain,
% 2.03/2.25 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[8270])).
% 2.03/2.25 tff(8272,plain,
% 2.03/2.25 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[5361, 8227, 385, 8230, 8202, 8233, 340])).
% 2.03/2.25 tff(8273,plain,
% 2.03/2.25 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1001, 8272])).
% 2.03/2.25 tff(8274,plain,
% 2.03/2.25 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8273, 8271])).
% 2.03/2.25 tff(8275,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8203])).
% 2.03/2.25 tff(8276,plain,
% 2.03/2.25 ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(z)), z)) | (~r(s(z), z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8126, 6735])).
% 2.03/2.25 tff(8277,plain,
% 2.03/2.25 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8276, 230, 7962])).
% 2.03/2.25 tff(8278,plain,
% 2.03/2.25 (b(s(s(s(s(s(elem!1))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[894, 8277])).
% 2.03/2.25 tff(8279,plain,
% 2.03/2.25 (b(s(s(s(s(s(z))))), z)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8278, 8275])).
% 2.03/2.25 tff(8280,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8281,plain,
% 2.03/2.25 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8282,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8281])).
% 2.03/2.25 tff(8283,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[8282, 8280])).
% 2.03/2.25 tff(8284,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(8285,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8284, 8283])).
% 2.03/2.25 tff(8286,plain,
% 2.03/2.25 (~b(z, s(s(s(s(s(z))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8285, 162, 6116, 6783, 8279, 8274])).
% 2.03/2.25 tff(8287,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8286, 8269])).
% 2.03/2.25 tff(8288,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(8289,plain,
% 2.03/2.25 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8288, 8001, 54, 444, 385, 97, 395, 55])).
% 2.03/2.25 tff(8290,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[360, 8289])).
% 2.03/2.25 tff(8291,plain,
% 2.03/2.25 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[5632, 8177, 8290])).
% 2.03/2.25 tff(8292,plain,
% 2.03/2.25 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[763, 47, 8291, 8188])).
% 2.03/2.25 tff(8293,plain,
% 2.03/2.25 (~b(s(s(s(s(z)))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[3219, 8292, 7995, 8187, 7952])).
% 2.03/2.25 tff(8294,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6793, 8293, 8185])).
% 2.03/2.25 tff(8295,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(8296,plain,
% 2.03/2.25 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8295, 97, 395, 55, 54, 385])).
% 2.03/2.25 tff(8297,plain,
% 2.03/2.25 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[442, 8296])).
% 2.03/2.25 tff(8298,plain,
% 2.03/2.25 (~r(s(s(s(s(z)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8166, 65, 97, 55, 644])).
% 2.03/2.25 tff(8299,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1089, 8298])).
% 2.03/2.25 tff(8300,plain,
% 2.03/2.25 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8176, 8299, 6783, 298, 2649])).
% 2.03/2.25 tff(8301,plain,
% 2.03/2.25 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6804, 8300])).
% 2.03/2.25 tff(8302,plain,
% 2.03/2.25 (((~![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(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(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8303,plain,
% 2.03/2.25 (((~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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(8304,plain,
% 2.03/2.25 (((~![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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[8303])).
% 2.03/2.25 tff(8305,plain,
% 2.03/2.25 (((~![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(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[8304, 8302])).
% 2.03/2.25 tff(8306,plain,
% 2.03/2.25 ((~![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)))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(8307,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8306, 8305])).
% 2.03/2.25 tff(8308,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8307, 65, 417, 8301, 644])).
% 2.03/2.25 tff(8309,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(8310,plain,
% 2.03/2.25 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8309, 8297, 6116, 97, 55])).
% 2.03/2.25 tff(8311,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6873, 8310])).
% 2.03/2.25 tff(8312,plain,
% 2.03/2.25 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8011, 6735])).
% 2.03/2.25 tff(8313,plain,
% 2.03/2.25 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8312, 8311, 6849, 7995])).
% 2.03/2.25 tff(8314,plain,
% 2.03/2.25 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[801, 634])).
% 2.03/2.25 tff(8315,plain,
% 2.03/2.25 (r(s(s(z)), s(s(s(s(z)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8314, 8313])).
% 2.03/2.25 tff(8316,plain,
% 2.03/2.25 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[796, 8315, 8297])).
% 2.03/2.25 tff(8317,plain,
% 2.03/2.25 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6804, 8316])).
% 2.03/2.25 tff(8318,plain,
% 2.03/2.25 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[6350, 8297, 7954])).
% 2.03/2.25 tff(8319,plain,
% 2.03/2.25 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[216, 8318])).
% 2.03/2.26 tff(8320,plain,
% 2.03/2.26 (~r(z, s(s(s(s(z)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8022, 230, 383, 694, 55])).
% 2.03/2.26 tff(8321,plain,
% 2.03/2.26 (b(z, s(s(s(s(z)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[823, 8320])).
% 2.03/2.26 tff(8322,plain,
% 2.03/2.26 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8158, 8321, 54, 84, 151, 970, 694, 383, 194, 230])).
% 2.03/2.26 tff(8323,plain,
% 2.03/2.26 (r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6873, 8322])).
% 2.03/2.26 tff(8324,plain,
% 2.03/2.26 (~r(s(s(s(s(z)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8166, 65, 97, 55, 8323])).
% 2.03/2.26 tff(8325,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1089, 8324])).
% 2.03/2.26 tff(8326,plain,
% 2.03/2.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8176, 8325, 6783, 298, 8321])).
% 2.03/2.26 tff(8327,plain,
% 2.03/2.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6804, 8326])).
% 2.03/2.26 tff(8328,plain,
% 2.03/2.26 (((~![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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8329,plain,
% 2.03/2.26 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8330,plain,
% 2.03/2.26 (((~![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)), 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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[8329])).
% 2.03/2.26 tff(8331,plain,
% 2.03/2.26 (((~![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)), 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(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[8330, 8328])).
% 2.03/2.26 tff(8332,plain,
% 2.03/2.26 ((~![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)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(8333,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[8332, 8331])).
% 2.03/2.26 tff(8334,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8333, 65, 230, 417, 8327, 8323])).
% 2.03/2.26 tff(8335,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(8336,plain,
% 2.03/2.26 (~r(s(s(z)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8335, 8297, 6116, 97, 55, 54, 7952, 8050, 7995, 6849, 7962])).
% 2.03/2.26 tff(8337,plain,
% 2.03/2.26 (b(s(s(z)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[245, 8336])).
% 2.03/2.26 tff(8338,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8339,plain,
% 2.03/2.26 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(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(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8340,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)))), s(s(s(z)))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[8339])).
% 2.03/2.26 tff(8341,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(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(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[8340, 8338])).
% 2.03/2.26 tff(8342,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(8343,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[8342, 8341])).
% 2.03/2.26 tff(8344,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8343, 162, 96, 8337, 7997, 8319, 8311, 8317])).
% 2.03/2.26 tff(8345,plain,((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(8346,plain,
% 2.03/2.26 (~r(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8345, 395, 54, 55, 385])).
% 2.03/2.26 tff(8347,plain,
% 2.03/2.26 (b(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[117, 8346])).
% 2.03/2.26 tff(8348,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6843, 8347, 385, 395, 54, 96, 84, 7952])).
% 2.03/2.26 tff(8349,plain,
% 2.03/2.26 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6758, 8347, 6849, 54, 55])).
% 2.03/2.26 tff(8350,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[459, 8349, 8348])).
% 2.03/2.26 tff(8351,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(8352,plain,
% 2.03/2.26 (~r(s(z), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8351, 385, 55, 54])).
% 2.03/2.26 tff(8353,plain,
% 2.03/2.26 (b(s(z), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[493, 8352])).
% 2.03/2.26 tff(8354,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6831, 162, 118, 227, 96, 6813, 6735, 8353])).
% 2.03/2.26 tff(8355,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(8356,plain,
% 2.03/2.26 (~r(s(s(z)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8355, 385, 54, 55])).
% 2.03/2.26 tff(8357,plain,
% 2.03/2.26 (b(s(s(z)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[271, 8356])).
% 2.03/2.26 tff(8358,plain,
% 2.03/2.26 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6758, 121, 8357, 54, 55])).
% 2.03/2.26 tff(8359,plain,
% 2.03/2.26 (b(s(s(s(z))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[459, 8358])).
% 2.03/2.26 tff(8360,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8361,plain,
% 2.03/2.26 (((~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(s(z)))) | (~b(s(z), 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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8362,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[8361])).
% 2.03/2.26 tff(8363,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[8362, 8360])).
% 2.03/2.26 tff(8364,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(8365,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[8364, 8363])).
% 2.03/2.26 tff(8366,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8365, 162, 444, 445, 383, 6735, 599])).
% 2.03/2.26 tff(8367,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(8368,plain,
% 2.03/2.26 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8367, 8359, 8357, 8353])).
% 2.03/2.26 tff(8369,plain,
% 2.03/2.26 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[442, 8368])).
% 2.03/2.26 tff(8370,plain,
% 2.03/2.26 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3094, 8369, 54])).
% 2.03/2.26 tff(8371,plain,
% 2.03/2.26 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[360, 8370])).
% 2.03/2.26 tff(8372,plain,
% 2.03/2.26 (~r(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[833, 8369, 55])).
% 2.03/2.26 tff(8373,plain,
% 2.03/2.26 (b(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[295, 8372])).
% 2.03/2.26 tff(8374,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8375,plain,
% 2.03/2.26 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8376,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[8375])).
% 2.03/2.26 tff(8377,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[8376, 8374])).
% 2.03/2.26 tff(8378,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(8379,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[8378, 8377])).
% 2.03/2.26 tff(8380,plain,
% 2.03/2.26 (~b(s(s(z)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8379, 162, 121, 8359, 8357, 6735, 8353])).
% 2.03/2.26 tff(8381,plain,
% 2.03/2.26 (r(s(s(z)), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[245, 8380])).
% 2.03/2.26 tff(8382,plain,
% 2.03/2.26 (~r(s(s(s(z))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1353, 8369, 385, 8381])).
% 2.03/2.26 tff(8383,plain,
% 2.03/2.26 (b(s(s(s(z))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[381, 8382])).
% 2.03/2.26 tff(8384,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[371, 8383, 96, 8373, 8371])).
% 2.03/2.26 tff(8385,plain,
% 2.03/2.26 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[338, 8384])).
% 2.03/2.26 tff(8386,plain,
% 2.03/2.26 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2517, 8385, 385])).
% 2.03/2.26 tff(8387,plain,
% 2.03/2.26 (b(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[191, 8386])).
% 2.03/2.26 tff(8388,plain,
% 2.03/2.26 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[185, 8387, 96, 121, 84])).
% 2.03/2.26 tff(8389,plain,
% 2.03/2.26 (~b(s(z), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7960, 8385, 96, 84, 385])).
% 2.03/2.26 tff(8390,plain,
% 2.03/2.26 (r(s(z), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[175, 8389])).
% 2.03/2.26 tff(8391,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6271, 5573, 120, 298, 297])).
% 2.03/2.26 tff(8392,plain,
% 2.03/2.26 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[337, 8391, 3642])).
% 2.03/2.26 tff(8393,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6251, 65, 123, 385, 8392])).
% 2.03/2.26 tff(8394,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(8395,plain,
% 2.03/2.26 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(z), z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8394, 333])).
% 2.03/2.26 tff(8396,plain,
% 2.03/2.26 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8395, 8390, 385, 8383, 84, 8373])).
% 2.03/2.26 tff(8397,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[149, 8396, 8388])).
% 2.03/2.26 tff(8398,plain,((~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(8399,plain,
% 2.03/2.26 (~b(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8398, 385, 55, 54])).
% 2.03/2.26 tff(8400,plain,
% 2.03/2.26 (r(z, s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[117, 8399])).
% 2.03/2.26 tff(8401,plain,
% 2.03/2.26 (~r(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6781, 8400, 55])).
% 2.03/2.26 tff(8402,plain,
% 2.03/2.26 (b(z, s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[295, 8401])).
% 2.03/2.26 tff(8403,plain,
% 2.03/2.26 (~r(s(s(s(z))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1377, 8400, 385])).
% 2.03/2.26 tff(8404,plain,
% 2.03/2.26 (b(s(s(s(z))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[381, 8403])).
% 2.03/2.26 tff(8405,plain,
% 2.03/2.26 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6271, 8404, 84, 96, 8402])).
% 2.03/2.26 tff(8406,plain,
% 2.03/2.26 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[338, 8405])).
% 2.03/2.26 tff(8407,plain,
% 2.03/2.26 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[373, 8404, 54, 96, 8402])).
% 2.03/2.26 tff(8408,plain,
% 2.03/2.26 (b(s(s(s(z))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[459, 8407])).
% 2.03/2.26 tff(8409,plain,
% 2.03/2.26 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8367, 8408, 8357, 8353])).
% 2.03/2.26 tff(8410,plain,
% 2.03/2.26 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[442, 8409])).
% 2.03/2.26 tff(8411,plain,
% 2.03/2.26 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[6350, 8410, 8406])).
% 2.03/2.26 tff(8412,plain,
% 2.03/2.26 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[216, 8411])).
% 2.03/2.26 tff(8413,plain,
% 2.03/2.26 (~b(s(z), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7960, 8406, 96, 84, 385])).
% 2.03/2.26 tff(8414,plain,
% 2.03/2.26 (r(s(z), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[175, 8413])).
% 2.03/2.26 tff(8415,plain,
% 2.03/2.26 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8395, 8414, 385, 8404, 84, 8402])).
% 2.03/2.26 tff(8416,plain,
% 2.03/2.26 (b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[149, 8415])).
% 2.03/2.26 tff(8417,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(8418,plain,
% 2.03/2.26 (((~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(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8419,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[8418])).
% 2.03/2.27 tff(8420,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[8419, 8417])).
% 2.03/2.27 tff(8421,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(8422,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8421, 8420])).
% 2.03/2.27 tff(8423,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8422, 162, 8416, 8408, 8412, 8357, 6735, 8353])).
% 2.03/2.27 tff(8424,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(8425,plain,
% 2.03/2.27 (~r(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8424, 55, 54])).
% 2.03/2.27 tff(8426,plain,
% 2.03/2.27 (b(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[595, 8425])).
% 2.03/2.27 tff(8427,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8428,plain,
% 2.03/2.27 (((~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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8429,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[8428])).
% 2.03/2.27 tff(8430,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[8429, 8427])).
% 2.03/2.27 tff(8431,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(8432,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8431, 8430])).
% 2.03/2.27 tff(8433,plain,
% 2.03/2.27 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8432, 162, 6770, 272, 6735, 8426])).
% 2.03/2.27 tff(8434,plain,
% 2.03/2.27 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[442, 8433])).
% 2.03/2.27 tff(8435,plain,
% 2.03/2.27 (~r(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[833, 8434, 55])).
% 2.03/2.27 tff(8436,plain,
% 2.03/2.27 (b(z, s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[295, 8435])).
% 2.03/2.27 tff(8437,plain,
% 2.03/2.27 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[3094, 8434, 54])).
% 2.03/2.27 tff(8438,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[360, 8437])).
% 2.03/2.27 tff(8439,plain,
% 2.03/2.27 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8432, 162, 445, 383, 6735, 600])).
% 2.03/2.27 tff(8440,plain,
% 2.03/2.27 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[442, 8439])).
% 2.03/2.27 tff(8441,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(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(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(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(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8442,plain,
% 2.03/2.27 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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(z, s(z))) | (~b(s(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(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8443,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(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(z)), s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[8442])).
% 2.03/2.27 tff(8444,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(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(z)), s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[8443, 8441])).
% 2.03/2.27 tff(8445,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(8446,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(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(z)), s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8445, 8444])).
% 2.03/2.27 tff(8447,plain,
% 2.03/2.27 (~b(s(s(z)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8446, 162, 121, 445, 383, 6735, 600])).
% 2.03/2.27 tff(8448,plain,
% 2.03/2.27 (r(s(s(z)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[245, 8447])).
% 2.03/2.27 tff(8449,plain,
% 2.03/2.27 (((~![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)), 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(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8450,plain,
% 2.03/2.27 (((~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(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8451,plain,
% 2.03/2.27 (((~![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(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[8450])).
% 2.03/2.27 tff(8452,plain,
% 2.03/2.27 (((~![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(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[8451, 8449])).
% 2.03/2.27 tff(8453,plain,
% 2.03/2.27 ((~![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))))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(8454,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8453, 8452])).
% 2.03/2.27 tff(8455,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8454, 65, 230, 417, 866])).
% 2.03/2.27 tff(8456,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(8457,plain,
% 2.03/2.27 (~r(s(s(s(z))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8456, 8448, 8440])).
% 2.03/2.27 tff(8458,plain,
% 2.03/2.27 (b(s(s(s(z))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[381, 8457])).
% 2.03/2.27 tff(8459,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8460,plain,
% 2.03/2.27 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8461,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[8460])).
% 2.03/2.27 tff(8462,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[8461, 8459])).
% 2.03/2.27 tff(8463,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(8464,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8463, 8462])).
% 2.03/2.27 tff(8465,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8464, 162, 121, 122, 363, 8458, 600, 297])).
% 2.03/2.27 tff(8466,plain,((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(8467,plain,
% 2.03/2.27 (~b(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8466, 96, 8438, 8426, 8436, 6770, 272])).
% 2.03/2.27 tff(8468,plain,
% 2.03/2.27 (r(z, s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[117, 8467])).
% 2.03/2.27 tff(8469,plain,
% 2.03/2.27 (~b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4407, 162, 6770, 272, 6735, 8426])).
% 2.03/2.27 tff(8470,plain,
% 2.03/2.27 (r(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[493, 8469])).
% 2.03/2.27 tff(8471,plain,
% 2.03/2.27 (~r(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1377, 866, 97])).
% 2.03/2.27 tff(8472,plain,
% 2.03/2.27 (b(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[595, 8471])).
% 2.03/2.27 tff(8473,plain,
% 2.03/2.27 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8432, 162, 445, 383, 4039, 8472])).
% 2.03/2.27 tff(8474,plain,
% 2.03/2.27 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[442, 8473])).
% 2.03/2.27 tff(8475,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8454, 65, 230, 8474, 866])).
% 2.03/2.27 tff(8476,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(8477,plain,
% 2.03/2.27 ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(z, s(z)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8476, 6735])).
% 2.03/2.27 tff(8478,plain,
% 2.03/2.27 (~r(s(s(z)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8477, 866, 383, 445, 97])).
% 2.03/2.27 tff(8479,plain,
% 2.03/2.27 (b(s(s(z)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[245, 8478])).
% 2.03/2.27 tff(8480,plain,
% 2.03/2.27 (~b(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4407, 162, 445, 383, 6735, 600])).
% 2.03/2.27 tff(8481,plain,
% 2.03/2.27 (r(s(z), s(s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[493, 8480])).
% 2.03/2.27 tff(8482,plain,
% 2.03/2.27 (~r(s(z), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2271, 866, 8481])).
% 2.03/2.27 tff(8483,plain,
% 2.03/2.27 (b(s(z), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[175, 8482])).
% 2.03/2.27 tff(8484,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8485,plain,
% 2.03/2.27 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(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(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8486,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[8485])).
% 2.03/2.27 tff(8487,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[8486, 8484])).
% 2.03/2.27 tff(8488,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(8489,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8488, 8487])).
% 2.03/2.27 tff(8490,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8489, 162, 8483, 8479, 445, 383, 6735, 600])).
% 2.03/2.27 tff(8491,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(8492,plain,
% 2.03/2.27 (~r(s(s(s(z))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[8491, 6770, 272, 8426, 8468])).
% 2.03/2.27 tff(8493,plain,
% 2.03/2.27 (b(s(s(s(z))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[381, 8492])).
% 2.03/2.27 tff(8494,plain,
% 2.03/2.27 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[6271, 8493, 84, 96, 8436])).
% 2.03/2.27 tff(8495,plain,
% 2.03/2.27 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[338, 8494])).
% 2.03/2.27 tff(8496,plain,
% 2.03/2.27 (~r(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7960, 152, 122, 120, 299])).
% 2.03/2.27 tff(8497,plain,
% 2.03/2.27 (b(s(s(s(z))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[595, 8496])).
% 2.03/2.27 tff(8498,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8499,plain,
% 2.03/2.27 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(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(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(8500,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[8499])).
% 2.03/2.28 tff(8501,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[8500, 8498])).
% 2.03/2.28 tff(8502,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(8503,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[8502, 8501])).
% 2.03/2.28 tff(8504,plain,
% 2.03/2.28 (~b(s(z), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8503, 162, 152, 445, 383, 298, 8497])).
% 2.03/2.28 tff(8505,plain,
% 2.03/2.28 (r(s(z), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[493, 8504])).
% 2.03/2.28 tff(8506,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8507,plain,
% 2.03/2.28 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8508,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[8507])).
% 2.03/2.28 tff(8509,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[8508, 8506])).
% 2.03/2.28 tff(8510,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(8511,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[8510, 8509])).
% 2.03/2.28 tff(8512,plain,
% 2.03/2.28 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8511, 162, 152, 122, 445, 383, 8497])).
% 2.03/2.28 tff(8513,plain,
% 2.03/2.28 (r(s(z), s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[191, 8512])).
% 2.03/2.28 tff(8514,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[476, 65, 8513, 8505, 299])).
% 2.03/2.28 tff(8515,plain,((~b(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(8516,plain,
% 2.03/2.28 (~b(s(z), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8515, 8495, 96, 272, 6770, 8493, 84])).
% 2.03/2.28 tff(8517,plain,
% 2.03/2.28 (r(s(z), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[175, 8516])).
% 2.03/2.28 tff(8518,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8309, 8493, 8434, 8468, 55])).
% 2.03/2.28 tff(8519,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[6873, 8518])).
% 2.03/2.28 tff(8520,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8521,plain,
% 2.03/2.28 (((~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(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8522,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[8521])).
% 2.03/2.28 tff(8523,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[8522, 8520])).
% 2.03/2.28 tff(8524,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(8525,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[8524, 8523])).
% 2.03/2.28 tff(8526,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8525, 162, 445, 383, 4039, 600, 825, 694])).
% 2.03/2.28 tff(8527,plain,((~b(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(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(8528,plain,
% 2.03/2.28 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8527, 6735])).
% 2.03/2.28 tff(8529,plain,
% 2.03/2.28 (~b(s(z), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8528, 8519, 8426, 272, 6770])).
% 2.03/2.28 tff(8530,plain,
% 2.03/2.28 (r(s(z), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[6862, 8529])).
% 2.03/2.28 tff(8531,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7993, 8530, 8517, 8470, 8436, 8468])).
% 2.03/2.28 tff(8532,plain,((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(8533,plain,
% 2.03/2.28 (~r(z, s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8532, 54])).
% 2.03/2.28 tff(8534,plain,
% 2.03/2.28 (b(z, s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[524, 8533])).
% 2.03/2.28 tff(8535,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8536,plain,
% 2.03/2.28 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8537,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[8536])).
% 2.03/2.28 tff(8538,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[8537, 8535])).
% 2.03/2.28 tff(8539,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(8540,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[8539, 8538])).
% 2.03/2.28 tff(8541,plain,
% 2.03/2.28 ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8540, 162, 121, 227, 8534, 6735])).
% 2.03/2.28 tff(8542,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8541, 3130])).
% 2.03/2.28 tff(8543,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[95, 8542])).
% 2.03/2.28 tff(8544,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3138, 65, 54, 8543, 230])).
% 2.03/2.28 tff(8545,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(8546,plain,
% 2.03/2.28 (~r(s(s(z)), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8545, 121, 54, 2])).
% 2.03/2.28 tff(8547,plain,
% 2.03/2.28 (b(s(s(z)), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[245, 8546])).
% 2.03/2.28 tff(8548,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[6811, 65, 385, 273, 2])).
% 2.03/2.28 tff(8549,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(8550,plain,
% 2.03/2.28 (~r(s(s(s(z))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8549, 273, 2])).
% 2.03/2.28 tff(8551,plain,
% 2.03/2.28 (b(s(s(s(z))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[595, 8550])).
% 2.03/2.28 tff(8552,plain,
% 2.03/2.28 (~b(s(z), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3288, 8551, 54, 227, 273])).
% 2.03/2.28 tff(8553,plain,
% 2.03/2.28 (r(s(z), s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[493, 8552])).
% 2.03/2.28 tff(8554,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8555,plain,
% 2.03/2.28 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8556,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[8555])).
% 2.03/2.28 tff(8557,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[8556, 8554])).
% 2.03/2.28 tff(8558,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(8559,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[8558, 8557])).
% 2.03/2.28 tff(8560,plain,
% 2.03/2.28 (~b(s(z), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8559, 162, 227, 8534, 3286, 6735, 8551])).
% 2.03/2.28 tff(8561,plain,
% 2.03/2.28 (r(s(z), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[175, 8560])).
% 2.03/2.28 tff(8562,plain,
% 2.03/2.28 (~r(z, s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1966, 8561, 8553])).
% 2.03/2.28 tff(8563,plain,
% 2.03/2.28 (b(z, s(s(s(z))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[295, 8562])).
% 2.03/2.28 tff(8564,plain,
% 2.03/2.28 (~r(s(s(z)), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[238, 8561, 2])).
% 2.03/2.28 tff(8565,plain,
% 2.03/2.28 (b(s(s(z)), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[245, 8564])).
% 2.03/2.28 tff(8566,plain,
% 2.03/2.28 (~r(s(s(s(z))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2271, 8561, 8553])).
% 2.03/2.28 tff(8567,plain,
% 2.03/2.28 (b(s(s(s(z))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[381, 8566])).
% 2.03/2.28 tff(8568,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8569,plain,
% 2.03/2.28 (((~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(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(8570,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[8569])).
% 2.03/2.28 tff(8571,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[8570, 8568])).
% 2.03/2.28 tff(8572,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(8573,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[8572, 8571])).
% 2.03/2.29 tff(8574,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8573, 162, 538, 537, 444, 298, 297])).
% 2.03/2.29 tff(8575,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(8576,plain,
% 2.03/2.29 (~b(s(s(z)), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8575, 8567, 8534, 8565, 8563])).
% 2.03/2.29 tff(8577,plain,
% 2.03/2.29 (r(s(s(z)), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[442, 8576])).
% 2.03/2.29 tff(8578,plain,
% 2.03/2.29 (((~![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(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), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8579,plain,
% 2.03/2.29 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8580,plain,
% 2.03/2.29 (((~![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), 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(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[8579])).
% 2.03/2.29 tff(8581,plain,
% 2.03/2.29 (((~![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), 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(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[8580, 8578])).
% 2.03/2.29 tff(8582,plain,
% 2.03/2.29 ((~![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), z)) | (~r(s(s(z)), s(z))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(8583,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[8582, 8581])).
% 2.03/2.29 tff(8584,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8583, 65, 8561, 8553, 8577, 2])).
% 2.03/2.29 tff(8585,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(8586,plain,
% 2.03/2.29 (~r(s(s(s(z))), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8585, 2, 54])).
% 2.03/2.29 tff(8587,plain,
% 2.03/2.29 (b(s(s(s(z))), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[459, 8586])).
% 2.03/2.29 tff(8588,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8589,plain,
% 2.03/2.29 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8590,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[8589])).
% 2.03/2.29 tff(8591,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[8590, 8588])).
% 2.03/2.29 tff(8592,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(8593,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[8592, 8591])).
% 2.03/2.29 tff(8594,plain,
% 2.03/2.29 ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8593, 162, 151, 537, 6735, 600])).
% 2.03/2.29 tff(8595,plain,
% 2.03/2.29 (~b(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8594, 363])).
% 2.03/2.29 tff(8596,plain,
% 2.03/2.29 (r(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[175, 8595])).
% 2.03/2.29 tff(8597,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8598,plain,
% 2.03/2.29 (((~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(s(elem!1)))), 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), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8599,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[8598])).
% 2.03/2.29 tff(8600,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), 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(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[8599, 8597])).
% 2.03/2.29 tff(8601,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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))))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(8602,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[8601, 8600])).
% 2.03/2.29 tff(8603,plain,
% 2.03/2.29 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8602, 162, 151, 445, 6735, 600])).
% 2.03/2.29 tff(8604,plain,
% 2.03/2.29 (~b(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8603, 363])).
% 2.03/2.29 tff(8605,plain,
% 2.03/2.29 (r(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[493, 8604])).
% 2.03/2.29 tff(8606,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2271, 8605, 8596, 866])).
% 2.03/2.29 tff(8607,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(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(8608,plain,
% 2.03/2.29 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8607, 866, 151, 445, 600, 8534])).
% 2.03/2.29 tff(8609,plain,
% 2.03/2.29 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[360, 8608])).
% 2.03/2.29 tff(8610,plain,
% 2.03/2.29 (~r(s(s(s(s(elem!1)))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[2601, 8609, 1])).
% 2.03/2.29 tff(8611,plain,
% 2.03/2.29 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[95, 8610])).
% 2.03/2.29 tff(8612,plain,
% 2.03/2.29 (~r(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[566, 8609, 1])).
% 2.03/2.29 tff(8613,plain,
% 2.03/2.29 (b(z, s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[83, 8612])).
% 2.03/2.29 tff(8614,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[6833, 8613, 8611, 54, 151, 445, 866, 121])).
% 2.03/2.29 tff(8615,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(8616,plain,
% 2.03/2.29 (~r(s(s(s(z))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8615, 600, 151, 445, 121, 1, 54])).
% 2.03/2.29 tff(8617,plain,
% 2.03/2.29 (b(s(s(s(z))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[381, 8616])).
% 2.03/2.29 tff(8618,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8619,plain,
% 2.03/2.29 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8620,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[8619])).
% 2.03/2.29 tff(8621,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[8620, 8618])).
% 2.03/2.29 tff(8622,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(8623,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[8622, 8621])).
% 2.03/2.29 tff(8624,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8623, 162, 121, 445, 4039, 298, 600, 599])).
% 2.03/2.29 tff(8625,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(8626,plain,
% 2.03/2.29 ((~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8625, 6735])).
% 2.03/2.29 tff(8627,plain,
% 2.03/2.29 (~b(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8626, 8617, 600, 445, 121])).
% 2.03/2.29 tff(8628,plain,
% 2.03/2.29 (r(s(z), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[493, 8627])).
% 2.03/2.29 tff(8629,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8630,plain,
% 2.03/2.29 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(8631,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[8630])).
% 2.03/2.29 tff(8632,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[8631, 8629])).
% 2.03/2.29 tff(8633,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(8634,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[8633, 8632])).
% 2.03/2.29 tff(8635,plain,
% 2.03/2.29 ((~b(s(z), z)) | (~b(s(s(s(z))), z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8634, 162, 121, 8534, 6735, 600])).
% 2.03/2.29 tff(8636,plain,
% 2.03/2.29 (~b(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8635, 8617])).
% 2.03/2.29 tff(8637,plain,
% 2.03/2.29 (r(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[175, 8636])).
% 2.03/2.29 tff(8638,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1966, 8637, 8628, 1])).
% 2.03/2.29 tff(8639,plain,((~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(8640,plain,
% 2.03/2.29 (~b(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8639, 121, 1, 8587, 227, 54])).
% 2.03/2.29 tff(8641,plain,
% 2.03/2.29 (r(s(s(s(z))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[595, 8640])).
% 2.03/2.29 tff(8642,plain,
% 2.03/2.29 (~r(s(s(z)), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[586, 8641, 2])).
% 2.03/2.29 tff(8643,plain,
% 2.03/2.29 (b(s(s(z)), s(s(s(z))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[442, 8642])).
% 2.03/2.29 tff(8644,plain,
% 2.03/2.29 (~b(s(s(s(z))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[3150, 8547, 8534, 8587, 8643])).
% 2.03/2.29 tff(8645,plain,
% 2.03/2.29 (r(s(s(s(z))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[381, 8644])).
% 2.03/2.29 tff(8646,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1389, 65, 194, 385, 866])).
% 2.03/2.29 tff(8647,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(8648,plain,
% 2.03/2.29 (~r(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8647, 8641, 8645])).
% 2.03/2.29 tff(8649,plain,
% 2.03/2.29 (b(s(z), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[175, 8648])).
% 2.03/2.29 tff(8650,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8651,plain,
% 2.13/2.30 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8652,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[8651])).
% 2.13/2.30 tff(8653,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[8652, 8650])).
% 2.13/2.30 tff(8654,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(8655,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[8654, 8653])).
% 2.13/2.30 tff(8656,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8655, 162, 8649, 121, 8547, 8534, 6735])).
% 2.13/2.30 tff(8657,plain,((~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8658,plain,
% 2.13/2.30 (~b(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8657, 1, 2, 54])).
% 2.13/2.30 tff(8659,plain,
% 2.13/2.30 (r(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[117, 8658])).
% 2.13/2.30 tff(8660,plain,
% 2.13/2.30 (~r(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3102, 8659, 1])).
% 2.13/2.30 tff(8661,plain,
% 2.13/2.30 (b(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[493, 8660])).
% 2.13/2.30 tff(8662,plain,
% 2.13/2.30 (~r(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2611, 8659, 1])).
% 2.13/2.30 tff(8663,plain,
% 2.13/2.30 (b(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[595, 8662])).
% 2.13/2.30 tff(8664,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8665,plain,
% 2.13/2.30 (((~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(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8666,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[8665])).
% 2.13/2.30 tff(8667,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[8666, 8664])).
% 2.13/2.30 tff(8668,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(8669,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[8668, 8667])).
% 2.13/2.30 tff(8670,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8669, 162, 444, 445, 4039, 600, 599])).
% 2.13/2.30 tff(8671,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8672,plain,
% 2.13/2.30 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8671, 6735])).
% 2.13/2.30 tff(8673,plain,
% 2.13/2.30 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8672, 8661, 8663, 8587])).
% 2.13/2.30 tff(8674,plain,
% 2.13/2.30 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[442, 8673])).
% 2.13/2.30 tff(8675,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3094, 8674, 54])).
% 2.13/2.30 tff(8676,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[360, 8675])).
% 2.13/2.30 tff(8677,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8602, 162, 227, 8676, 8587, 6735, 8663, 8661])).
% 2.13/2.30 tff(8678,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8679,plain,
% 2.13/2.30 (~r(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8678, 2, 54])).
% 2.13/2.30 tff(8680,plain,
% 2.13/2.30 (b(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[295, 8679])).
% 2.13/2.30 tff(8681,plain,
% 2.13/2.30 (~b(s(s(s(z))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3056, 538, 8534, 8587, 8680])).
% 2.13/2.30 tff(8682,plain,
% 2.13/2.30 (r(s(s(s(z))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[381, 8681])).
% 2.13/2.30 tff(8683,plain,
% 2.13/2.30 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1465, 538, 8534, 8587, 8680])).
% 2.13/2.30 tff(8684,plain,
% 2.13/2.30 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[442, 8683])).
% 2.13/2.30 tff(8685,plain,
% 2.13/2.30 (~r(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[586, 8684, 2])).
% 2.13/2.30 tff(8686,plain,
% 2.13/2.30 (b(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[595, 8685])).
% 2.13/2.30 tff(8687,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3094, 8684, 54])).
% 2.13/2.30 tff(8688,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[360, 8687])).
% 2.13/2.30 tff(8689,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8607, 8688, 8686, 227, 8587, 8682, 8534])).
% 2.13/2.30 tff(8690,plain,((~b(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8691,plain,
% 2.13/2.30 (~b(s(s(z)), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8690, 2, 54])).
% 2.13/2.30 tff(8692,plain,
% 2.13/2.30 (r(s(s(z)), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[245, 8691])).
% 2.13/2.30 tff(8693,plain,
% 2.13/2.30 (~b(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8545, 8692, 54, 2])).
% 2.13/2.30 tff(8694,plain,
% 2.13/2.30 (r(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[117, 8693])).
% 2.13/2.30 tff(8695,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[554, 65, 8694, 8692, 2])).
% 2.13/2.30 tff(8696,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8697,plain,
% 2.13/2.30 (~r(s(s(z)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8696, 53])).
% 2.13/2.30 tff(8698,plain,
% 2.13/2.30 (b(s(s(z)), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[271, 8697])).
% 2.13/2.30 tff(8699,plain,
% 2.13/2.30 (~r(z, s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8532, 53])).
% 2.13/2.30 tff(8700,plain,
% 2.13/2.30 (b(z, s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[524, 8699])).
% 2.13/2.30 tff(8701,plain,
% 2.13/2.30 (~b(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[373, 298, 53, 273, 6408])).
% 2.13/2.30 tff(8702,plain,
% 2.13/2.30 (r(z, s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[295, 8701])).
% 2.13/2.30 tff(8703,plain,
% 2.13/2.30 (~r(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2611, 8702, 97])).
% 2.13/2.30 tff(8704,plain,
% 2.13/2.30 (b(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[595, 8703])).
% 2.13/2.30 tff(8705,plain,
% 2.13/2.30 (~r(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3102, 8702, 97])).
% 2.13/2.30 tff(8706,plain,
% 2.13/2.30 (b(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[493, 8705])).
% 2.13/2.30 tff(8707,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6804, 686])).
% 2.13/2.30 tff(8708,plain,
% 2.13/2.30 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6855, 671])).
% 2.13/2.30 tff(8709,plain,
% 2.13/2.30 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[702, 8708, 599, 8707, 600])).
% 2.13/2.30 tff(8710,plain,
% 2.13/2.30 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6862, 8709])).
% 2.13/2.30 tff(8711,plain,
% 2.13/2.30 (~r(z, s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7971, 8710, 97])).
% 2.13/2.30 tff(8712,plain,
% 2.13/2.30 (b(z, s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[823, 8711])).
% 2.13/2.30 tff(8713,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4462, 8712, 298, 8708, 8707])).
% 2.13/2.30 tff(8714,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1089, 8713])).
% 2.13/2.30 tff(8715,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1634, 8708, 599, 8707, 600])).
% 2.13/2.30 tff(8716,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6793, 8715])).
% 2.13/2.30 tff(8717,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4524, 65, 97, 8716, 8714])).
% 2.13/2.30 tff(8718,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8719,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8718, 298, 97, 8706, 8704, 273])).
% 2.13/2.30 tff(8720,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6873, 8719])).
% 2.13/2.30 tff(8721,plain,
% 2.13/2.30 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4145, 6735])).
% 2.13/2.30 tff(8722,plain,
% 2.13/2.30 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8721, 8706, 8698, 8704])).
% 2.13/2.30 tff(8723,plain,
% 2.13/2.30 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[442, 8722])).
% 2.13/2.30 tff(8724,plain,
% 2.13/2.30 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[307, 273, 53])).
% 2.13/2.30 tff(8725,plain,
% 2.13/2.30 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[338, 8724])).
% 2.13/2.30 tff(8726,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[348, 273, 53])).
% 2.13/2.30 tff(8727,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[360, 8726])).
% 2.13/2.30 tff(8728,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[727])).
% 2.13/2.30 tff(8729,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[8728])).
% 2.13/2.30 tff(8730,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[825, 8729])).
% 2.13/2.30 tff(8731,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3, 8730])).
% 2.13/2.30 tff(8732,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(z))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8733,plain,
% 2.13/2.30 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8732, 825, 3])).
% 2.13/2.30 tff(8734,plain,
% 2.13/2.30 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7971, 803, 97])).
% 2.13/2.30 tff(8735,plain,
% 2.13/2.30 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6862, 8734])).
% 2.13/2.30 tff(8736,plain,
% 2.13/2.30 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8312, 8735, 383, 825])).
% 2.13/2.30 tff(8737,plain,
% 2.13/2.30 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8314, 8736])).
% 2.13/2.30 tff(8738,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8019, 65, 230, 8737, 803])).
% 2.13/2.30 tff(8739,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8740,plain,
% 2.13/2.30 (~r(z, s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8739, 825, 8698, 230, 97])).
% 2.13/2.30 tff(8741,plain,
% 2.13/2.30 (b(z, s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[823, 8740])).
% 2.13/2.30 tff(8742,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8743,plain,
% 2.13/2.30 (((~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)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(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)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8744,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[8743])).
% 2.13/2.30 tff(8745,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[8744, 8742])).
% 2.13/2.30 tff(8746,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(8747,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[8746, 8745])).
% 2.13/2.30 tff(8748,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8747, 162, 537, 825, 1075, 1369])).
% 2.13/2.30 tff(8749,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1089, 8748])).
% 2.13/2.30 tff(8750,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8751,plain,
% 2.13/2.30 (((~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)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(z, 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(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8752,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[8751])).
% 2.13/2.30 tff(8753,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[8752, 8750])).
% 2.13/2.30 tff(8754,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(8755,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8754, 8753])).
% 2.13/2.31 tff(8756,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8755, 162, 537, 6735, 825, 1075, 1369])).
% 2.13/2.31 tff(8757,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6793, 8756])).
% 2.13/2.31 tff(8758,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4524, 65, 97, 8757, 8749])).
% 2.13/2.31 tff(8759,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8760,plain,
% 2.13/2.31 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8759, 8741, 8700, 825, 97])).
% 2.13/2.31 tff(8761,plain,
% 2.13/2.31 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8314, 8760])).
% 2.13/2.31 tff(8762,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[796, 8761, 417])).
% 2.13/2.31 tff(8763,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6804, 8762])).
% 2.13/2.31 tff(8764,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8765,plain,
% 2.13/2.31 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8766,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8765])).
% 2.13/2.31 tff(8767,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8766, 8764])).
% 2.13/2.31 tff(8768,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~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)))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8769,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8768, 8767])).
% 2.13/2.31 tff(8770,plain,
% 2.13/2.31 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8769, 162, 6590, 363, 362, 298, 8763])).
% 2.13/2.31 tff(8771,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[763, 47, 8770, 8733])).
% 2.13/2.31 tff(8772,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8773,plain,
% 2.13/2.31 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8774,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8773])).
% 2.13/2.31 tff(8775,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8774, 8772])).
% 2.13/2.31 tff(8776,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8777,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8776, 8775])).
% 2.13/2.31 tff(8778,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8777, 162, 6590, 362, 298, 599, 8763])).
% 2.13/2.31 tff(8779,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6793, 8778])).
% 2.13/2.31 tff(8780,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[782, 65, 123, 8779, 8771])).
% 2.13/2.31 tff(8781,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(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(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | b(s(s(s(s(elem!1)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8782,plain,
% 2.13/2.31 (~r(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8781, 8720, 8727, 8725, 298, 8706, 8723, 97, 123, 3])).
% 2.13/2.31 tff(8783,plain,
% 2.13/2.31 (b(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[245, 8782])).
% 2.13/2.31 tff(8784,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8785,plain,
% 2.13/2.31 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8786,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8785])).
% 2.13/2.31 tff(8787,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8786, 8784])).
% 2.13/2.31 tff(8788,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8789,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8788, 8787])).
% 2.13/2.31 tff(8790,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8789, 162, 152, 538, 537, 383, 6735])).
% 2.13/2.31 tff(8791,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8792,plain,
% 2.13/2.31 (~b(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8791, 8783, 8700, 8698])).
% 2.13/2.31 tff(8793,plain,
% 2.13/2.31 (r(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[175, 8792])).
% 2.13/2.31 tff(8794,plain,
% 2.13/2.31 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8759, 1075, 537, 825, 97])).
% 2.13/2.31 tff(8795,plain,
% 2.13/2.31 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8314, 8794])).
% 2.13/2.31 tff(8796,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[796, 8795, 417])).
% 2.13/2.31 tff(8797,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6804, 8796])).
% 2.13/2.31 tff(8798,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1084, 1075, 537, 538, 825])).
% 2.13/2.31 tff(8799,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1089, 8798])).
% 2.13/2.31 tff(8800,plain,
% 2.13/2.31 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[5600, 8799, 194])).
% 2.13/2.31 tff(8801,plain,
% 2.13/2.31 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6862, 8800])).
% 2.13/2.31 tff(8802,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8803,plain,
% 2.13/2.31 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8804,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8803])).
% 2.13/2.31 tff(8805,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8804, 8802])).
% 2.13/2.31 tff(8806,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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)))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8807,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8806, 8805])).
% 2.13/2.31 tff(8808,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8807, 162, 120, 362, 298, 599, 8801, 8797])).
% 2.13/2.31 tff(8809,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8810,plain,
% 2.13/2.31 (~b(z, s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8809, 298, 8725, 6590, 8706, 8793, 8723, 8700, 8783, 8720, 97])).
% 2.13/2.31 tff(8811,plain,
% 2.13/2.31 (r(z, s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[823, 8810])).
% 2.13/2.31 tff(8812,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[811, 8811, 8702])).
% 2.13/2.31 tff(8813,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6804, 8812])).
% 2.13/2.31 tff(8814,plain,
% 2.13/2.31 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7971, 8811, 97])).
% 2.13/2.31 tff(8815,plain,
% 2.13/2.31 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6862, 8814])).
% 2.13/2.31 tff(8816,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8807, 162, 6590, 8725, 298, 8706, 8815, 8813])).
% 2.13/2.31 tff(8817,plain,((~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8818,plain,
% 2.13/2.31 (~b(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8817, 97, 123, 3, 273])).
% 2.13/2.31 tff(8819,plain,
% 2.13/2.31 (r(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[381, 8818])).
% 2.13/2.31 tff(8820,plain,
% 2.13/2.31 (~r(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1377, 8819, 97])).
% 2.13/2.31 tff(8821,plain,
% 2.13/2.31 (b(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[595, 8820])).
% 2.13/2.31 tff(8822,plain,
% 2.13/2.31 (~r(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2028, 8819, 273])).
% 2.13/2.31 tff(8823,plain,
% 2.13/2.31 (b(s(s(z)), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[245, 8822])).
% 2.13/2.31 tff(8824,plain,
% 2.13/2.31 (~b(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8791, 8823, 8700, 8698])).
% 2.13/2.31 tff(8825,plain,
% 2.13/2.31 (r(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[175, 8824])).
% 2.13/2.31 tff(8826,plain,
% 2.13/2.31 (~r(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2271, 8825, 8819])).
% 2.13/2.31 tff(8827,plain,
% 2.13/2.31 (b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[493, 8826])).
% 2.13/2.31 tff(8828,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8829,plain,
% 2.13/2.31 (((~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(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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8830,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8829])).
% 2.13/2.31 tff(8831,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(elem!1)))))) | (~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(s(z)))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8830, 8828])).
% 2.13/2.31 tff(8832,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8833,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8832, 8831])).
% 2.13/2.31 tff(8834,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8833, 162, 363, 362, 693, 692, 3211])).
% 2.13/2.31 tff(8835,plain,((~b(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8836,plain,
% 2.13/2.31 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8835, 8708, 3286, 3284, 8707])).
% 2.13/2.31 tff(8837,plain,
% 2.13/2.31 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[763, 47, 8836, 6885])).
% 2.13/2.31 tff(8838,plain,
% 2.13/2.31 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8837])).
% 2.13/2.31 tff(8839,plain,
% 2.13/2.31 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[20, 8838, 630])).
% 2.13/2.31 tff(8840,plain,
% 2.13/2.31 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8839])).
% 2.13/2.31 tff(8841,plain,
% 2.13/2.31 (s(s(elem!1)) = s(s(z))),
% 2.13/2.31 inference(transitivity,[status(thm)],[25, 8840, 312])).
% 2.13/2.31 tff(8842,plain,
% 2.13/2.31 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8841])).
% 2.13/2.31 tff(8843,plain,
% 2.13/2.31 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.13/2.31 inference(symmetry,[status(thm)],[8842])).
% 2.13/2.31 tff(8844,plain,
% 2.13/2.31 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8841])).
% 2.13/2.31 tff(8845,plain,
% 2.13/2.31 (s(elem!1) = s(z)),
% 2.13/2.31 inference(transitivity,[status(thm)],[325, 8844, 15])).
% 2.13/2.31 tff(8846,plain,
% 2.13/2.31 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8845])).
% 2.13/2.31 tff(8847,plain,
% 2.13/2.31 (elem!1 = z),
% 2.13/2.31 inference(transitivity,[status(thm)],[1171, 8846, 13])).
% 2.13/2.31 tff(8848,plain,
% 2.13/2.31 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8847])).
% 2.13/2.32 tff(8849,plain,
% 2.13/2.32 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.13/2.32 inference(symmetry,[status(thm)],[8848])).
% 2.13/2.32 tff(8850,plain,
% 2.13/2.32 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[8849, 8843])).
% 2.13/2.32 tff(8851,plain,
% 2.13/2.32 (b(elem!1, s(s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8534, 8850])).
% 2.13/2.32 tff(8852,plain,
% 2.13/2.32 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8841])).
% 2.13/2.32 tff(8853,plain,
% 2.13/2.32 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8852])).
% 2.13/2.32 tff(8854,plain,
% 2.13/2.32 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8847])).
% 2.13/2.32 tff(8855,plain,
% 2.13/2.32 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8854])).
% 2.13/2.32 tff(8856,plain,
% 2.13/2.32 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(transitivity,[status(thm)],[8855, 8853])).
% 2.13/2.32 tff(8857,plain,
% 2.13/2.32 (b(s(s(z)), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[245, 3420])).
% 2.13/2.32 tff(8858,plain,
% 2.13/2.32 (b(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8857, 8856])).
% 2.13/2.32 tff(8859,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8837])).
% 2.13/2.32 tff(8860,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[8859])).
% 2.13/2.32 tff(8861,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8847])).
% 2.13/2.32 tff(8862,plain,
% 2.13/2.32 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[8861])).
% 2.13/2.32 tff(8863,plain,
% 2.13/2.32 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[8862, 8860])).
% 2.13/2.32 tff(8864,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8712, 8863])).
% 2.13/2.32 tff(8865,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8837])).
% 2.13/2.32 tff(8866,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8865])).
% 2.13/2.32 tff(8867,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8847])).
% 2.13/2.32 tff(8868,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8867])).
% 2.13/2.32 tff(8869,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.32 inference(transitivity,[status(thm)],[8868, 8866])).
% 2.13/2.32 tff(8870,plain,
% 2.13/2.32 (~r(s(s(z)), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8696, 54])).
% 2.13/2.32 tff(8871,plain,
% 2.13/2.32 (b(s(s(z)), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[271, 8870])).
% 2.13/2.32 tff(8872,plain,
% 2.13/2.32 (~b(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8791, 8857, 8534, 8871])).
% 2.13/2.32 tff(8873,plain,
% 2.13/2.32 (r(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[175, 8872])).
% 2.13/2.32 tff(8874,plain,
% 2.13/2.32 (~r(s(s(s(s(z)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[5600, 8710, 8873])).
% 2.13/2.32 tff(8875,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1089, 8874])).
% 2.13/2.32 tff(8876,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8875, 8869])).
% 2.13/2.32 tff(8877,plain,
% 2.13/2.32 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8845])).
% 2.13/2.32 tff(8878,plain,
% 2.13/2.32 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8877])).
% 2.13/2.32 tff(8879,plain,
% 2.13/2.32 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8847])).
% 2.13/2.32 tff(8880,plain,
% 2.13/2.32 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8879])).
% 2.13/2.32 tff(8881,plain,
% 2.13/2.32 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.13/2.32 inference(transitivity,[status(thm)],[8880, 8878])).
% 2.13/2.32 tff(8882,plain,
% 2.13/2.32 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8881])).
% 2.13/2.32 tff(8883,plain,
% 2.13/2.32 (~b(s(elem!1), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8872, 8882])).
% 2.13/2.32 tff(8884,plain,
% 2.13/2.32 (r(s(elem!1), z) <=> r(s(z), z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8845])).
% 2.13/2.32 tff(8885,plain,
% 2.13/2.32 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8884])).
% 2.13/2.32 tff(8886,plain,
% 2.13/2.32 (r(s(elem!1), z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8873, 8885])).
% 2.13/2.32 tff(8887,plain,
% 2.13/2.32 (b(elem!1, z) <=> b(z, z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8847])).
% 2.13/2.32 tff(8888,plain,
% 2.13/2.32 (b(z, z) <=> b(elem!1, z)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8887])).
% 2.13/2.32 tff(8889,plain,
% 2.13/2.32 ((~b(z, z)) <=> (~b(elem!1, z))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8888])).
% 2.13/2.32 tff(8890,plain,
% 2.13/2.32 (~b(elem!1, z)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[3433, 8889])).
% 2.13/2.32 tff(8891,plain,
% 2.13/2.32 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8841])).
% 2.13/2.32 tff(8892,plain,
% 2.13/2.32 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8891])).
% 2.13/2.32 tff(8893,plain,
% 2.13/2.32 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8847])).
% 2.13/2.32 tff(8894,plain,
% 2.13/2.32 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.13/2.32 inference(symmetry,[status(thm)],[8893])).
% 2.13/2.32 tff(8895,plain,
% 2.13/2.32 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(transitivity,[status(thm)],[8894, 8892])).
% 2.13/2.32 tff(8896,plain,
% 2.13/2.32 ((~r(s(s(z)), z)) <=> (~r(s(s(elem!1)), elem!1))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8895])).
% 2.13/2.32 tff(8897,plain,
% 2.13/2.32 (~r(s(s(elem!1)), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[3420, 8896])).
% 2.13/2.32 tff(8898,plain,
% 2.13/2.32 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[4497, 8897, 122, 8890, 8886, 8883])).
% 2.13/2.32 tff(8899,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7507, 8898, 8876, 8864, 8858, 8851])).
% 2.13/2.32 tff(8900,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | r(s(s(z)), z) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(8901,plain,
% 2.13/2.32 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8900, 6408, 8822, 97, 8827, 8821, 273, 53])).
% 2.13/2.32 tff(8902,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6873, 8901])).
% 2.13/2.32 tff(8903,plain,
% 2.13/2.32 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8721, 599, 383, 8472])).
% 2.13/2.32 tff(8904,plain,
% 2.13/2.32 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[442, 8903])).
% 2.13/2.32 tff(8905,plain,
% 2.13/2.32 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[796, 8737, 8904])).
% 2.13/2.32 tff(8906,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6804, 8905])).
% 2.13/2.32 tff(8907,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[702, 8906, 599, 8735, 8472])).
% 2.13/2.32 tff(8908,plain,
% 2.13/2.32 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6855, 8907])).
% 2.13/2.32 tff(8909,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[3182, 65, 803, 866, 8908])).
% 2.13/2.32 tff(8910,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(8911,plain,
% 2.13/2.32 (~r(z, s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8910, 8819, 8827, 8698, 8902, 97])).
% 2.13/2.32 tff(8912,plain,
% 2.13/2.32 (b(z, s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[823, 8911])).
% 2.13/2.32 tff(8913,plain,
% 2.13/2.32 (~b(s(s(s(s(z)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1084, 8912, 8700, 8823, 8902])).
% 2.13/2.32 tff(8914,plain,
% 2.13/2.32 (r(s(s(s(s(z)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1089, 8913])).
% 2.13/2.32 tff(8915,plain,
% 2.13/2.32 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[5600, 8914, 8825])).
% 2.13/2.32 tff(8916,plain,
% 2.13/2.32 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6862, 8915])).
% 2.13/2.32 tff(8917,plain,
% 2.13/2.32 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8721, 8827, 8698, 8821])).
% 2.13/2.32 tff(8918,plain,
% 2.13/2.32 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[442, 8917])).
% 2.13/2.32 tff(8919,plain,
% 2.13/2.32 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8759, 8912, 8700, 8902, 97])).
% 2.13/2.32 tff(8920,plain,
% 2.13/2.32 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8314, 8919])).
% 2.13/2.32 tff(8921,plain,
% 2.13/2.32 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[796, 8920, 8918])).
% 2.13/2.32 tff(8922,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6804, 8921])).
% 2.13/2.32 tff(8923,plain,
% 2.13/2.32 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[702, 8922, 8827, 8916, 8821])).
% 2.13/2.32 tff(8924,plain,
% 2.13/2.32 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6855, 8923])).
% 2.13/2.32 tff(8925,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2426, 65, 273, 8920, 8924])).
% 2.13/2.32 tff(8926,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | b(s(s(s(s(elem!1)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(8927,plain,
% 2.13/2.32 (~r(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8926, 123, 273, 3])).
% 2.13/2.32 tff(8928,plain,
% 2.13/2.32 (b(z, s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[117, 8927])).
% 2.13/2.32 tff(8929,plain,
% 2.13/2.32 ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[7028, 6735])).
% 2.13/2.32 tff(8930,plain,
% 2.13/2.32 (~b(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8929, 8928, 8700, 8698])).
% 2.13/2.32 tff(8931,plain,
% 2.13/2.32 (r(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[175, 8930])).
% 2.13/2.32 tff(8932,plain,
% 2.13/2.32 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[2260, 8931, 123])).
% 2.13/2.32 tff(8933,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[95, 8932])).
% 2.13/2.32 tff(8934,plain,
% 2.13/2.32 (~r(s(s(s(z))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6754, 8928, 8698, 273])).
% 2.13/2.32 tff(8935,plain,
% 2.13/2.32 (b(s(s(s(z))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[381, 8934])).
% 2.13/2.32 tff(8936,plain,
% 2.13/2.32 (~b(z, s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[373, 8933, 53, 273, 8935])).
% 2.13/2.32 tff(8937,plain,
% 2.13/2.32 (r(z, s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[295, 8936])).
% 2.13/2.32 tff(8938,plain,
% 2.13/2.32 (~r(s(z), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1966, 8937, 8931])).
% 2.13/2.32 tff(8939,plain,
% 2.13/2.32 (b(s(z), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[493, 8938])).
% 2.13/2.32 tff(8940,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(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(z))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8941,plain,
% 2.13/2.32 (((~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(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(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(z))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8942,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(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(z)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8941])).
% 2.13/2.32 tff(8943,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(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(z))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[8942, 8940])).
% 2.13/2.32 tff(8944,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(8945,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(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(z)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8944, 8943])).
% 2.13/2.32 tff(8946,plain,
% 2.13/2.32 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8945, 162, 8928, 8700, 8727, 8698, 8939])).
% 2.13/2.32 tff(8947,plain,
% 2.13/2.32 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[191, 8946])).
% 2.13/2.32 tff(8948,plain,
% 2.13/2.32 (~b(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8929, 121, 8700, 8698])).
% 2.13/2.32 tff(8949,plain,
% 2.13/2.32 (r(s(z), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[175, 8948])).
% 2.13/2.32 tff(8950,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8951,plain,
% 2.13/2.32 (((~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(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8952,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8951])).
% 2.13/2.32 tff(8953,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[8952, 8950])).
% 2.13/2.32 tff(8954,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(8955,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8954, 8953])).
% 2.13/2.32 tff(8956,plain,
% 2.13/2.32 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8955, 162, 121, 8700, 8698, 6735, 825])).
% 2.13/2.32 tff(8957,plain,
% 2.13/2.32 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6862, 8956])).
% 2.13/2.32 tff(8958,plain,
% 2.13/2.32 (~r(s(s(s(s(z)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[5600, 8957, 8949])).
% 2.13/2.32 tff(8959,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), z)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1089, 8958])).
% 2.13/2.32 tff(8960,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8961,plain,
% 2.13/2.32 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~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(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8962,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8961])).
% 2.13/2.32 tff(8963,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[8962, 8960])).
% 2.13/2.32 tff(8964,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(8965,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8964, 8963])).
% 2.13/2.32 tff(8966,plain,
% 2.13/2.32 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8965, 162, 121, 122, 8700, 8698, 8959])).
% 2.13/2.32 tff(8967,plain,
% 2.13/2.32 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[763, 47, 8966, 8733])).
% 2.13/2.32 tff(8968,plain,
% 2.13/2.32 (((~![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)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8969,plain,
% 2.13/2.32 (((~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)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(8970,plain,
% 2.13/2.32 (((~![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)))), 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))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[8969])).
% 2.13/2.32 tff(8971,plain,
% 2.13/2.32 (((~![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)))), 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)))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[8970, 8968])).
% 2.13/2.32 tff(8972,plain,
% 2.13/2.32 ((~![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)))), 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)))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(8973,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[8972, 8971])).
% 2.13/2.32 tff(8974,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8973, 65, 193, 8957, 8967])).
% 2.13/2.32 tff(8975,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | b(s(s(s(s(elem!1)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(8976,plain,
% 2.13/2.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8975, 8947, 8928, 8933, 3])).
% 2.13/2.32 tff(8977,plain,
% 2.13/2.32 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6873, 8976])).
% 2.13/2.32 tff(8978,plain,
% 2.13/2.32 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[685, 65, 273, 8977])).
% 2.13/2.32 tff(8979,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6804, 8978])).
% 2.13/2.32 tff(8980,plain,
% 2.13/2.32 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[670, 65, 273, 8977])).
% 2.13/2.32 tff(8981,plain,
% 2.13/2.32 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6855, 8980])).
% 2.13/2.32 tff(8982,plain,
% 2.13/2.32 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[503, 8947, 8931])).
% 2.13/2.32 tff(8983,plain,
% 2.13/2.32 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[83, 8982])).
% 2.13/2.33 tff(8984,plain,
% 2.13/2.33 (((~![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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(8985,plain,
% 2.13/2.33 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(8986,plain,
% 2.13/2.33 (((~![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(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(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[8985])).
% 2.13/2.33 tff(8987,plain,
% 2.13/2.33 (((~![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(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(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[8986, 8984])).
% 2.13/2.33 tff(8988,plain,
% 2.13/2.33 ((~![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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(8989,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[8988, 8987])).
% 2.13/2.33 tff(8990,plain,
% 2.13/2.33 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[8989, 65, 385, 273, 644])).
% 2.13/2.33 tff(8991,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6804, 8990])).
% 2.13/2.33 tff(8992,plain,
% 2.13/2.33 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[8807, 162, 120, 362, 298, 599, 8991])).
% 2.13/2.33 tff(8993,plain,
% 2.13/2.33 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6862, 8992])).
% 2.13/2.33 tff(8994,plain,
% 2.13/2.33 (~r(s(s(s(s(z)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[5600, 8993, 194])).
% 2.13/2.33 tff(8995,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1089, 8994])).
% 2.13/2.33 tff(8996,plain,
% 2.13/2.33 (~r(z, s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[5603, 8993, 194])).
% 2.13/2.33 tff(8997,plain,
% 2.13/2.33 (b(z, s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[823, 8996])).
% 2.13/2.33 tff(8998,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4462, 8997, 8995, 298, 8708, 8991])).
% 2.13/2.33 tff(8999,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9000,plain,
% 2.13/2.33 (~r(s(s(s(z))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[8999, 8977, 8931, 8983, 8725, 8939, 8935, 273])).
% 2.13/2.33 tff(9001,plain,
% 2.13/2.33 (b(s(s(s(z))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[595, 9000])).
% 2.13/2.33 tff(9002,plain,
% 2.13/2.33 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[702, 8981, 8939, 9001, 8979])).
% 2.13/2.33 tff(9003,plain,
% 2.13/2.33 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6862, 9002])).
% 2.13/2.33 tff(9004,plain,
% 2.13/2.33 (~r(s(s(s(s(z)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[5600, 9003, 8931])).
% 2.13/2.33 tff(9005,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1089, 9004])).
% 2.13/2.33 tff(9006,plain,
% 2.13/2.33 (~r(z, s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[5603, 9003, 8931])).
% 2.13/2.33 tff(9007,plain,
% 2.13/2.33 (b(z, s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[823, 9006])).
% 2.13/2.33 tff(9008,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[4462, 9007, 9005, 8935, 8981, 8979])).
% 2.13/2.33 tff(9009,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9010,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9009, 273, 3])).
% 2.13/2.33 tff(9011,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[149, 9010])).
% 2.13/2.33 tff(9012,plain,
% 2.13/2.33 ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6743, 6735])).
% 2.13/2.33 tff(9013,plain,
% 2.13/2.33 (~b(s(s(z)), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9012, 121, 8534, 8871])).
% 2.13/2.33 tff(9014,plain,
% 2.13/2.33 (r(s(s(z)), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[245, 9013])).
% 2.13/2.33 tff(9015,plain,
% 2.13/2.33 (~r(s(s(s(z))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6754, 121, 8871, 273])).
% 2.13/2.33 tff(9016,plain,
% 2.13/2.33 (b(s(s(s(z))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[381, 9015])).
% 2.13/2.33 tff(9017,plain,
% 2.13/2.33 (~b(s(z), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[8929, 121, 8534, 8871])).
% 2.13/2.33 tff(9018,plain,
% 2.13/2.33 (r(s(z), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[175, 9017])).
% 2.13/2.33 tff(9019,plain,
% 2.13/2.33 (~r(z, s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1966, 9018, 395])).
% 2.13/2.33 tff(9020,plain,
% 2.13/2.33 (b(z, s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[295, 9019])).
% 2.13/2.33 tff(9021,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[373, 9020, 54, 273, 9016])).
% 2.13/2.33 tff(9022,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[95, 9021])).
% 2.13/2.33 tff(9023,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3138, 65, 54, 9022, 9014])).
% 2.13/2.33 tff(9024,plain,((~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9025,plain,
% 2.13/2.33 (~b(z, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9024, 395, 273, 54])).
% 2.13/2.33 tff(9026,plain,
% 2.13/2.33 (r(z, s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[117, 9025])).
% 2.13/2.33 tff(9027,plain,
% 2.13/2.33 (~r(z, s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[3102, 9026, 395])).
% 2.13/2.33 tff(9028,plain,
% 2.13/2.33 (b(z, s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[295, 9027])).
% 2.13/2.33 tff(9029,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[5561, 2252, 97])).
% 2.13/2.33 tff(9030,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[149, 9029])).
% 2.13/2.33 tff(9031,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(9032,plain,
% 2.13/2.33 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(9033,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[9032])).
% 2.13/2.33 tff(9034,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[9033, 9031])).
% 2.13/2.33 tff(9035,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(9036,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[9035, 9034])).
% 2.13/2.33 tff(9037,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9036, 162, 416, 151, 526, 383, 4039])).
% 2.13/2.33 tff(9038,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9039,plain,
% 2.13/2.33 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9038, 4982, 383, 4039, 9030])).
% 2.13/2.33 tff(9040,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[214, 47, 4989, 9039, 209])).
% 2.13/2.33 tff(9041,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9042,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9041, 383, 4039, 230, 97])).
% 2.13/2.33 tff(9043,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[95, 9042])).
% 2.13/2.33 tff(9044,plain,
% 2.13/2.33 (~r(s(s(s(z))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2028, 273, 230])).
% 2.13/2.33 tff(9045,plain,
% 2.13/2.33 (b(s(s(s(z))), z)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[381, 9044])).
% 2.13/2.33 tff(9046,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[373, 9045, 9043, 297, 273])).
% 2.13/2.33 tff(9047,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[52, 9046])).
% 2.13/2.33 tff(9048,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1431, 495, 97])).
% 2.13/2.33 tff(9049,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[149, 9048])).
% 2.13/2.33 tff(9050,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7475, 162, 416, 177, 151, 383, 4039])).
% 2.13/2.33 tff(9051,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(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))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9052,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9051, 6655, 9049, 383, 416, 4039])).
% 2.13/2.33 tff(9053,plain,((~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9054,plain,
% 2.13/2.33 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9053, 9047, 383, 4039, 97])).
% 2.13/2.33 tff(9055,plain,
% 2.13/2.33 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[83, 9054])).
% 2.13/2.33 tff(9056,plain,
% 2.13/2.33 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[6271, 120, 297, 122, 298])).
% 2.13/2.33 tff(9057,plain,
% 2.13/2.33 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[338, 9056])).
% 2.13/2.33 tff(9058,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(9059,plain,
% 2.13/2.33 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), 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(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(9060,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[9059])).
% 2.13/2.33 tff(9061,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[9060, 9058])).
% 2.13/2.33 tff(9062,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(9063,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[9062, 9061])).
% 2.13/2.33 tff(9064,plain,
% 2.13/2.33 (~b(s(z), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9063, 162, 152, 416, 151, 383, 298])).
% 2.13/2.33 tff(9065,plain,
% 2.13/2.33 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9051, 151, 383, 416, 4039])).
% 2.13/2.33 tff(9066,plain,
% 2.13/2.33 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[191, 9065])).
% 2.13/2.33 tff(9067,plain,
% 2.13/2.33 (~r(s(z), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[476, 65, 9066, 299])).
% 2.13/2.33 tff(9068,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[493, 9067, 9064])).
% 2.13/2.33 tff(9069,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(9070,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9069, 152, 9057, 416, 383, 298, 4039])).
% 2.13/2.33 tff(9071,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[149, 9070])).
% 2.13/2.33 tff(9072,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(9073,plain,
% 2.13/2.33 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(9074,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[9073])).
% 2.13/2.33 tff(9075,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[9074, 9072])).
% 2.13/2.33 tff(9076,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), 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)))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(9077,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[9076, 9075])).
% 2.13/2.34 tff(9078,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9077, 162, 416, 177, 526, 383, 4039])).
% 2.13/2.34 tff(9079,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(9080,plain,
% 2.13/2.34 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9079, 177, 383, 4039, 416])).
% 2.13/2.34 tff(9081,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9082,plain,
% 2.13/2.34 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9083,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[9082])).
% 2.13/2.34 tff(9084,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.34 inference(transitivity,[status(thm)],[9083, 9081])).
% 2.13/2.34 tff(9085,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(9086,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[9085, 9084])).
% 2.13/2.34 tff(9087,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9086, 162, 152, 177, 122, 120, 298])).
% 2.13/2.34 tff(9088,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[360, 9087])).
% 2.13/2.34 tff(9089,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2549, 9088, 123])).
% 2.13/2.34 tff(9090,plain,
% 2.13/2.34 (b(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[595, 9089])).
% 2.13/2.34 tff(9091,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9092,plain,
% 2.13/2.34 (((~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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9093,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[9092])).
% 2.13/2.34 tff(9094,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[9093, 9091])).
% 2.13/2.34 tff(9095,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(9096,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[9095, 9094])).
% 2.13/2.34 tff(9097,plain,
% 2.13/2.34 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9096, 162, 152, 177, 122, 383, 9090])).
% 2.13/2.34 tff(9098,plain,
% 2.13/2.34 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[442, 9097])).
% 2.13/2.34 tff(9099,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(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(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(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9100,plain,
% 2.13/2.34 (((~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(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(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9101,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), 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(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[9100])).
% 2.13/2.34 tff(9102,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), 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(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[9101, 9099])).
% 2.13/2.34 tff(9103,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(9104,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[9103, 9102])).
% 2.13/2.34 tff(9105,plain,
% 2.13/2.34 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9104, 65, 123, 9098, 9088])).
% 2.13/2.34 tff(9106,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[214, 47, 9105, 9080, 209])).
% 2.13/2.34 tff(9107,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(9108,plain,
% 2.13/2.34 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9107, 9071, 152, 122, 383, 120, 298, 4039, 416])).
% 2.13/2.34 tff(9109,plain,
% 2.13/2.34 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[191, 9108])).
% 2.13/2.34 tff(9110,plain,
% 2.13/2.34 (~r(s(z), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[476, 65, 9109, 9057])).
% 2.13/2.34 tff(9111,plain,
% 2.13/2.34 (b(s(z), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[493, 9110])).
% 2.13/2.34 tff(9112,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2515, 65, 9109, 9057])).
% 2.13/2.34 tff(9113,plain,
% 2.13/2.34 (b(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[595, 9112])).
% 2.13/2.34 tff(9114,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[5887, 162, 152, 298, 9113, 9111, 297])).
% 2.13/2.34 tff(9115,plain,((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(9116,plain,
% 2.13/2.34 (~b(s(z), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9115, 9045, 297, 9043, 383, 9055, 4039, 9047])).
% 2.13/2.34 tff(9117,plain,
% 2.13/2.34 (r(s(z), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[175, 9116])).
% 2.13/2.34 tff(9118,plain,
% 2.13/2.34 (~r(z, s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2609, 65, 97, 385])).
% 2.13/2.34 tff(9119,plain,
% 2.13/2.34 (b(z, s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[293, 47, 9118, 288])).
% 2.13/2.34 tff(9120,plain,
% 2.13/2.34 (~r(s(s(z)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[236, 65, 194, 230])).
% 2.13/2.34 tff(9121,plain,
% 2.13/2.34 (b(s(s(z)), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[271, 9120])).
% 2.13/2.34 tff(9122,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[8394, 120, 3642, 385, 298, 297, 194])).
% 2.13/2.34 tff(9123,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[149, 9122])).
% 2.13/2.34 tff(9124,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9051, 9123, 177, 9121, 4039])).
% 2.13/2.34 tff(9125,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[52, 9124])).
% 2.13/2.34 tff(9126,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[307, 9125, 273])).
% 2.13/2.34 tff(9127,plain,
% 2.13/2.34 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[337, 9126, 3642])).
% 2.13/2.34 tff(9128,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6271, 9127, 120, 298, 297])).
% 2.13/2.34 tff(9129,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[95, 9128])).
% 2.13/2.34 tff(9130,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3138, 65, 9125, 9129, 230])).
% 2.13/2.34 tff(9131,plain,((~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(9132,plain,
% 2.13/2.34 (~b(z, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9131, 3642, 298, 9119, 230, 273, 177, 4039, 385, 194])).
% 2.13/2.34 tff(9133,plain,
% 2.13/2.34 (r(z, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[83, 9132])).
% 2.13/2.34 tff(9134,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1431, 9133, 97])).
% 2.13/2.34 tff(9135,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[149, 9134])).
% 2.13/2.34 tff(9136,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9051, 9135, 177, 9121, 4039])).
% 2.13/2.34 tff(9137,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[52, 9136])).
% 2.13/2.34 tff(9138,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[307, 9137, 273])).
% 2.13/2.34 tff(9139,plain,
% 2.13/2.34 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[337, 9138, 3642])).
% 2.13/2.34 tff(9140,plain,
% 2.13/2.34 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[7252])).
% 2.13/2.34 tff(9141,plain,
% 2.13/2.34 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[3642, 9140])).
% 2.13/2.34 tff(9142,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9143,plain,
% 2.13/2.34 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(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(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9144,plain,
% 2.13/2.34 (((~![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(z)))) | (~r(s(s(s(s(elem!1)))), s(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(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[9143])).
% 2.13/2.34 tff(9145,plain,
% 2.13/2.34 (((~![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(z)))) | (~r(s(s(s(s(elem!1)))), s(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(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[9144, 9142])).
% 2.13/2.34 tff(9146,plain,
% 2.13/2.34 ((~![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(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(9147,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[9146, 9145])).
% 2.13/2.34 tff(9148,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9147, 65, 9137, 385, 273])).
% 2.13/2.34 tff(9149,plain,
% 2.13/2.34 ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[358, 47, 9148])).
% 2.13/2.34 tff(9150,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9149, 9141])).
% 2.13/2.34 tff(9151,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[371, 9150, 9139, 298, 9119])).
% 2.13/2.34 tff(9152,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[95, 9151])).
% 2.13/2.34 tff(9153,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3138, 65, 9137, 9152, 230])).
% 2.13/2.34 tff(9154,plain,((s(s(s(z))) = s(s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(9155,plain,
% 2.13/2.34 ((~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9154, 333])).
% 2.13/2.34 tff(9156,plain,
% 2.13/2.34 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9155, 194, 97, 273, 230, 4039, 9045, 385])).
% 2.13/2.34 tff(9157,plain,
% 2.13/2.34 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[191, 9156])).
% 2.13/2.34 tff(9158,plain,
% 2.13/2.34 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[534, 9157, 97])).
% 2.13/2.34 tff(9159,plain,
% 2.13/2.34 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[83, 9158])).
% 2.13/2.34 tff(9160,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2561, 9157, 194])).
% 2.13/2.34 tff(9161,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[95, 9160])).
% 2.13/2.34 tff(9162,plain,
% 2.13/2.34 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6271, 9161, 297, 9159, 9045])).
% 2.13/2.34 tff(9163,plain,
% 2.13/2.34 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[338, 9162])).
% 2.13/2.34 tff(9164,plain,
% 2.13/2.34 (((~![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(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9165,plain,
% 2.13/2.34 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~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(z))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(9166,plain,
% 2.13/2.34 (((~![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(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[9165])).
% 2.13/2.34 tff(9167,plain,
% 2.13/2.34 (((~![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(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[9166, 9164])).
% 2.13/2.34 tff(9168,plain,
% 2.13/2.34 ((~![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(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(9169,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[9168, 9167])).
% 2.13/2.34 tff(9170,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9169, 65, 194, 9157, 385, 9163])).
% 2.13/2.34 tff(9171,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(9172,plain,
% 2.13/2.34 (~r(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9171, 9117, 297, 97, 273, 230, 4039])).
% 2.13/2.34 tff(9173,plain,
% 2.13/2.34 (b(s(s(s(z))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[595, 9172])).
% 2.13/2.34 tff(9174,plain,
% 2.13/2.34 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6271, 9055, 297, 9043, 9045])).
% 2.13/2.34 tff(9175,plain,
% 2.13/2.34 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[338, 9174])).
% 2.13/2.34 tff(9176,plain,
% 2.13/2.34 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[6509, 9175, 273])).
% 2.13/2.34 tff(9177,plain,
% 2.13/2.34 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[214, 47, 9176, 209])).
% 2.13/2.34 tff(9178,plain,
% 2.13/2.34 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9079, 9177, 383, 4039, 9047])).
% 2.13/2.34 tff(9179,plain,
% 2.13/2.34 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[191, 9178])).
% 2.13/2.34 tff(9180,plain,
% 2.13/2.34 (~r(s(z), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[476, 65, 9179, 9175])).
% 2.13/2.34 tff(9181,plain,
% 2.13/2.34 (b(s(z), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[493, 9180])).
% 2.13/2.34 tff(9182,plain,
% 2.13/2.34 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[4145, 9181, 383, 4039, 9173])).
% 2.13/2.34 tff(9183,plain,
% 2.13/2.34 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[442, 9182])).
% 2.13/2.34 tff(9184,plain,
% 2.13/2.34 (~r(s(z), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[476, 65, 193, 299])).
% 2.13/2.34 tff(9185,plain,
% 2.13/2.34 (b(s(z), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[493, 9184])).
% 2.13/2.34 tff(9186,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.13/2.34 tff(9187,plain,
% 2.13/2.34 (((~![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(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), 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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9188,plain,
% 2.13/2.35 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9189,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), 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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9188])).
% 2.13/2.35 tff(9190,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), 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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[9189, 9187])).
% 2.13/2.35 tff(9191,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(9192,plain,
% 2.13/2.35 ((~![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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[9191, 9190])).
% 2.13/2.35 tff(9193,plain,
% 2.13/2.35 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9192, 65, 299, 9186])).
% 2.13/2.35 tff(9194,plain,
% 2.13/2.35 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1001, 9193])).
% 2.13/2.35 tff(9195,plain,
% 2.13/2.35 (((~![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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9196,plain,
% 2.13/2.35 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9197,plain,
% 2.13/2.35 (((~![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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(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), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9196])).
% 2.13/2.35 tff(9198,plain,
% 2.13/2.35 (((~![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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(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), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[9197, 9195])).
% 2.13/2.35 tff(9199,plain,
% 2.13/2.35 ((~![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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(9200,plain,
% 2.13/2.35 ((~![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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[9199, 9198])).
% 2.13/2.35 tff(9201,plain,
% 2.13/2.35 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9200, 65, 194, 193, 9186])).
% 2.13/2.35 tff(9202,plain,
% 2.13/2.35 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[968, 9201])).
% 2.13/2.35 tff(9203,plain,
% 2.13/2.35 (((~![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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), 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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9204,plain,
% 2.13/2.35 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9205,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), 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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9204])).
% 2.13/2.35 tff(9206,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), 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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[9205, 9203])).
% 2.13/2.35 tff(9207,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(9208,plain,
% 2.13/2.35 ((~![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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[9207, 9206])).
% 2.13/2.35 tff(9209,plain,
% 2.13/2.35 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9208, 65, 193, 9186])).
% 2.13/2.35 tff(9210,plain,
% 2.13/2.35 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1050, 9209])).
% 2.13/2.35 tff(9211,plain,
% 2.13/2.35 (((~![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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9212,plain,
% 2.13/2.35 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9213,plain,
% 2.13/2.35 (((~![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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9212])).
% 2.13/2.35 tff(9214,plain,
% 2.13/2.35 (((~![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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[9213, 9211])).
% 2.13/2.35 tff(9215,plain,
% 2.13/2.35 ((~![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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(9216,plain,
% 2.13/2.35 ((~![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(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[9215, 9214])).
% 2.13/2.35 tff(9217,plain,
% 2.13/2.35 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9216, 65, 299, 9186])).
% 2.13/2.35 tff(9218,plain,
% 2.13/2.35 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[2375, 47, 995, 9217])).
% 2.13/2.35 tff(9219,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9220,plain,
% 2.13/2.35 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9221,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9220])).
% 2.13/2.35 tff(9222,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[9221, 9219])).
% 2.13/2.35 tff(9223,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(9224,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[9223, 9222])).
% 2.13/2.35 tff(9225,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9224, 162, 9218, 9210, 600, 9202, 9194, 9185])).
% 2.13/2.35 tff(9226,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(9227,plain,
% 2.13/2.35 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9226, 9173, 9175, 9117, 9179])).
% 2.13/2.35 tff(9228,plain,
% 2.13/2.35 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9038, 9177, 383, 4039, 9047])).
% 2.13/2.35 tff(9229,plain,
% 2.13/2.35 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[6271, 120, 297, 122, 9045])).
% 2.13/2.35 tff(9230,plain,
% 2.13/2.35 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[338, 9229])).
% 2.13/2.35 tff(9231,assumption,(~b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 2.13/2.35 tff(9232,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9233,plain,
% 2.13/2.35 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9234,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9233])).
% 2.13/2.35 tff(9235,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 2.13/2.35 inference(transitivity,[status(thm)],[9234, 9232])).
% 2.13/2.35 tff(9236,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(9237,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[9236, 9235])).
% 2.13/2.35 tff(9238,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9237, 162, 122, 120, 363, 298, 2217, 926])).
% 2.13/2.35 tff(9239,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(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(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(9240,plain,
% 2.13/2.35 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9239, 2379, 120, 8128, 9045, 122])).
% 2.13/2.35 tff(9241,plain,
% 2.13/2.35 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[360, 9240])).
% 2.13/2.35 tff(9242,plain,
% 2.13/2.35 (~r(s(s(s(z))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[9171, 194, 297, 97, 273, 230, 4039])).
% 2.13/2.35 tff(9243,plain,
% 2.13/2.35 (b(s(s(s(z))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[595, 9242])).
% 2.13/2.35 tff(9244,plain,
% 2.13/2.35 ((z = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = z)),
% 2.13/2.35 inference(commutativity,[status(thm)],[])).
% 2.13/2.35 tff(9245,plain,
% 2.13/2.35 ((s(s(s(s(s(elem!1))))) = z) <=> (z = s(s(s(s(s(elem!1))))))),
% 2.13/2.35 inference(symmetry,[status(thm)],[9244])).
% 2.13/2.35 tff(9246,plain,
% 2.13/2.35 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(z = s(s(s(s(s(elem!1)))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9245])).
% 2.13/2.35 tff(9247,plain,
% 2.13/2.35 (~(z = s(s(s(s(s(elem!1))))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[863, 9246])).
% 2.13/2.35 tff(9248,plain,
% 2.13/2.35 (((~![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(s(elem!1))))), s(z))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9249,plain,
% 2.13/2.35 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(9250,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1)))))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[9249])).
% 2.13/2.35 tff(9251,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, 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(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[9250, 9248])).
% 2.13/2.36 tff(9252,plain,
% 2.13/2.36 ((~![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(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(9253,plain,
% 2.13/2.36 ((~![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(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[9252, 9251])).
% 2.13/2.36 tff(9254,plain,
% 2.13/2.36 (~r(z, s(s(s(s(s(elem!1))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9253, 65, 97, 945])).
% 2.13/2.36 tff(9255,plain,
% 2.13/2.36 ((z = s(s(s(s(s(elem!1)))))) | b(z, s(s(s(s(s(elem!1))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[983, 47, 9254])).
% 2.13/2.36 tff(9256,plain,
% 2.13/2.36 (b(z, s(s(s(s(s(elem!1))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9255, 9247])).
% 2.13/2.36 tff(9257,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9258,plain,
% 2.13/2.36 (((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9259,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9258])).
% 2.13/2.36 tff(9260,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[9259, 9257])).
% 2.13/2.36 tff(9261,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(9262,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[9261, 9260])).
% 2.13/2.36 tff(9263,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9262, 162, 9256, 298, 1003, 297, 5546])).
% 2.13/2.36 tff(9264,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(9265,plain,
% 2.13/2.36 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9264, 1003, 9045, 297, 97])).
% 2.13/2.36 tff(9266,plain,
% 2.13/2.36 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[968, 9265])).
% 2.13/2.36 tff(9267,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9268,plain,
% 2.13/2.36 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(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(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9269,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~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(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9268])).
% 2.13/2.36 tff(9270,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~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(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[9269, 9267])).
% 2.13/2.36 tff(9271,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(9272,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[9271, 9270])).
% 2.13/2.36 tff(9273,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9272, 65, 299, 273, 644])).
% 2.13/2.36 tff(9274,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[690, 9273, 679])).
% 2.13/2.36 tff(9275,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[702, 9274, 676, 599, 694, 600])).
% 2.13/2.36 tff(9276,plain,((~r(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(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(9277,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9276, 694, 599, 600, 299, 273])).
% 2.13/2.36 tff(9278,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[709, 9277, 635])).
% 2.13/2.36 tff(9279,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9280,plain,
% 2.13/2.36 (((~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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9281,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9280])).
% 2.13/2.36 tff(9282,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[9281, 9279])).
% 2.13/2.36 tff(9283,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(9284,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[9283, 9282])).
% 2.13/2.36 tff(9285,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9284, 162, 4039, 600, 970, 1003, 9278, 694])).
% 2.13/2.36 tff(9286,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(9287,plain,
% 2.13/2.36 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9286, 9266, 9243, 4039, 1003, 599, 9230, 273])).
% 2.13/2.36 tff(9288,plain,
% 2.13/2.36 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[658, 9287, 643])).
% 2.13/2.36 tff(9289,plain,
% 2.13/2.36 (~r(z, s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[7971, 9288, 97])).
% 2.13/2.36 tff(9290,plain,
% 2.13/2.36 (b(z, s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[823, 9289])).
% 2.13/2.36 tff(9291,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9292,plain,
% 2.13/2.36 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9293,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9292])).
% 2.13/2.36 tff(9294,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[9293, 9291])).
% 2.13/2.36 tff(9295,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(9296,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[9295, 9294])).
% 2.13/2.36 tff(9297,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9296, 162, 600, 970, 1003, 1075, 297, 692])).
% 2.13/2.36 tff(9298,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(9299,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9298, 9266, 9243, 1003, 9290, 297])).
% 2.13/2.36 tff(9300,plain,
% 2.13/2.36 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[690, 9299, 679])).
% 2.13/2.36 tff(9301,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8333, 65, 230, 417, 9300])).
% 2.13/2.36 tff(9302,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[709, 9301, 635])).
% 2.13/2.36 tff(9303,plain,
% 2.13/2.36 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[373, 9045, 122, 297, 273])).
% 2.13/2.36 tff(9304,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[52, 9303])).
% 2.13/2.36 tff(9305,plain,
% 2.13/2.36 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1037, 9266, 9243, 1003, 599])).
% 2.13/2.36 tff(9306,plain,
% 2.13/2.36 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1050, 9305])).
% 2.13/2.36 tff(9307,plain,
% 2.13/2.36 (~r(z, s(s(s(s(s(elem!1))))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[4443, 9306, 97])).
% 2.13/2.36 tff(9308,plain,
% 2.13/2.36 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[5714, 9306, 194])).
% 2.13/2.36 tff(9309,plain,
% 2.13/2.36 (b(s(s(s(s(s(elem!1))))), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[894, 9308])).
% 2.13/2.36 tff(9310,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9311,plain,
% 2.13/2.36 (((~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(9312,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9311])).
% 2.13/2.36 tff(9313,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[9312, 9310])).
% 2.13/2.36 tff(9314,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(9315,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[9314, 9313])).
% 2.13/2.36 tff(9316,plain,
% 2.13/2.36 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9315, 162, 416, 120, 2379, 825, 926])).
% 2.13/2.36 tff(9317,plain,
% 2.13/2.36 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[763, 47, 9316])).
% 2.13/2.36 tff(9318,plain,
% 2.13/2.36 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[9317, 2708])).
% 2.13/2.36 tff(9319,plain,
% 2.13/2.36 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9318])).
% 2.13/2.36 tff(9320,plain,
% 2.13/2.36 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9319])).
% 2.13/2.36 tff(9321,plain,
% 2.13/2.36 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[970, 9320])).
% 2.13/2.36 tff(9322,plain,
% 2.13/2.36 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.36 inference(symmetry,[status(thm)],[9319])).
% 2.13/2.36 tff(9323,plain,
% 2.13/2.36 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[9322])).
% 2.13/2.36 tff(9324,plain,
% 2.13/2.36 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9323])).
% 2.13/2.37 tff(9325,plain,
% 2.13/2.37 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[1003, 9324])).
% 2.13/2.37 tff(9326,plain,
% 2.13/2.37 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9322])).
% 2.13/2.37 tff(9327,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9326])).
% 2.13/2.37 tff(9328,plain,
% 2.13/2.37 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[5635, 2708])).
% 2.13/2.37 tff(9329,plain,
% 2.13/2.37 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9328])).
% 2.13/2.37 tff(9330,plain,
% 2.13/2.37 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.13/2.37 inference(transitivity,[status(thm)],[20, 9329, 630])).
% 2.13/2.37 tff(9331,plain,
% 2.13/2.37 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9330])).
% 2.13/2.37 tff(9332,plain,
% 2.13/2.37 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[9331, 987])).
% 2.13/2.37 tff(9333,plain,
% 2.13/2.37 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9332])).
% 2.13/2.37 tff(9334,plain,
% 2.13/2.37 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9333])).
% 2.13/2.37 tff(9335,plain,
% 2.13/2.37 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[996, 9334])).
% 2.13/2.37 tff(9336,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9330])).
% 2.13/2.37 tff(9337,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9336])).
% 2.13/2.37 tff(9338,plain,
% 2.13/2.37 ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9337])).
% 2.13/2.37 tff(9339,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 2.13/2.37 tff(9340,plain,
% 2.13/2.37 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9339, 9338])).
% 2.13/2.37 tff(9341,plain,
% 2.13/2.37 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1731, 9340, 9335])).
% 2.13/2.37 tff(9342,plain,
% 2.13/2.37 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9328, 9330])).
% 2.13/2.37 tff(9343,plain,
% 2.13/2.37 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9342])).
% 2.13/2.37 tff(9344,plain,
% 2.13/2.37 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[787, 9343])).
% 2.13/2.37 tff(9345,plain,
% 2.13/2.37 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[5748, 9344, 9341])).
% 2.13/2.37 tff(9346,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1789, 9345, 1692])).
% 2.13/2.37 tff(9347,plain,
% 2.13/2.37 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9330])).
% 2.13/2.37 tff(9348,plain,
% 2.13/2.37 (s(s(elem!1)) = s(s(z))),
% 2.13/2.37 inference(transitivity,[status(thm)],[25, 9347, 312])).
% 2.13/2.37 tff(9349,plain,
% 2.13/2.37 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9348])).
% 2.13/2.37 tff(9350,plain,
% 2.13/2.37 (s(elem!1) = s(z)),
% 2.13/2.37 inference(transitivity,[status(thm)],[325, 9349, 15])).
% 2.13/2.37 tff(9351,plain,
% 2.13/2.37 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9350])).
% 2.13/2.37 tff(9352,plain,
% 2.13/2.37 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9351])).
% 2.13/2.37 tff(9353,plain,
% 2.13/2.37 (z = elem!1),
% 2.13/2.37 inference(transitivity,[status(thm)],[1182, 9352, 1170])).
% 2.13/2.37 tff(9354,plain,
% 2.13/2.37 (elem!1 = z),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1208, 9353])).
% 2.13/2.37 tff(9355,plain,
% 2.13/2.37 (elem!1 = z),
% 2.13/2.37 inference(transitivity,[status(thm)],[1171, 9351, 13])).
% 2.13/2.37 tff(9356,plain,
% 2.13/2.37 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9355])).
% 2.13/2.37 tff(9357,plain,
% 2.13/2.37 (r(z, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9356])).
% 2.13/2.37 tff(9358,plain,
% 2.13/2.37 ((~r(z, s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9357])).
% 2.13/2.37 tff(9359,plain,
% 2.13/2.37 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[1739, 9358])).
% 2.13/2.37 tff(9360,plain,
% 2.13/2.37 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9328])).
% 2.13/2.37 tff(9361,plain,
% 2.13/2.37 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(z))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9355, 9360])).
% 2.13/2.37 tff(9362,plain,
% 2.13/2.37 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.13/2.37 inference(transitivity,[status(thm)],[9361, 2881])).
% 2.13/2.37 tff(9363,plain,
% 2.13/2.37 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9362])).
% 2.13/2.37 tff(9364,plain,
% 2.13/2.37 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9363])).
% 2.13/2.37 tff(9365,plain,
% 2.13/2.37 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[2888, 9364])).
% 2.13/2.37 tff(9366,plain,
% 2.13/2.37 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1813, 9365, 9359])).
% 2.13/2.37 tff(9367,plain,
% 2.13/2.37 (b(z, s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1821, 9366, 9354])).
% 2.13/2.37 tff(9368,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9369,plain,
% 2.13/2.37 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9370,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1)))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9369])).
% 2.13/2.37 tff(9371,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[9370, 9368])).
% 2.13/2.37 tff(9372,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(9373,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9372, 9371])).
% 2.13/2.37 tff(9374,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9373, 162, 122, 120, 2218, 971, 2217])).
% 2.13/2.37 tff(9375,plain,((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(9376,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9375, 9367, 9346, 120, 122, 2217])).
% 2.13/2.37 tff(9377,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(9378,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9377, 9316, 122, 787, 1692, 1739, 2379, 120, 340])).
% 2.13/2.37 tff(9379,plain,
% 2.13/2.37 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9378, 9327])).
% 2.13/2.37 tff(9380,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9319])).
% 2.13/2.37 tff(9381,plain,
% 2.13/2.37 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[926, 9380])).
% 2.13/2.37 tff(9382,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9383,plain,
% 2.13/2.37 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9384,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9383])).
% 2.13/2.37 tff(9385,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[9384, 9382])).
% 2.13/2.37 tff(9386,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(9387,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9386, 9385])).
% 2.13/2.37 tff(9388,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9387, 162, 298, 599, 9381, 9379, 9325, 9321])).
% 2.13/2.37 tff(9389,plain,((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | r(z, s(s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(9390,plain,
% 2.13/2.37 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9389, 9309, 599, 9045, 1003, 9266, 9300, 340, 122, 9307, 120, 9304, 9302, 2377])).
% 2.13/2.37 tff(9391,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9390])).
% 2.13/2.37 tff(9392,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9391])).
% 2.13/2.37 tff(9393,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9266, 9392])).
% 2.13/2.37 tff(9394,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9231, 9393])).
% 2.13/2.37 tff(9395,plain,((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(9396,plain,
% 2.13/2.37 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9395, 9241, 599, 9231, 122, 120, 2377, 230, 417, 297, 97, 4039, 273, 194])).
% 2.13/2.37 tff(9397,plain,
% 2.13/2.37 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1001, 9396])).
% 2.13/2.37 tff(9398,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9399,plain,
% 2.13/2.37 (((~b(s(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(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9400,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9399])).
% 2.13/2.37 tff(9401,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[9400, 9398])).
% 2.13/2.37 tff(9402,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(9403,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9402, 9401])).
% 2.13/2.37 tff(9404,plain,
% 2.13/2.37 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9403, 162, 122, 120, 2379, 8128])).
% 2.13/2.37 tff(9405,plain,
% 2.13/2.37 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1789, 9404, 1692])).
% 2.13/2.37 tff(9406,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), 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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9407,plain,
% 2.13/2.37 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(9408,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9407])).
% 2.13/2.37 tff(9409,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[9408, 9406])).
% 2.13/2.37 tff(9410,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(9411,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[9410, 9409])).
% 2.13/2.37 tff(9412,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9411, 65, 9405, 9397, 9230])).
% 2.13/2.37 tff(9413,plain,((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(9414,plain,
% 2.13/2.37 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[9413, 9055, 9043, 9181, 9228, 9227, 230, 9183, 297, 97, 4039, 273, 9117])).
% 2.13/2.37 tff(9415,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[9414])).
% 2.13/2.37 tff(9416,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.37 inference(symmetry,[status(thm)],[9415])).
% 2.13/2.37 tff(9417,plain,
% 2.13/2.37 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[149, 9228])).
% 2.13/2.37 tff(9418,plain,
% 2.13/2.37 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8126, 9117, 230, 4039])).
% 2.13/2.37 tff(9419,plain,
% 2.13/2.37 (b(s(s(s(s(s(elem!1))))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[894, 9418])).
% 2.13/2.37 tff(9420,plain,
% 2.13/2.37 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[4145, 599, 383, 4039, 600])).
% 2.13/2.37 tff(9421,plain,
% 2.13/2.37 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[442, 9420])).
% 2.13/2.37 tff(9422,plain,
% 2.13/2.37 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8011, 9278, 4039, 383, 694])).
% 2.13/2.37 tff(9423,plain,
% 2.13/2.37 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[801, 9422, 634])).
% 2.13/2.37 tff(9424,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[796, 9423, 9421])).
% 2.13/2.38 tff(9425,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[690, 9424, 679])).
% 2.13/2.38 tff(9426,plain,
% 2.13/2.38 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[702, 9425, 599, 694, 600])).
% 2.13/2.38 tff(9427,plain,
% 2.13/2.38 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[675, 9426, 664])).
% 2.13/2.38 tff(9428,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2426, 65, 273, 9423, 9427])).
% 2.13/2.38 tff(9429,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(9430,plain,
% 2.13/2.38 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9429, 273, 9181, 9173, 4039, 383, 9175])).
% 2.13/2.38 tff(9431,plain,
% 2.13/2.38 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[658, 9430, 643])).
% 2.13/2.38 tff(9432,plain,
% 2.13/2.38 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1026, 945, 123])).
% 2.13/2.38 tff(9433,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9375, 2379, 2380, 120, 122, 971])).
% 2.13/2.38 tff(9434,plain,((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(9435,plain,
% 2.13/2.38 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9434, 9256, 122, 120, 2377, 9432])).
% 2.13/2.38 tff(9436,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9435])).
% 2.13/2.38 tff(9437,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9436])).
% 2.13/2.38 tff(9438,plain,
% 2.13/2.38 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1259, 2743])).
% 2.13/2.38 tff(9439,plain,
% 2.13/2.38 (elem!1 = s(s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1540, 9438])).
% 2.13/2.38 tff(9440,plain,
% 2.13/2.38 (s(s(s(s(elem!1)))) = elem!1),
% 2.13/2.38 inference(symmetry,[status(thm)],[9439])).
% 2.13/2.38 tff(9441,plain,
% 2.13/2.38 (s(s(s(s(s(elem!1))))) = elem!1),
% 2.13/2.38 inference(transitivity,[status(thm)],[1513, 9440])).
% 2.13/2.38 tff(9442,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9441])).
% 2.13/2.38 tff(9443,plain,
% 2.13/2.38 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9442])).
% 2.13/2.38 tff(9444,plain,
% 2.13/2.38 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1255, 2743])).
% 2.13/2.38 tff(9445,plain,
% 2.13/2.38 (~(elem!1 = s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2411, 9444, 9438])).
% 2.13/2.38 tff(9446,plain,
% 2.13/2.38 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9439])).
% 2.13/2.38 tff(9447,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9446])).
% 2.13/2.38 tff(9448,plain,
% 2.13/2.38 ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9447])).
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% 2.13/2.38 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8142, 7963, 971, 1508, 7973, 926])).
% 2.13/2.38 tff(9450,plain,
% 2.13/2.38 (~b(elem!1, s(s(s(s(z)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9449, 9448])).
% 2.13/2.38 tff(9451,plain,
% 2.13/2.38 (r(elem!1, s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2445, 9450, 9445])).
% 2.13/2.38 tff(9452,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9451, 9443])).
% 2.13/2.38 tff(9453,plain,
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% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(9454,plain,
% 2.13/2.38 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(9455,plain,
% 2.13/2.38 (((~![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(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), 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(z), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9454])).
% 2.13/2.38 tff(9456,plain,
% 2.13/2.38 (((~![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(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), 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(z), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[9455, 9453])).
% 2.13/2.38 tff(9457,plain,
% 2.13/2.38 ((~![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(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(9458,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9457, 9456])).
% 2.13/2.38 tff(9459,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9458, 65, 2860, 645, 9452])).
% 2.13/2.38 tff(9460,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(9461,plain,
% 2.13/2.38 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9460, 9435, 645, 9256, 926, 194, 97])).
% 2.13/2.38 tff(9462,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1050, 9461])).
% 2.13/2.38 tff(9463,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9462, 9437])).
% 2.13/2.38 tff(9464,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[7521, 9463])).
% 2.13/2.38 tff(9465,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | b(s(z), s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(9466,plain,
% 2.13/2.38 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9465, 9178, 9431, 9419, 9117, 97, 9043, 9055, 9227, 9417])).
% 2.13/2.38 tff(9467,plain,
% 2.13/2.38 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[968, 9466])).
% 2.13/2.38 tff(9468,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9467, 9416])).
% 2.13/2.38 tff(9469,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9228, 9468])).
% 2.13/2.38 tff(9470,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(9471,plain,
% 2.13/2.38 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(z)), s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9470, 6735])).
% 2.13/2.38 tff(9472,plain,
% 2.13/2.38 (~r(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9471, 9028, 273, 9026, 8871])).
% 2.13/2.38 tff(9473,plain,
% 2.13/2.38 (b(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[245, 9472])).
% 2.13/2.38 tff(9474,plain,
% 2.13/2.38 (~b(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8791, 9473, 8534, 8871])).
% 2.13/2.38 tff(9475,plain,
% 2.13/2.38 (r(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[175, 9474])).
% 2.13/2.38 tff(9476,plain,
% 2.13/2.38 (~r(s(s(s(z))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2271, 9475, 395])).
% 2.13/2.38 tff(9477,plain,
% 2.13/2.38 (b(s(s(s(z))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[381, 9476])).
% 2.13/2.38 tff(9478,plain,
% 2.13/2.38 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[7993, 9475, 395, 9026, 9028])).
% 2.13/2.38 tff(9479,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[6862, 9478])).
% 2.13/2.38 tff(9480,plain,
% 2.13/2.38 (~r(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9471, 297, 273, 97, 8871])).
% 2.13/2.38 tff(9481,plain,
% 2.13/2.38 (b(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[245, 9480])).
% 2.13/2.38 tff(9482,plain,
% 2.13/2.38 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8575, 298, 8534, 297, 9481])).
% 2.13/2.38 tff(9483,plain,
% 2.13/2.38 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[442, 9482])).
% 2.13/2.38 tff(9484,plain,
% 2.13/2.38 (~b(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8791, 9481, 8534, 8871])).
% 2.13/2.38 tff(9485,plain,
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% 2.13/2.38 inference(unit_resolution,[status(thm)],[175, 9484])).
% 2.13/2.38 tff(9486,plain,
% 2.13/2.38 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[373, 298, 54, 273, 297])).
% 2.13/2.38 tff(9487,plain,
% 2.13/2.38 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[95, 9486])).
% 2.13/2.38 tff(9488,plain,
% 2.13/2.38 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2561, 9487, 9485])).
% 2.13/2.38 tff(9489,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[191, 9488])).
% 2.13/2.38 tff(9490,plain,
% 2.13/2.38 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8048, 385, 297, 97, 298])).
% 2.13/2.38 tff(9491,plain,
% 2.13/2.38 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[968, 9490])).
% 2.13/2.38 tff(9492,plain,
% 2.13/2.38 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8835, 8708, 3286, 3284, 8991])).
% 2.13/2.38 tff(9493,plain,
% 2.13/2.38 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[763, 47, 9492, 6885])).
% 2.13/2.38 tff(9494,plain,
% 2.13/2.38 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9493])).
% 2.13/2.38 tff(9495,plain,
% 2.13/2.38 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9494])).
% 2.13/2.38 tff(9496,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9495])).
% 2.13/2.38 tff(9497,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9496])).
% 2.13/2.38 tff(9498,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9493])).
% 2.13/2.38 tff(9499,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[9498, 9497])).
% 2.13/2.38 tff(9500,plain,
% 2.13/2.38 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9493])).
% 2.13/2.38 tff(9501,plain,
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% 2.13/2.38 inference(transitivity,[status(thm)],[20, 9500, 630])).
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% 2.13/2.38 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9501])).
% 2.13/2.38 tff(9503,plain,
% 2.13/2.38 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[9502, 987])).
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% 2.13/2.38 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9503])).
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% 2.13/2.38 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9504])).
% 2.13/2.38 tff(9506,plain,
% 2.13/2.38 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[996, 9505])).
% 2.13/2.38 tff(9507,plain,
% 2.13/2.38 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2746, 9506])).
% 2.13/2.38 tff(9508,plain,
% 2.13/2.38 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2197, 9507])).
% 2.13/2.38 tff(9509,plain,
% 2.13/2.38 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9501])).
% 2.13/2.38 tff(9510,plain,
% 2.13/2.38 (s(s(elem!1)) = s(s(z))),
% 2.13/2.38 inference(transitivity,[status(thm)],[25, 9509, 312])).
% 2.13/2.38 tff(9511,plain,
% 2.13/2.38 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510])).
% 2.13/2.38 tff(9512,plain,
% 2.13/2.38 (s(elem!1) = s(z)),
% 2.13/2.38 inference(transitivity,[status(thm)],[325, 9511, 15])).
% 2.13/2.38 tff(9513,plain,
% 2.13/2.38 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9512])).
% 2.13/2.38 tff(9514,plain,
% 2.13/2.38 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9513])).
% 2.13/2.38 tff(9515,plain,
% 2.13/2.38 (z = elem!1),
% 2.13/2.38 inference(transitivity,[status(thm)],[1182, 9514, 1170])).
% 2.13/2.38 tff(9516,plain,
% 2.13/2.38 (elem!1 = z),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1208, 9515])).
% 2.13/2.38 tff(9517,plain,
% 2.13/2.38 (~b(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8791, 538, 8534, 8871])).
% 2.13/2.38 tff(9518,plain,
% 2.13/2.38 (r(s(z), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[175, 9517])).
% 2.13/2.38 tff(9519,plain,
% 2.13/2.38 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1781, 1004, 644, 1211])).
% 2.13/2.38 tff(9520,plain,
% 2.13/2.38 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[923, 9519])).
% 2.13/2.38 tff(9521,plain,
% 2.13/2.38 ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8123, 6735])).
% 2.13/2.38 tff(9522,plain,
% 2.13/2.38 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9521, 8248, 970, 9520])).
% 2.13/2.38 tff(9523,plain,
% 2.13/2.38 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1050, 9522])).
% 2.13/2.38 tff(9524,plain,
% 2.13/2.38 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[935, 9520, 8534, 8248, 538])).
% 2.13/2.38 tff(9525,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[894, 9524])).
% 2.13/2.38 tff(9526,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5714, 9525, 9523, 9518])).
% 2.13/2.38 tff(9527,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = z)) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(9528,plain,
% 2.13/2.38 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9527, 644, 970, 538, 9516, 54])).
% 2.13/2.38 tff(9529,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1789, 9528, 9507])).
% 2.13/2.38 tff(9530,plain,
% 2.13/2.38 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5274, 9529, 151, 177, 970])).
% 2.13/2.38 tff(9531,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2214, 9530, 9508])).
% 2.13/2.38 tff(9532,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9531, 9499])).
% 2.13/2.38 tff(9533,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9494, 9510])).
% 2.13/2.38 tff(9534,plain,
% 2.13/2.38 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510])).
% 2.13/2.38 tff(9535,plain,
% 2.13/2.38 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[9534, 1917])).
% 2.13/2.38 tff(9536,plain,
% 2.13/2.38 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9535])).
% 2.13/2.38 tff(9537,plain,
% 2.13/2.38 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9536])).
% 2.13/2.38 tff(9538,plain,
% 2.13/2.38 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[914, 9537])).
% 2.13/2.38 tff(9539,plain,
% 2.13/2.38 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510])).
% 2.13/2.38 tff(9540,plain,
% 2.13/2.38 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.38 inference(symmetry,[status(thm)],[9539])).
% 2.13/2.38 tff(9541,plain,
% 2.13/2.38 (elem!1 = z),
% 2.13/2.38 inference(transitivity,[status(thm)],[1171, 9513, 13])).
% 2.13/2.38 tff(9542,plain,
% 2.13/2.38 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9541])).
% 2.13/2.38 tff(9543,plain,
% 2.13/2.38 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.13/2.38 inference(symmetry,[status(thm)],[9542])).
% 2.13/2.38 tff(9544,plain,
% 2.13/2.38 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.38 inference(transitivity,[status(thm)],[9543, 9540])).
% 2.13/2.38 tff(9545,plain,
% 2.13/2.38 (b(s(s(elem!1)), elem!1)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[538, 9544])).
% 2.13/2.38 tff(9546,plain,
% 2.13/2.38 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(z))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9541, 9494])).
% 2.13/2.38 tff(9547,plain,
% 2.13/2.38 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.13/2.38 inference(transitivity,[status(thm)],[9546, 2881])).
% 2.13/2.38 tff(9548,plain,
% 2.13/2.38 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9547])).
% 2.13/2.38 tff(9549,plain,
% 2.13/2.38 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 2.13/2.38 inference(transitivity,[status(thm)],[9548, 1831])).
% 2.13/2.38 tff(9550,plain,
% 2.13/2.38 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9549])).
% 2.13/2.38 tff(9551,plain,
% 2.13/2.38 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[2888, 9550])).
% 2.13/2.38 tff(9552,plain,
% 2.13/2.38 (b(s(s(s(s(s(elem!1))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9494, 9512])).
% 2.13/2.38 tff(9553,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9552])).
% 2.13/2.38 tff(9554,plain,
% 2.13/2.38 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9494])).
% 2.13/2.38 tff(9555,plain,
% 2.13/2.38 (b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[970, 9554])).
% 2.13/2.38 tff(9556,plain,
% 2.13/2.38 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9555, 9553])).
% 2.13/2.38 tff(9557,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9493, 9512])).
% 2.13/2.38 tff(9558,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9557])).
% 2.13/2.38 tff(9559,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9493])).
% 2.13/2.38 tff(9560,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[151, 9559])).
% 2.13/2.38 tff(9561,plain,
% 2.13/2.38 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9560, 9558])).
% 2.13/2.38 tff(9562,plain,
% 2.13/2.38 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9512, 9493])).
% 2.13/2.38 tff(9563,plain,
% 2.13/2.38 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9562])).
% 2.13/2.38 tff(9564,plain,
% 2.13/2.38 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[694, 9563])).
% 2.13/2.38 tff(9565,plain,
% 2.13/2.38 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5331, 9529, 9564, 9561, 9556])).
% 2.13/2.38 tff(9566,plain,
% 2.13/2.38 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5338, 9565, 9516])).
% 2.13/2.38 tff(9567,plain,
% 2.13/2.38 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1050, 9566])).
% 2.13/2.38 tff(9568,plain,
% 2.13/2.38 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5714, 9567, 9518])).
% 2.13/2.38 tff(9569,plain,
% 2.13/2.38 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4286, 9568, 9516])).
% 2.13/2.38 tff(9570,plain,
% 2.13/2.38 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1858, 9569, 9551])).
% 2.13/2.38 tff(9571,plain,
% 2.13/2.38 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510])).
% 2.13/2.38 tff(9572,plain,
% 2.13/2.38 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9571])).
% 2.13/2.38 tff(9573,plain,
% 2.13/2.38 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9541])).
% 2.13/2.38 tff(9574,plain,
% 2.13/2.38 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9573])).
% 2.13/2.38 tff(9575,plain,
% 2.13/2.38 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.13/2.38 inference(transitivity,[status(thm)],[9574, 9572])).
% 2.13/2.38 tff(9576,plain,
% 2.13/2.38 (b(elem!1, s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[8534, 9575])).
% 2.13/2.38 tff(9577,plain,
% 2.13/2.38 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9548])).
% 2.13/2.38 tff(9578,plain,
% 2.13/2.38 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[2888, 9577])).
% 2.13/2.38 tff(9579,plain,
% 2.13/2.38 (~r(z, s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[4443, 9567, 97])).
% 2.13/2.38 tff(9580,plain,
% 2.13/2.38 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1741, 9579, 9516])).
% 2.13/2.38 tff(9581,plain,
% 2.13/2.38 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1813, 9580, 9578])).
% 2.13/2.38 tff(9582,plain,
% 2.13/2.38 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1853, 9581, 9576, 9570, 9545])).
% 2.13/2.38 tff(9583,plain,
% 2.13/2.38 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1760, 9582, 9538])).
% 2.13/2.38 tff(9584,plain,
% 2.13/2.38 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9583, 9533])).
% 2.13/2.38 tff(9585,plain,
% 2.13/2.38 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510, 9493])).
% 2.13/2.38 tff(9586,plain,
% 2.13/2.38 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510, 9493])).
% 2.13/2.38 tff(9587,plain,
% 2.13/2.38 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9586])).
% 2.13/2.38 tff(9588,plain,
% 2.13/2.38 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9587])).
% 2.13/2.38 tff(9589,plain,
% 2.13/2.38 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[634, 9588])).
% 2.13/2.38 tff(9590,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510])).
% 2.13/2.38 tff(9591,plain,
% 2.13/2.38 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9590])).
% 2.13/2.38 tff(9592,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[8871, 9591])).
% 2.13/2.38 tff(9593,plain,
% 2.13/2.38 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9510])).
% 2.13/2.38 tff(9594,plain,
% 2.13/2.38 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[9593])).
% 2.13/2.38 tff(9595,plain,
% 2.13/2.38 (b(s(z), s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[6735, 9594])).
% 2.13/2.38 tff(9596,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(9597,plain,
% 2.13/2.38 (((~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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(9598,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[9597])).
% 2.13/2.38 tff(9599,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[9598, 9596])).
% 2.13/2.38 tff(9600,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(9601,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9600, 9599])).
% 2.13/2.38 tff(9602,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9601, 162, 3577, 3576, 177, 1147, 151])).
% 2.13/2.38 tff(9603,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(9604,plain,
% 2.13/2.38 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[9603, 9595, 151, 9592, 177])).
% 2.13/2.38 tff(9605,plain,
% 2.13/2.38 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1493, 9604, 9589])).
% 2.13/2.38 tff(9606,plain,
% 2.13/2.38 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[9605, 9585])).
% 2.13/2.38 tff(9607,plain,
% 2.13/2.38 (((~![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(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(9608,plain,
% 2.13/2.38 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(9609,plain,
% 2.13/2.38 (((~![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(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9608])).
% 2.13/2.39 tff(9610,plain,
% 2.13/2.39 (((~![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(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[9609, 9607])).
% 2.13/2.39 tff(9611,plain,
% 2.13/2.39 ((~![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(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(9612,plain,
% 2.13/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[9611, 9610])).
% 2.13/2.39 tff(9613,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9612, 65, 417, 9606, 9584, 9532])).
% 2.13/2.39 tff(9614,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9615,plain,
% 2.13/2.39 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9614, 9491, 97, 151, 9489, 9483, 9481, 54, 694, 385, 273])).
% 2.13/2.39 tff(9616,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6873, 9615])).
% 2.13/2.39 tff(9617,plain,
% 2.13/2.39 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8056, 162, 151, 6735, 9491, 9616, 694])).
% 2.13/2.39 tff(9618,plain,
% 2.13/2.39 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8063, 162, 8871, 6735, 9491, 9616, 694])).
% 2.13/2.39 tff(9619,plain,
% 2.13/2.39 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[943, 9618])).
% 2.13/2.39 tff(9620,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[4330, 9619, 54])).
% 2.13/2.39 tff(9621,plain,
% 2.13/2.39 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1789, 9620, 9617])).
% 2.13/2.39 tff(9622,plain,
% 2.13/2.39 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1517, 9621])).
% 2.13/2.39 tff(9623,plain,
% 2.13/2.39 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1259, 9622])).
% 2.13/2.39 tff(9624,plain,
% 2.13/2.39 (elem!1 = s(s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1540, 9623])).
% 2.13/2.39 tff(9625,plain,
% 2.13/2.39 (elem!1 = s(s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[9624, 9621])).
% 2.13/2.39 tff(9626,plain,
% 2.13/2.39 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9625])).
% 2.13/2.39 tff(9627,plain,
% 2.13/2.39 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1255, 9622])).
% 2.13/2.39 tff(9628,plain,
% 2.13/2.39 (~(elem!1 = s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2411, 9627, 9623])).
% 2.13/2.39 tff(9629,plain,
% 2.13/2.39 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9625])).
% 2.13/2.39 tff(9630,plain,
% 2.13/2.39 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[9629])).
% 2.13/2.39 tff(9631,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9621])).
% 2.13/2.39 tff(9632,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[9631, 9630])).
% 2.13/2.39 tff(9633,plain,
% 2.13/2.39 ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9632])).
% 2.13/2.39 tff(9634,plain,
% 2.13/2.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8312, 9616, 8871, 694])).
% 2.13/2.39 tff(9635,plain,
% 2.13/2.39 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8314, 9634])).
% 2.13/2.39 tff(9636,plain,
% 2.13/2.39 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[796, 9635, 9483])).
% 2.13/2.39 tff(9637,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6804, 9636])).
% 2.13/2.39 tff(9638,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3686, 65, 417, 788, 5623])).
% 2.13/2.39 tff(9639,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9640,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9639, 9635, 9483])).
% 2.13/2.39 tff(9641,plain,
% 2.13/2.39 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6855, 9640])).
% 2.13/2.39 tff(9642,plain,
% 2.13/2.39 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8835, 9641, 3286, 3284, 9637])).
% 2.13/2.39 tff(9643,plain,
% 2.13/2.39 (~b(elem!1, s(s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[9642, 9633])).
% 2.13/2.39 tff(9644,plain,
% 2.13/2.39 (r(elem!1, s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2445, 9643, 9628])).
% 2.13/2.39 tff(9645,plain,
% 2.13/2.39 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[9644, 9626])).
% 2.13/2.39 tff(9646,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8155, 65, 9619, 9635, 9645])).
% 2.13/2.39 tff(9647,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9648,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9647, 9479, 151, 54, 9026, 273, 9028, 9477])).
% 2.13/2.39 tff(9649,plain,
% 2.13/2.39 (b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[595, 9648])).
% 2.13/2.39 tff(9650,plain,
% 2.13/2.39 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[373, 9477, 54, 273, 9028])).
% 2.13/2.39 tff(9651,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[95, 9650])).
% 2.13/2.39 tff(9652,plain,
% 2.13/2.39 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2561, 9651, 9475])).
% 2.13/2.39 tff(9653,plain,
% 2.13/2.39 (b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[191, 9652])).
% 2.13/2.39 tff(9654,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3328, 162, 9653, 151, 3284, 3286, 9649])).
% 2.13/2.39 tff(9655,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9656,plain,
% 2.13/2.39 (~r(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9655, 9011, 53, 273])).
% 2.13/2.39 tff(9657,plain,
% 2.13/2.39 (b(s(z), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[493, 9656])).
% 2.13/2.39 tff(9658,plain,
% 2.13/2.39 (~b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3288, 9657, 53, 273, 9011])).
% 2.13/2.39 tff(9659,plain,
% 2.13/2.39 (r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[595, 9658])).
% 2.13/2.39 tff(9660,plain,
% 2.13/2.39 (~b(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8929, 152, 537, 383])).
% 2.13/2.39 tff(9661,plain,
% 2.13/2.39 (r(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[117, 9660])).
% 2.13/2.39 tff(9662,plain,
% 2.13/2.39 (~r(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2611, 9661, 385])).
% 2.13/2.39 tff(9663,plain,
% 2.13/2.39 (~b(s(s(z)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8791, 152, 537, 383])).
% 2.13/2.39 tff(9664,plain,
% 2.13/2.39 (r(s(s(z)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[245, 9663])).
% 2.13/2.39 tff(9665,plain,
% 2.13/2.39 (~b(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9471, 9664, 273, 9661, 383])).
% 2.13/2.39 tff(9666,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[295, 9665, 9662])).
% 2.13/2.39 tff(9667,plain,((~b(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9668,plain,
% 2.13/2.39 (~b(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9667, 273, 8698, 9659, 8700])).
% 2.13/2.39 tff(9669,plain,
% 2.13/2.39 (r(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[175, 9668])).
% 2.13/2.39 tff(9670,plain,
% 2.13/2.39 (~r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8647, 9669, 9659])).
% 2.13/2.39 tff(9671,plain,
% 2.13/2.39 (b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[381, 9670])).
% 2.13/2.39 tff(9672,plain,
% 2.13/2.39 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8945, 162, 121, 8700, 8727, 8698, 9657])).
% 2.13/2.39 tff(9673,plain,
% 2.13/2.39 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[191, 9672])).
% 2.13/2.39 tff(9674,plain,
% 2.13/2.39 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[503, 9673, 9669])).
% 2.13/2.39 tff(9675,plain,
% 2.13/2.39 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[83, 9674])).
% 2.13/2.39 tff(9676,plain,
% 2.13/2.39 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8999, 9675, 9657, 9659, 8725, 9669, 9671, 273])).
% 2.13/2.39 tff(9677,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2561, 9673, 9669])).
% 2.13/2.39 tff(9678,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[95, 9677])).
% 2.13/2.39 tff(9679,plain,
% 2.13/2.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8975, 9678, 121, 9673, 3])).
% 2.13/2.39 tff(9680,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6873, 9679, 9676])).
% 2.13/2.39 tff(9681,plain,((~b(z, s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9682,plain,
% 2.13/2.39 (~b(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9681, 273, 3])).
% 2.13/2.39 tff(9683,plain,
% 2.13/2.39 (r(z, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[117, 9682])).
% 2.13/2.39 tff(9684,plain,
% 2.13/2.39 (~r(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2611, 9683, 9659])).
% 2.13/2.39 tff(9685,plain,
% 2.13/2.39 (b(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[295, 9684])).
% 2.13/2.39 tff(9686,plain,
% 2.13/2.39 (~r(s(s(z)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9471, 9685, 273, 9683, 8698])).
% 2.13/2.39 tff(9687,plain,
% 2.13/2.39 (b(s(s(z)), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[245, 9686])).
% 2.13/2.39 tff(9688,plain,
% 2.13/2.39 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8575, 9687, 8700, 9671, 9685])).
% 2.13/2.39 tff(9689,plain,
% 2.13/2.39 (r(s(s(z)), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[442, 9688])).
% 2.13/2.39 tff(9690,plain,
% 2.13/2.39 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9647, 9685, 9011, 53, 9659, 273, 9683, 9671])).
% 2.13/2.39 tff(9691,plain,
% 2.13/2.39 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6862, 9690])).
% 2.13/2.39 tff(9692,plain,
% 2.13/2.39 (~r(s(s(s(s(z)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5600, 9691, 9669])).
% 2.13/2.39 tff(9693,plain,
% 2.13/2.39 (b(s(s(s(s(z)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1089, 9692])).
% 2.13/2.39 tff(9694,plain,
% 2.13/2.39 (~r(z, s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5603, 9691, 9669])).
% 2.13/2.39 tff(9695,plain,
% 2.13/2.39 (b(z, s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[823, 9694])).
% 2.13/2.39 tff(9696,plain,
% 2.13/2.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8176, 9695, 9685, 9671, 9693])).
% 2.13/2.39 tff(9697,plain,
% 2.13/2.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6804, 9696])).
% 2.13/2.39 tff(9698,plain,
% 2.13/2.39 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[796, 9697, 9689])).
% 2.13/2.39 tff(9699,plain,
% 2.13/2.39 (b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8314, 9698])).
% 2.13/2.39 tff(9700,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(9701,plain,
% 2.13/2.39 (((~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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(9702,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9701])).
% 2.13/2.39 tff(9703,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[9702, 9700])).
% 2.13/2.39 tff(9704,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(9705,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[9704, 9703])).
% 2.13/2.39 tff(9706,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9705, 162, 9687, 8700, 9693, 9695, 9699])).
% 2.13/2.39 tff(9707,plain,((~r(s(s(s(z))), s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9708,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9707, 3])).
% 2.13/2.39 tff(9709,plain,
% 2.13/2.39 (b(s(s(s(z))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[459, 9708])).
% 2.13/2.39 tff(9710,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(9711,plain,
% 2.13/2.39 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(9712,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9711])).
% 2.13/2.39 tff(9713,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[9712, 9710])).
% 2.13/2.39 tff(9714,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(9715,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[9714, 9713])).
% 2.13/2.39 tff(9716,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9715, 162, 152, 537, 445, 383, 6735, 600])).
% 2.13/2.39 tff(9717,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9718,plain,
% 2.13/2.39 (~b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9717, 152, 537, 445, 383])).
% 2.13/2.39 tff(9719,plain,
% 2.13/2.39 (r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[595, 9718])).
% 2.13/2.39 tff(9720,plain,
% 2.13/2.39 (~r(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2611, 9719, 9661])).
% 2.13/2.39 tff(9721,plain,
% 2.13/2.39 (b(z, s(s(s(z))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[295, 9720])).
% 2.13/2.39 tff(9722,plain,
% 2.13/2.39 (~r(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8477, 9664, 383, 445, 9661])).
% 2.13/2.39 tff(9723,plain,
% 2.13/2.39 (b(s(s(s(z))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[381, 9722])).
% 2.13/2.39 tff(9724,plain,
% 2.13/2.39 ((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9041, 6735])).
% 2.13/2.39 tff(9725,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9724, 9664, 383, 9661])).
% 2.13/2.39 tff(9726,plain,
% 2.13/2.39 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[95, 9725])).
% 2.13/2.39 tff(9727,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(9728,plain,
% 2.13/2.39 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(9729,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[9728])).
% 2.13/2.39 tff(9730,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[9729, 9727])).
% 2.13/2.39 tff(9731,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, 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)))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(9732,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[9731, 9730])).
% 2.13/2.39 tff(9733,plain,
% 2.13/2.39 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9732, 162, 152, 9726, 537, 445])).
% 2.13/2.39 tff(9734,plain,
% 2.13/2.39 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9733, 9721])).
% 2.13/2.39 tff(9735,plain,
% 2.13/2.39 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[191, 9734])).
% 2.13/2.39 tff(9736,plain,
% 2.13/2.39 (~r(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[534, 9735, 9661])).
% 2.13/2.39 tff(9737,plain,
% 2.13/2.39 (b(z, s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[83, 9736])).
% 2.13/2.39 tff(9738,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2517, 9735, 9719])).
% 2.13/2.39 tff(9739,plain,
% 2.13/2.39 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[338, 9738])).
% 2.13/2.39 tff(9740,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6271, 9739, 9737, 9726, 9723, 9721])).
% 2.13/2.39 tff(9741,plain,((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(9742,plain,
% 2.13/2.39 (~b(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9741, 8700, 9709, 8698])).
% 2.13/2.39 tff(9743,plain,
% 2.13/2.39 (r(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[175, 9742])).
% 2.13/2.39 tff(9744,plain,
% 2.13/2.39 (~b(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9741, 537, 445, 383])).
% 2.13/2.39 tff(9745,plain,
% 2.13/2.39 (r(s(z), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[175, 9744])).
% 2.13/2.39 tff(9746,plain,
% 2.13/2.39 (~r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[8647, 866, 9745])).
% 2.13/2.39 tff(9747,plain,
% 2.13/2.39 (b(s(s(s(z))), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[595, 9746])).
% 2.13/2.40 tff(9748,plain,
% 2.13/2.40 (~r(z, s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[8491, 9747, 383, 445, 866])).
% 2.13/2.40 tff(9749,plain,
% 2.13/2.40 (b(z, s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[117, 9748])).
% 2.13/2.40 tff(9750,plain,
% 2.13/2.40 (~r(s(z), s(s(z)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2537, 65, 194, 230])).
% 2.13/2.40 tff(9751,plain,
% 2.13/2.40 (b(s(z), s(s(z)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[3713, 9750])).
% 2.13/2.40 tff(9752,plain,
% 2.13/2.40 (~r(s(s(s(z))), s(s(z)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2028, 866, 230])).
% 2.13/2.40 tff(9753,plain,
% 2.13/2.40 (b(s(s(s(z))), s(s(z)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[459, 9752])).
% 2.13/2.40 tff(9754,plain,
% 2.13/2.40 ($false),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[4407, 162, 9753, 383, 9751, 600, 2273])).
% 2.13/2.40 tff(9755,plain,((~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.40 tff(9756,plain,
% 2.13/2.40 (~r(s(s(z)), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[9755, 9747, 383, 9745, 866])).
% 2.13/2.40 tff(9757,plain,
% 2.13/2.40 (b(s(s(z)), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[245, 9756])).
% 2.13/2.40 tff(9758,plain,
% 2.13/2.40 ($false),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[9012, 9757, 9749, 537, 383])).
% 2.13/2.40 tff(9759,plain,((~r(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.40 tff(9760,plain,
% 2.13/2.40 (~r(s(s(s(z))), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[9759, 8534, 8871, 445])).
% 2.13/2.40 tff(9761,plain,
% 2.13/2.40 (b(s(s(s(z))), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[381, 9760])).
% 2.13/2.40 tff(9762,plain,
% 2.13/2.40 (~b(s(z), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[9741, 8534, 445, 8871])).
% 2.13/2.40 tff(9763,plain,
% 2.13/2.40 (r(s(z), z)),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[175, 9762])).
% 2.13/2.40 tff(9764,plain,
% 2.13/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.40 inference(rewrite,[status(thm)],[])).
% 2.13/2.40 tff(9765,plain,
% 2.13/2.40 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.40 inference(rewrite,[status(thm)],[])).
% 2.13/2.40 tff(9766,plain,
% 2.13/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[9765])).
% 2.13/2.40 tff(9767,plain,
% 2.13/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.13/2.40 inference(transitivity,[status(thm)],[9766, 9764])).
% 2.13/2.40 tff(9768,plain,
% 2.13/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(9769,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[9768, 9767])).
% 2.23/2.40 tff(9770,plain,
% 2.23/2.40 (~b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9769, 162, 121, 8534, 445, 8871, 6735])).
% 2.23/2.40 tff(9771,plain,
% 2.23/2.40 (r(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[493, 9770])).
% 2.23/2.40 tff(9772,plain,
% 2.23/2.40 (~r(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1966, 9771, 9763])).
% 2.23/2.40 tff(9773,plain,
% 2.23/2.40 (b(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[295, 9772])).
% 2.23/2.40 tff(9774,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3138, 65, 54, 2252, 230])).
% 2.23/2.40 tff(9775,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(9776,plain,
% 2.23/2.40 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9775, 9014, 54])).
% 2.23/2.40 tff(9777,plain,
% 2.23/2.40 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[95, 9776])).
% 2.23/2.40 tff(9778,plain,
% 2.23/2.40 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6381, 162, 8534, 445, 8871, 9761, 600])).
% 2.23/2.40 tff(9779,plain,
% 2.23/2.40 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[442, 9778])).
% 2.23/2.40 tff(9780,plain,
% 2.23/2.40 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3094, 9779, 54])).
% 2.23/2.40 tff(9781,plain,
% 2.23/2.40 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[360, 9780])).
% 2.23/2.40 tff(9782,plain,
% 2.23/2.40 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8466, 9781, 121, 600, 9773, 445, 8871])).
% 2.23/2.40 tff(9783,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[95, 9782])).
% 2.23/2.40 tff(9784,plain,
% 2.23/2.40 (((~![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(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9785,plain,
% 2.23/2.40 (((~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9786,plain,
% 2.23/2.40 (((~![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(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(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[9785])).
% 2.23/2.40 tff(9787,plain,
% 2.23/2.40 (((~![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(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(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[9786, 9784])).
% 2.23/2.40 tff(9788,plain,
% 2.23/2.40 ((~![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(z))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(9789,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[9788, 9787])).
% 2.23/2.40 tff(9790,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9789, 65, 54, 9783, 9014, 9779])).
% 2.23/2.40 tff(9791,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(9792,plain,
% 2.23/2.40 (~b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9791, 121, 54, 445])).
% 2.23/2.40 tff(9793,plain,
% 2.23/2.40 (r(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[595, 9792])).
% 2.23/2.40 tff(9794,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9795,plain,
% 2.23/2.40 (((~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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9796,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[9795])).
% 2.23/2.40 tff(9797,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[9796, 9794])).
% 2.23/2.40 tff(9798,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(9799,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[9798, 9797])).
% 2.23/2.40 tff(9800,plain,
% 2.23/2.40 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9799, 162, 151, 8534, 445, 8871, 9761])).
% 2.23/2.40 tff(9801,plain,
% 2.23/2.40 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[216, 9800])).
% 2.23/2.40 tff(9802,plain,
% 2.23/2.40 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6843, 151, 445, 121, 54, 9771, 9793, 9777])).
% 2.23/2.40 tff(9803,plain,
% 2.23/2.40 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[83, 9802])).
% 2.23/2.40 tff(9804,plain,
% 2.23/2.40 (((~![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)))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9805,plain,
% 2.23/2.40 (((~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)))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9806,plain,
% 2.23/2.40 (((~![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))))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[9805])).
% 2.23/2.40 tff(9807,plain,
% 2.23/2.40 (((~![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)))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[9806, 9804])).
% 2.23/2.40 tff(9808,plain,
% 2.23/2.40 ((~![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)))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(9809,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[9808, 9807])).
% 2.23/2.40 tff(9810,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9809, 65, 9803, 9801, 9014])).
% 2.23/2.40 tff(9811,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(9812,plain,
% 2.23/2.40 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9811, 121, 445, 54])).
% 2.23/2.40 tff(9813,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[149, 9812])).
% 2.23/2.40 tff(9814,plain,
% 2.23/2.40 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2549, 9813, 9793])).
% 2.23/2.40 tff(9815,plain,
% 2.23/2.40 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[360, 9814])).
% 2.23/2.40 tff(9816,plain,
% 2.23/2.40 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[371, 9815, 9777, 9773, 9761])).
% 2.23/2.40 tff(9817,plain,
% 2.23/2.40 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[338, 9816])).
% 2.23/2.40 tff(9818,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6251, 65, 9813, 9793, 9817])).
% 2.23/2.40 tff(9819,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(9820,plain,
% 2.23/2.40 (~b(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9819, 9709, 53])).
% 2.23/2.40 tff(9821,plain,
% 2.23/2.40 (r(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[117, 9820])).
% 2.23/2.40 tff(9822,plain,
% 2.23/2.40 (~r(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1966, 1, 194])).
% 2.23/2.40 tff(9823,plain,
% 2.23/2.40 (b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[493, 9822])).
% 2.23/2.40 tff(9824,plain,
% 2.23/2.40 (~r(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2611, 1, 97])).
% 2.23/2.40 tff(9825,plain,
% 2.23/2.40 (b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[595, 9824])).
% 2.23/2.40 tff(9826,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[4407, 162, 445, 383, 6735, 9825, 9823])).
% 2.23/2.40 tff(9827,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(9828,plain,
% 2.23/2.40 (~r(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9827, 9709, 8698, 9821, 9743])).
% 2.23/2.40 tff(9829,plain,
% 2.23/2.40 (b(z, s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[295, 9828])).
% 2.23/2.40 tff(9830,plain,
% 2.23/2.40 (~r(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9759, 8700, 8698, 9709])).
% 2.23/2.40 tff(9831,plain,
% 2.23/2.40 (b(s(s(s(z))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[381, 9830])).
% 2.23/2.40 tff(9832,plain,
% 2.23/2.40 (~b(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3056, 9829, 8700, 9709, 9831])).
% 2.23/2.40 tff(9833,plain,
% 2.23/2.40 (r(s(s(z)), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[245, 9832])).
% 2.23/2.40 tff(9834,plain,
% 2.23/2.40 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9775, 9833, 53])).
% 2.23/2.40 tff(9835,plain,
% 2.23/2.40 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[95, 9834])).
% 2.23/2.40 tff(9836,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9837,plain,
% 2.23/2.40 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9838,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[9837])).
% 2.23/2.40 tff(9839,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[9838, 9836])).
% 2.23/2.40 tff(9840,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(9841,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 2.23/2.40 tff(9842,plain,
% 2.23/2.40 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9841, 162, 9835, 8700, 9709, 9831, 9829])).
% 2.23/2.40 tff(9843,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[360, 9842])).
% 2.23/2.40 tff(9844,plain,
% 2.23/2.40 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3094, 9843, 53])).
% 2.23/2.40 tff(9845,plain,
% 2.23/2.40 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[442, 9844])).
% 2.23/2.40 tff(9846,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[5856, 162, 8700, 9845, 9709, 9831, 9829])).
% 2.23/2.40 tff(9847,plain,(b(s(s(s(s(elem!1)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(9848,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[6751, 65, 273, 55, 866])).
% 2.23/2.40 tff(9849,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(9850,plain,
% 2.23/2.40 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9849, 866, 55])).
% 2.23/2.40 tff(9851,plain,
% 2.23/2.40 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[459, 9850])).
% 2.23/2.40 tff(9852,plain,
% 2.23/2.40 (~r(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[105, 55, 2])).
% 2.23/2.40 tff(9853,plain,
% 2.23/2.40 (b(z, s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[117, 9852])).
% 2.23/2.40 tff(9854,plain,
% 2.23/2.40 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8672, 599, 445, 600])).
% 2.23/2.40 tff(9855,plain,
% 2.23/2.40 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[442, 9854])).
% 2.23/2.40 tff(9856,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9857,plain,
% 2.23/2.40 (((~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(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(9858,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[9857])).
% 2.23/2.40 tff(9859,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[9858, 9856])).
% 2.23/2.41 tff(9860,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(9861,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[9860, 9859])).
% 2.23/2.41 tff(9862,plain,
% 2.23/2.41 ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9861, 162, 121, 445, 6735, 600])).
% 2.23/2.41 tff(9863,plain,
% 2.23/2.41 (~b(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9862, 599])).
% 2.23/2.41 tff(9864,plain,
% 2.23/2.41 (r(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[295, 9863])).
% 2.23/2.41 tff(9865,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[833, 9864, 9855, 55])).
% 2.23/2.41 tff(9866,plain,((~b(s(z), s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9867,plain,
% 2.23/2.41 (~b(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9866, 600, 9853, 9851, 55])).
% 2.23/2.41 tff(9868,plain,
% 2.23/2.41 (r(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[493, 9867])).
% 2.23/2.41 tff(9869,plain,
% 2.23/2.41 (~r(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2271, 9868, 866])).
% 2.23/2.41 tff(9870,plain,
% 2.23/2.41 (b(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[175, 9869])).
% 2.23/2.41 tff(9871,plain,
% 2.23/2.41 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8549, 385, 2])).
% 2.23/2.41 tff(9872,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[459, 9871])).
% 2.23/2.41 tff(9873,plain,
% 2.23/2.41 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2986, 363, 9847, 9872, 588])).
% 2.23/2.41 tff(9874,plain,
% 2.23/2.41 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[216, 9873])).
% 2.23/2.41 tff(9875,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[131, 9874, 2])).
% 2.23/2.41 tff(9876,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[149, 9875])).
% 2.23/2.41 tff(9877,plain,
% 2.23/2.41 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6166, 9874, 55])).
% 2.23/2.41 tff(9878,plain,
% 2.23/2.41 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[83, 9877])).
% 2.23/2.41 tff(9879,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[453, 363, 9847, 9872, 588])).
% 2.23/2.41 tff(9880,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[338, 9879])).
% 2.23/2.41 tff(9881,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2517, 9880, 385])).
% 2.23/2.41 tff(9882,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[191, 9881])).
% 2.23/2.41 tff(9883,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4610, 9882, 9878, 9853, 152, 9876])).
% 2.23/2.41 tff(9884,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9885,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9884, 385, 152, 2, 55])).
% 2.23/2.41 tff(9886,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[360, 9885])).
% 2.23/2.41 tff(9887,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2549, 9886, 385])).
% 2.23/2.41 tff(9888,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[149, 9887])).
% 2.23/2.41 tff(9889,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9890,plain,
% 2.23/2.41 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), 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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9891,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[9890])).
% 2.23/2.41 tff(9892,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[9891, 9889])).
% 2.23/2.41 tff(9893,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(9894,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[9893, 9892])).
% 2.23/2.41 tff(9895,plain,
% 2.23/2.41 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9894, 162, 152, 9853, 9888, 538, 6735])).
% 2.23/2.41 tff(9896,plain,
% 2.23/2.41 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[83, 9895])).
% 2.23/2.41 tff(9897,plain,
% 2.23/2.41 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6166, 9896, 55])).
% 2.23/2.41 tff(9898,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[216, 9897])).
% 2.23/2.41 tff(9899,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5846, 9898, 9847, 9872, 588])).
% 2.23/2.41 tff(9900,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[338, 9899])).
% 2.23/2.41 tff(9901,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[3304, 65, 9896, 9900, 866])).
% 2.23/2.41 tff(9902,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9903,plain,
% 2.23/2.41 (~r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9902, 152, 55, 866, 538, 2])).
% 2.23/2.41 tff(9904,plain,
% 2.23/2.41 (b(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[595, 9903])).
% 2.23/2.41 tff(9905,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9906,plain,
% 2.23/2.41 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9907,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[9906])).
% 2.23/2.41 tff(9908,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[9907, 9905])).
% 2.23/2.41 tff(9909,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(9910,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[9909, 9908])).
% 2.23/2.41 tff(9911,plain,
% 2.23/2.41 (~b(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9910, 162, 152, 9853, 538, 6735, 9904])).
% 2.23/2.41 tff(9912,plain,
% 2.23/2.41 (r(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[295, 9911])).
% 2.23/2.41 tff(9913,plain,
% 2.23/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[833, 9912, 55])).
% 2.23/2.41 tff(9914,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[442, 9913])).
% 2.23/2.41 tff(9915,plain,
% 2.23/2.41 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[281, 9912, 55])).
% 2.23/2.41 tff(9916,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[459, 9915])).
% 2.23/2.41 tff(9917,plain,
% 2.23/2.41 (~b(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8672, 9916, 9904, 9914])).
% 2.23/2.41 tff(9918,plain,
% 2.23/2.41 (r(s(z), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[493, 9917])).
% 2.23/2.41 tff(9919,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[413, 340, 395])).
% 2.23/2.41 tff(9920,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[191, 9919])).
% 2.23/2.41 tff(9921,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5481, 340, 395])).
% 2.23/2.41 tff(9922,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[149, 9921])).
% 2.23/2.41 tff(9923,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2601, 340, 1])).
% 2.23/2.41 tff(9924,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[95, 9923])).
% 2.23/2.41 tff(9925,plain,
% 2.23/2.41 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[566, 340, 1])).
% 2.23/2.41 tff(9926,plain,
% 2.23/2.41 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[83, 9925])).
% 2.23/2.41 tff(9927,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[185, 9926, 9924, 121, 9922, 9920])).
% 2.23/2.41 tff(9928,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9929,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9928, 9918, 9853, 9912])).
% 2.23/2.41 tff(9930,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[360, 9929])).
% 2.23/2.41 tff(9931,plain,
% 2.23/2.41 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2986, 9930, 9847, 9916, 9914])).
% 2.23/2.41 tff(9932,plain,
% 2.23/2.41 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[216, 9931])).
% 2.23/2.41 tff(9933,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[131, 9932, 2])).
% 2.23/2.41 tff(9934,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[149, 9933])).
% 2.23/2.41 tff(9935,plain,
% 2.23/2.41 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6166, 9932, 55])).
% 2.23/2.41 tff(9936,plain,
% 2.23/2.41 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[83, 9935])).
% 2.23/2.41 tff(9937,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[453, 9930, 9847, 9916, 9914])).
% 2.23/2.41 tff(9938,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[338, 9937])).
% 2.23/2.41 tff(9939,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[476, 65, 193, 395, 299])).
% 2.23/2.41 tff(9940,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9941,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9940, 9938, 9918])).
% 2.23/2.41 tff(9942,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[191, 9941])).
% 2.23/2.41 tff(9943,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4610, 9942, 9936, 9853, 152, 9934])).
% 2.23/2.41 tff(9944,plain,((~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9945,plain,
% 2.23/2.41 (~b(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9944, 9870, 55, 2, 866])).
% 2.23/2.41 tff(9946,plain,
% 2.23/2.41 (r(s(s(z)), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[245, 9945])).
% 2.23/2.41 tff(9947,plain,
% 2.23/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8456, 9946, 866])).
% 2.23/2.41 tff(9948,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[442, 9947])).
% 2.23/2.41 tff(9949,plain,
% 2.23/2.41 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2986, 363, 9847, 445, 444])).
% 2.23/2.41 tff(9950,plain,
% 2.23/2.41 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[216, 9949])).
% 2.23/2.41 tff(9951,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[131, 9950, 2])).
% 2.23/2.41 tff(9952,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[149, 9951])).
% 2.23/2.41 tff(9953,plain,
% 2.23/2.41 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6166, 9950, 55])).
% 2.23/2.41 tff(9954,plain,
% 2.23/2.41 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[83, 9953])).
% 2.23/2.41 tff(9955,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[453, 363, 9847, 445, 444])).
% 2.23/2.41 tff(9956,plain,
% 2.23/2.41 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[338, 9955])).
% 2.23/2.41 tff(9957,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9940, 9956, 395])).
% 2.23/2.41 tff(9958,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[191, 9957])).
% 2.23/2.41 tff(9959,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4610, 9958, 9954, 9853, 152, 9952])).
% 2.23/2.41 tff(9960,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9961,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9960, 9870, 9868, 2, 55, 9851, 9948])).
% 2.23/2.41 tff(9962,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[360, 9961])).
% 2.23/2.41 tff(9963,plain,
% 2.23/2.41 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[413, 9962, 9868])).
% 2.23/2.41 tff(9964,plain,
% 2.23/2.41 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[191, 9963])).
% 2.23/2.41 tff(9965,plain,
% 2.23/2.41 (~r(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9928, 9962, 9853, 9868])).
% 2.23/2.41 tff(9966,plain,
% 2.23/2.41 (b(z, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[295, 9965])).
% 2.23/2.41 tff(9967,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9968,plain,
% 2.23/2.41 (((~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(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9969,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[9968])).
% 2.23/2.41 tff(9970,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[9969, 9967])).
% 2.23/2.41 tff(9971,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(9972,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[9971, 9970])).
% 2.23/2.41 tff(9973,plain,
% 2.23/2.41 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9972, 162, 9853, 9847, 6735, 600])).
% 2.23/2.41 tff(9974,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9973, 9966, 9964])).
% 2.23/2.41 tff(9975,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(9976,plain,
% 2.23/2.41 (~b(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9975, 866, 55, 2])).
% 2.23/2.41 tff(9977,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[595, 9976])).
% 2.23/2.41 tff(9978,plain,
% 2.23/2.41 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[586, 9977, 2])).
% 2.23/2.41 tff(9979,plain,
% 2.23/2.41 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[442, 9978])).
% 2.23/2.41 tff(9980,plain,
% 2.23/2.41 (~r(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8647, 9977, 866])).
% 2.23/2.41 tff(9981,plain,
% 2.23/2.41 (b(s(z), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[175, 9980])).
% 2.23/2.41 tff(9982,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9884, 9981, 9977, 2, 55])).
% 2.23/2.41 tff(9983,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[360, 9982])).
% 2.23/2.41 tff(9984,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2549, 9983, 9977])).
% 2.23/2.41 tff(9985,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[149, 9984])).
% 2.23/2.41 tff(9986,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9987,plain,
% 2.23/2.41 (((~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(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(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(9988,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[9987])).
% 2.23/2.41 tff(9989,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[9988, 9986])).
% 2.23/2.42 tff(9990,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(9991,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[9990, 9989])).
% 2.23/2.42 tff(9992,plain,
% 2.23/2.42 ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9991, 162, 121, 151, 9851, 6735])).
% 2.23/2.42 tff(9993,plain,
% 2.23/2.42 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9992, 599])).
% 2.23/2.42 tff(9994,plain,
% 2.23/2.42 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[83, 9993])).
% 2.23/2.42 tff(9995,plain,
% 2.23/2.42 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6166, 9994, 55])).
% 2.23/2.42 tff(9996,plain,
% 2.23/2.42 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[216, 9995])).
% 2.23/2.42 tff(9997,plain,
% 2.23/2.42 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[5846, 9996, 9847, 9851, 444])).
% 2.23/2.42 tff(9998,plain,
% 2.23/2.42 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[338, 9997])).
% 2.23/2.42 tff(9999,plain,
% 2.23/2.42 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6831, 162, 121, 151, 9851, 6735])).
% 2.23/2.42 tff(10000,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9999, 599])).
% 2.23/2.42 tff(10001,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[95, 10000])).
% 2.23/2.42 tff(10002,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), 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))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10003,plain,
% 2.23/2.42 (((~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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10004,plain,
% 2.23/2.42 (((~![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(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[10003])).
% 2.23/2.42 tff(10005,plain,
% 2.23/2.42 (((~![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(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(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[10004, 10002])).
% 2.23/2.42 tff(10006,plain,
% 2.23/2.42 ((~![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(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)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(10007,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[10006, 10005])).
% 2.23/2.42 tff(10008,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10007, 65, 10001, 9998, 866])).
% 2.23/2.42 tff(10009,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(10010,plain,
% 2.23/2.42 (~b(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10009, 866, 9979, 55, 9853, 9985])).
% 2.23/2.42 tff(10011,plain,
% 2.23/2.42 (r(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[493, 10010])).
% 2.23/2.42 tff(10012,plain,
% 2.23/2.42 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[413, 10011, 9983])).
% 2.23/2.42 tff(10013,plain,
% 2.23/2.42 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[191, 10012])).
% 2.23/2.42 tff(10014,plain,
% 2.23/2.42 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4610, 10013, 9853, 9981, 9985])).
% 2.23/2.42 tff(10015,plain,
% 2.23/2.42 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[83, 10014])).
% 2.23/2.42 tff(10016,plain,
% 2.23/2.42 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6166, 10015, 55])).
% 2.23/2.42 tff(10017,plain,
% 2.23/2.42 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[216, 10016])).
% 2.23/2.42 tff(10018,plain,
% 2.23/2.42 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[5846, 10017, 9847, 9851, 9979])).
% 2.23/2.42 tff(10019,plain,
% 2.23/2.42 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[338, 10018])).
% 2.23/2.42 tff(10020,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[3122, 10013, 9853, 9981, 9985])).
% 2.23/2.42 tff(10021,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[95, 10020])).
% 2.23/2.42 tff(10022,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10007, 65, 10021, 10019, 866])).
% 2.23/2.42 tff(10023,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(10024,plain,
% 2.23/2.42 (~r(s(s(s(z))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10023, 55, 2])).
% 2.23/2.42 tff(10025,plain,
% 2.23/2.42 (b(s(s(s(z))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[381, 10024])).
% 2.23/2.42 tff(10026,plain,
% 2.23/2.42 (~b(s(z), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[5513, 296, 9853, 10025, 8551])).
% 2.23/2.42 tff(10027,plain,
% 2.23/2.42 (r(s(z), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[175, 10026])).
% 2.23/2.42 tff(10028,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10029,plain,
% 2.23/2.42 (((~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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10030,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[10029])).
% 2.23/2.42 tff(10031,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[10030, 10028])).
% 2.23/2.42 tff(10032,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(10033,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[10032, 10031])).
% 2.23/2.42 tff(10034,plain,
% 2.23/2.42 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10033, 162, 9853, 9847, 6735, 10025, 8551])).
% 2.23/2.42 tff(10035,plain,
% 2.23/2.42 (r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[191, 10034])).
% 2.23/2.42 tff(10036,plain,
% 2.23/2.42 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[503, 10035, 10027])).
% 2.23/2.42 tff(10037,plain,
% 2.23/2.42 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[83, 10036])).
% 2.23/2.42 tff(10038,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2561, 10035, 10027])).
% 2.23/2.42 tff(10039,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[95, 10038])).
% 2.23/2.42 tff(10040,plain,
% 2.23/2.42 (~b(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[5781, 296, 9853, 10025, 8551])).
% 2.23/2.42 tff(10041,plain,
% 2.23/2.42 (r(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[493, 10040])).
% 2.23/2.42 tff(10042,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9940, 10035, 10041])).
% 2.23/2.42 tff(10043,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[338, 10042])).
% 2.23/2.42 tff(10044,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6271, 10043, 10039, 10025, 10037, 296])).
% 2.23/2.42 tff(10045,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(10046,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10045, 55, 2])).
% 2.23/2.42 tff(10047,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[459, 10046])).
% 2.23/2.42 tff(10048,plain,
% 2.23/2.42 (~r(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1966, 194, 395])).
% 2.23/2.42 tff(10049,plain,
% 2.23/2.42 (b(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[295, 10048])).
% 2.23/2.42 tff(10050,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[7999, 10049, 5571, 298, 445, 444])).
% 2.23/2.42 tff(10051,plain,((~r(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(10052,plain,
% 2.23/2.42 (~r(s(z), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10051, 588, 10047, 10025, 395, 2])).
% 2.23/2.42 tff(10053,plain,
% 2.23/2.42 (b(s(z), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[175, 10052])).
% 2.23/2.42 tff(10054,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9884, 10053, 385, 2, 55])).
% 2.23/2.42 tff(10055,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[360, 10054])).
% 2.23/2.42 tff(10056,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2549, 10055, 385])).
% 2.23/2.42 tff(10057,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[149, 10056])).
% 2.23/2.42 tff(10058,plain,
% 2.23/2.42 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[413, 10055, 395])).
% 2.23/2.42 tff(10059,plain,
% 2.23/2.42 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[191, 10058])).
% 2.23/2.42 tff(10060,plain,
% 2.23/2.42 (~r(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9928, 10055, 9853, 395])).
% 2.23/2.42 tff(10061,plain,
% 2.23/2.42 (b(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[295, 10060])).
% 2.23/2.42 tff(10062,plain,
% 2.23/2.42 (~b(s(s(z)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[7999, 10061, 10025, 10047, 588])).
% 2.23/2.42 tff(10063,plain,
% 2.23/2.42 (r(s(s(z)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[245, 10062])).
% 2.23/2.42 tff(10064,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[5451, 10063, 9847, 2, 385, 55, 10047, 10055, 10059, 10053, 9853, 10057])).
% 2.23/2.42 tff(10065,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6873, 10064])).
% 2.23/2.42 tff(10066,plain,
% 2.23/2.42 (~r(z, s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2647, 10065, 55])).
% 2.23/2.42 tff(10067,plain,
% 2.23/2.42 (b(z, s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[823, 10066])).
% 2.23/2.42 tff(10068,plain,
% 2.23/2.42 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4610, 10059, 9853, 10053, 10057])).
% 2.23/2.42 tff(10069,plain,
% 2.23/2.42 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[83, 10068])).
% 2.23/2.42 tff(10070,plain,
% 2.23/2.42 (((~![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(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10071,plain,
% 2.23/2.42 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10072,plain,
% 2.23/2.42 (((~![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(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[10071])).
% 2.23/2.42 tff(10073,plain,
% 2.23/2.42 (((~![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(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.23/2.42 inference(transitivity,[status(thm)],[10072, 10070])).
% 2.23/2.42 tff(10074,plain,
% 2.23/2.42 ((~![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(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(10075,plain,
% 2.23/2.42 ((~![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(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[10074, 10073])).
% 2.23/2.42 tff(10076,plain,
% 2.23/2.42 (~r(s(s(s(s(z)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10075, 65, 10069, 55, 10065])).
% 2.23/2.42 tff(10077,plain,
% 2.23/2.42 (b(s(s(s(s(z)))), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1089, 10076])).
% 2.23/2.42 tff(10078,plain,
% 2.23/2.42 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8176, 10077, 10025, 10061, 10067])).
% 2.23/2.42 tff(10079,plain,
% 2.23/2.42 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6804, 10078])).
% 2.23/2.42 tff(10080,plain,
% 2.23/2.42 (~r(s(z), s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[7981, 10079, 395])).
% 2.23/2.42 tff(10081,plain,
% 2.23/2.42 (b(s(z), s(s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[6862, 10080])).
% 2.23/2.42 tff(10082,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10083,plain,
% 2.23/2.42 (((~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)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10084,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[10083])).
% 2.23/2.42 tff(10085,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[10084, 10082])).
% 2.23/2.42 tff(10086,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(10087,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[10086, 10085])).
% 2.23/2.42 tff(10088,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10087, 162, 10053, 9853, 10077, 10081, 10067])).
% 2.23/2.42 tff(10089,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(10090,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10089, 395, 55, 2])).
% 2.23/2.42 tff(10091,plain,
% 2.23/2.42 (b(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[595, 10090])).
% 2.23/2.42 tff(10092,plain,
% 2.23/2.42 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10033, 162, 9853, 9847, 6735, 10025, 10091])).
% 2.23/2.42 tff(10093,plain,
% 2.23/2.42 (r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[191, 10092])).
% 2.23/2.42 tff(10094,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[413, 10093, 395])).
% 2.23/2.42 tff(10095,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[360, 10094])).
% 2.23/2.42 tff(10096,plain,
% 2.23/2.42 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9940, 10093, 395])).
% 2.23/2.42 tff(10097,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[338, 10096])).
% 2.23/2.42 tff(10098,plain,
% 2.23/2.42 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[620, 10097, 9847, 10047, 10095])).
% 2.23/2.42 tff(10099,plain,
% 2.23/2.42 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[216, 10098])).
% 2.23/2.42 tff(10100,plain,
% 2.23/2.42 (~r(s(z), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[202, 10099, 2, 10093])).
% 2.23/2.42 tff(10101,plain,
% 2.23/2.42 (b(s(z), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[175, 10100])).
% 2.23/2.42 tff(10102,plain,
% 2.23/2.42 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[453, 10095, 9847, 10047, 10097])).
% 2.23/2.42 tff(10103,plain,
% 2.23/2.42 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[442, 10102])).
% 2.23/2.42 tff(10104,plain,
% 2.23/2.42 (~r(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[833, 10103, 55])).
% 2.23/2.42 tff(10105,plain,
% 2.23/2.42 (b(z, s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[295, 10104])).
% 2.23/2.42 tff(10106,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[5513, 10105, 10101, 9853, 10025, 10091])).
% 2.23/2.42 tff(10107,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(10108,plain,
% 2.23/2.42 (~r(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10107, 55, 2])).
% 2.23/2.42 tff(10109,plain,
% 2.23/2.42 (b(s(z), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[493, 10108])).
% 2.23/2.42 tff(10110,plain,
% 2.23/2.42 (~b(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9866, 10109, 9853, 10047, 55])).
% 2.23/2.42 tff(10111,plain,
% 2.23/2.42 (r(s(s(s(z))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[595, 10110])).
% 2.23/2.42 tff(10112,plain,
% 2.23/2.42 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[586, 10111, 2])).
% 2.23/2.42 tff(10113,plain,
% 2.23/2.42 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[442, 10112])).
% 2.23/2.42 tff(10114,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10115,plain,
% 2.23/2.42 (((~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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(10116,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[10115])).
% 2.23/2.43 tff(10117,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[10116, 10114])).
% 2.23/2.43 tff(10118,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(10119,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[10118, 10117])).
% 2.23/2.43 tff(10120,plain,
% 2.23/2.43 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10119, 162, 9847, 10113, 10047, 6735, 10109])).
% 2.23/2.43 tff(10121,plain,
% 2.23/2.43 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[338, 10120])).
% 2.23/2.43 tff(10122,plain,
% 2.23/2.43 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2517, 10121, 10111])).
% 2.23/2.43 tff(10123,plain,
% 2.23/2.43 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[191, 10122])).
% 2.23/2.43 tff(10124,plain,
% 2.23/2.43 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9884, 152, 10111, 2, 55])).
% 2.23/2.43 tff(10125,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[360, 10124])).
% 2.23/2.43 tff(10126,plain,
% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2549, 10125, 10111])).
% 2.23/2.43 tff(10127,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[149, 10126])).
% 2.23/2.43 tff(10128,plain,
% 2.23/2.43 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[4610, 10127, 9853, 10123, 152])).
% 2.23/2.43 tff(10129,plain,
% 2.23/2.43 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[83, 10128])).
% 2.23/2.43 tff(10130,plain,
% 2.23/2.43 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[6166, 10129, 55])).
% 2.23/2.43 tff(10131,plain,
% 2.23/2.43 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[216, 10130])).
% 2.23/2.43 tff(10132,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10133,plain,
% 2.23/2.43 (((~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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10134,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[10133])).
% 2.23/2.43 tff(10135,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[10134, 10132])).
% 2.23/2.43 tff(10136,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(10137,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[10136, 10135])).
% 2.23/2.43 tff(10138,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10137, 162, 9847, 10123, 10127, 10131, 6735])).
% 2.23/2.43 tff(10139,plain,((~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(10140,plain,
% 2.23/2.43 (~b(s(z), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10139, 55, 2])).
% 2.23/2.43 tff(10141,plain,
% 2.23/2.43 (r(s(z), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[175, 10140])).
% 2.23/2.43 tff(10142,plain,
% 2.23/2.43 (~r(s(s(z)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[238, 10141, 2])).
% 2.23/2.43 tff(10143,plain,
% 2.23/2.43 (b(s(s(z)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[245, 10142])).
% 2.23/2.43 tff(10144,plain,
% 2.23/2.43 (~b(z, s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7999, 10143, 10025, 10047, 10113])).
% 2.23/2.43 tff(10145,plain,
% 2.23/2.43 (r(z, s(s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[295, 10144])).
% 2.23/2.43 tff(10146,plain,
% 2.23/2.43 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2507, 10145, 10121])).
% 2.23/2.43 tff(10147,plain,
% 2.23/2.43 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[83, 10146])).
% 2.23/2.43 tff(10148,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10149,plain,
% 2.23/2.43 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10150,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[10149])).
% 2.23/2.43 tff(10151,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[10150, 10148])).
% 2.23/2.43 tff(10152,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(10153,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[10152, 10151])).
% 2.23/2.43 tff(10154,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10153, 162, 9853, 10123, 10147, 10143, 10113, 10025])).
% 2.23/2.43 tff(10155,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(10156,plain,
% 2.23/2.43 (~r(z, s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10155, 2])).
% 2.23/2.43 tff(10157,plain,
% 2.23/2.43 (b(z, s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[524, 10156])).
% 2.23/2.43 tff(10158,plain,
% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5582, 194, 2, 10157, 9847])).
% 2.23/2.43 tff(10159,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[149, 10158])).
% 2.23/2.43 tff(10160,plain,
% 2.23/2.43 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[556, 193, 9847, 2, 97])).
% 2.23/2.43 tff(10161,plain,
% 2.23/2.43 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[202, 193, 2, 194])).
% 2.23/2.43 tff(10162,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[216, 10161, 10160])).
% 2.23/2.43 tff(10163,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(10164,plain,
% 2.23/2.43 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10163, 194, 2, 97])).
% 2.23/2.43 tff(10165,plain,
% 2.23/2.43 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[191, 10164])).
% 2.23/2.43 tff(10166,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10167,plain,
% 2.23/2.43 (((~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(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10168,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[10167])).
% 2.23/2.43 tff(10169,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[10168, 10166])).
% 2.23/2.43 tff(10170,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(10171,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[10170, 10169])).
% 2.23/2.43 tff(10172,plain,
% 2.23/2.43 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10171, 162, 9847, 6735, 8551, 5553])).
% 2.23/2.43 tff(10173,plain,
% 2.23/2.43 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10172, 10165])).
% 2.23/2.43 tff(10174,plain,
% 2.23/2.43 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1001, 10173])).
% 2.23/2.43 tff(10175,plain,
% 2.23/2.43 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[904, 10174, 273])).
% 2.23/2.43 tff(10176,plain,
% 2.23/2.43 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[923, 10175])).
% 2.23/2.43 tff(10177,plain,
% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5567, 3044, 9847, 10157, 97])).
% 2.23/2.43 tff(10178,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[149, 10177])).
% 2.23/2.43 tff(10179,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10180,plain,
% 2.23/2.43 (((~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(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(10181,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[10180])).
% 2.23/2.43 tff(10182,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[10181, 10179])).
% 2.23/2.43 tff(10183,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(10184,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[10183, 10182])).
% 2.23/2.43 tff(10185,plain,
% 2.23/2.43 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10184, 162, 9847, 10178, 6735, 8551])).
% 2.23/2.43 tff(10186,plain,
% 2.23/2.43 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10185, 10165])).
% 2.23/2.43 tff(10187,plain,
% 2.23/2.43 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[338, 10186])).
% 2.23/2.43 tff(10188,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10189,plain,
% 2.23/2.44 (((~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(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10190,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10189])).
% 2.23/2.44 tff(10191,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[10190, 10188])).
% 2.23/2.44 tff(10192,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(10193,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[10192, 10191])).
% 2.23/2.44 tff(10194,plain,
% 2.23/2.44 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10193, 162, 9847, 10178, 6735, 5553])).
% 2.23/2.44 tff(10195,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10194, 10165])).
% 2.23/2.44 tff(10196,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10197,plain,
% 2.23/2.44 (((~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(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(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10198,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10197])).
% 2.23/2.44 tff(10199,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[10198, 10196])).
% 2.23/2.44 tff(10200,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(10201,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[10200, 10199])).
% 2.23/2.44 tff(10202,plain,
% 2.23/2.44 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10201, 162, 9847, 10178, 6735, 8551])).
% 2.23/2.44 tff(10203,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10202, 10165])).
% 2.23/2.44 tff(10204,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[360, 10203])).
% 2.23/2.44 tff(10205,plain,
% 2.23/2.44 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5320, 10174, 10204])).
% 2.23/2.44 tff(10206,plain,
% 2.23/2.44 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1789, 10205, 10195])).
% 2.23/2.44 tff(10207,plain,
% 2.23/2.44 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5940, 10206, 2, 9847, 97, 10187])).
% 2.23/2.44 tff(10208,plain,
% 2.23/2.44 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[943, 10207])).
% 2.23/2.44 tff(10209,plain,
% 2.23/2.44 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[9521, 10208, 5553, 10176])).
% 2.23/2.44 tff(10210,plain,
% 2.23/2.44 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1050, 10209])).
% 2.23/2.44 tff(10211,plain,
% 2.23/2.44 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[935, 10208, 10157, 10176, 3044])).
% 2.23/2.44 tff(10212,plain,
% 2.23/2.44 (r(s(s(s(s(s(elem!1))))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[894, 10211])).
% 2.23/2.44 tff(10213,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5714, 10212, 10210, 194])).
% 2.23/2.44 tff(10214,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(10215,plain,
% 2.23/2.44 (~r(s(z), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10214, 273, 97, 2])).
% 2.23/2.44 tff(10216,plain,
% 2.23/2.44 (b(s(z), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[175, 10215])).
% 2.23/2.44 tff(10217,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10218,plain,
% 2.23/2.44 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10219,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10218])).
% 2.23/2.44 tff(10220,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[10219, 10217])).
% 2.23/2.44 tff(10221,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(10222,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[10221, 10220])).
% 2.23/2.44 tff(10223,plain,
% 2.23/2.44 ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10222, 162, 10178, 10157, 6735, 5553])).
% 2.23/2.44 tff(10224,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10223, 10216])).
% 2.23/2.44 tff(10225,plain,
% 2.23/2.44 ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8593, 162, 10178, 10157, 6735, 8551])).
% 2.23/2.44 tff(10226,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10225, 10216])).
% 2.23/2.44 tff(10227,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[360, 10226])).
% 2.23/2.44 tff(10228,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10229,plain,
% 2.23/2.44 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10230,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10229])).
% 2.23/2.44 tff(10231,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[10230, 10228])).
% 2.23/2.44 tff(10232,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(10233,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[10232, 10231])).
% 2.23/2.44 tff(10234,plain,
% 2.23/2.44 ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10233, 162, 10157, 6735, 8551, 5553])).
% 2.23/2.44 tff(10235,plain,
% 2.23/2.44 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10234, 10216])).
% 2.23/2.44 tff(10236,plain,
% 2.23/2.44 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1001, 10235])).
% 2.23/2.44 tff(10237,plain,
% 2.23/2.44 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5320, 10236, 10227])).
% 2.23/2.44 tff(10238,plain,
% 2.23/2.44 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1789, 10237, 10224])).
% 2.23/2.44 tff(10239,plain,
% 2.23/2.44 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10238])).
% 2.23/2.44 tff(10240,plain,
% 2.23/2.44 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(symmetry,[status(thm)],[10239])).
% 2.23/2.44 tff(10241,plain,
% 2.23/2.44 ((~b(s(z), s(s(s(s(s(elem!1))))))) <=> (~b(s(z), s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10240])).
% 2.23/2.44 tff(10242,plain,
% 2.23/2.44 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[904, 10236, 273])).
% 2.23/2.44 tff(10243,plain,
% 2.23/2.44 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[923, 10242])).
% 2.23/2.44 tff(10244,plain,
% 2.23/2.44 ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8559, 162, 10178, 10157, 6735, 8551])).
% 2.23/2.44 tff(10245,plain,
% 2.23/2.44 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10244, 10216])).
% 2.23/2.44 tff(10246,plain,
% 2.23/2.44 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[338, 10245])).
% 2.23/2.44 tff(10247,plain,
% 2.23/2.44 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5940, 10238, 2, 9847, 97, 10246])).
% 2.23/2.44 tff(10248,plain,
% 2.23/2.44 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[943, 10247])).
% 2.23/2.44 tff(10249,plain,
% 2.23/2.44 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[9521, 10248, 5553, 10243])).
% 2.23/2.44 tff(10250,plain,
% 2.23/2.44 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[10249, 10241])).
% 2.23/2.44 tff(10251,plain,
% 2.23/2.44 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[6509, 10246, 273])).
% 2.23/2.44 tff(10252,plain,
% 2.23/2.44 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[216, 10251])).
% 2.23/2.44 tff(10253,plain,
% 2.23/2.44 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[556, 10252, 9847, 2, 97])).
% 2.23/2.44 tff(10254,plain,
% 2.23/2.44 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[191, 10253])).
% 2.23/2.44 tff(10255,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10254, 10250])).
% 2.23/2.44 tff(10256,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(10257,plain,
% 2.23/2.44 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10256, 97, 2])).
% 2.23/2.44 tff(10258,plain,
% 2.23/2.44 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[459, 10257])).
% 2.23/2.44 tff(10259,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10260,plain,
% 2.23/2.44 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10261,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[10260])).
% 2.23/2.44 tff(10262,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[10261, 10259])).
% 2.23/2.44 tff(10263,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(10264,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[10263, 10262])).
% 2.23/2.44 tff(10265,plain,
% 2.23/2.44 (~b(z, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10264, 162, 152, 538, 537, 445, 6735])).
% 2.23/2.44 tff(10266,plain,
% 2.23/2.44 (r(z, s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[295, 10265])).
% 2.23/2.44 tff(10267,plain,
% 2.23/2.44 (~r(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[3102, 10266, 97])).
% 2.23/2.44 tff(10268,plain,
% 2.23/2.44 (b(s(z), s(s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[493, 10267])).
% 2.23/2.44 tff(10269,plain,
% 2.23/2.44 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5567, 538, 9847, 537, 97])).
% 2.23/2.44 tff(10270,plain,
% 2.23/2.44 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[149, 10269])).
% 2.23/2.44 tff(10271,plain,
% 2.23/2.44 (~r(s(s(s(z))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2611, 10266, 97])).
% 2.23/2.44 tff(10272,plain,
% 2.23/2.44 (b(s(s(s(z))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[595, 10271])).
% 2.23/2.44 tff(10273,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10274,plain,
% 2.23/2.44 (((~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(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(10275,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[10274])).
% 2.23/2.45 tff(10276,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[10275, 10273])).
% 2.23/2.45 tff(10277,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(10278,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[10277, 10276])).
% 2.23/2.45 tff(10279,plain,
% 2.23/2.45 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10278, 162, 152, 9847, 538, 537, 6735])).
% 2.23/2.45 tff(10280,plain,
% 2.23/2.45 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[83, 10279])).
% 2.23/2.45 tff(10281,plain,
% 2.23/2.45 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[534, 10280, 97])).
% 2.23/2.45 tff(10282,plain,
% 2.23/2.45 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[191, 10281])).
% 2.23/2.45 tff(10283,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2507, 10266, 10280])).
% 2.23/2.45 tff(10284,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[338, 10283])).
% 2.23/2.45 tff(10285,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5901, 10284, 10282, 10272, 10270, 10268])).
% 2.23/2.45 tff(10286,plain,((~b(s(z), z)) | (~r(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10287,plain,
% 2.23/2.45 (~b(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10286, 97, 3044, 10157, 10258])).
% 2.23/2.45 tff(10288,plain,
% 2.23/2.45 (r(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[175, 10287])).
% 2.23/2.45 tff(10289,plain,
% 2.23/2.45 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10163, 10288, 2, 97])).
% 2.23/2.45 tff(10290,plain,
% 2.23/2.45 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[191, 10289])).
% 2.23/2.45 tff(10291,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10194, 10290])).
% 2.23/2.45 tff(10292,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10201, 162, 9847, 10290, 10178, 6735, 600])).
% 2.23/2.45 tff(10293,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[360, 10292])).
% 2.23/2.45 tff(10294,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10171, 162, 9847, 10290, 6735, 600, 5553])).
% 2.23/2.45 tff(10295,plain,
% 2.23/2.45 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1001, 10294])).
% 2.23/2.45 tff(10296,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5320, 10295, 10293])).
% 2.23/2.45 tff(10297,plain,
% 2.23/2.45 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1789, 10296, 10291])).
% 2.23/2.45 tff(10298,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[10297])).
% 2.23/2.45 tff(10299,plain,
% 2.23/2.45 (b(s(s(s(s(s(elem!1))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.45 inference(symmetry,[status(thm)],[10298])).
% 2.23/2.45 tff(10300,plain,
% 2.23/2.45 ((~b(s(s(s(s(s(elem!1))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[10299])).
% 2.23/2.45 tff(10301,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10184, 162, 9847, 10290, 10178, 6735, 600])).
% 2.23/2.45 tff(10302,plain,
% 2.23/2.45 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[338, 10301])).
% 2.23/2.45 tff(10303,plain,
% 2.23/2.45 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5940, 10297, 2, 9847, 97, 10302])).
% 2.23/2.45 tff(10304,plain,
% 2.23/2.45 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[943, 10303])).
% 2.23/2.45 tff(10305,plain,
% 2.23/2.45 (~r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5777, 10293, 9847, 10157, 3044])).
% 2.23/2.45 tff(10306,plain,
% 2.23/2.45 (b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[295, 10305])).
% 2.23/2.45 tff(10307,plain,
% 2.23/2.45 (~b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3056, 10306, 10157, 3044, 10258])).
% 2.23/2.45 tff(10308,plain,
% 2.23/2.45 (r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[381, 10307])).
% 2.23/2.45 tff(10309,plain,
% 2.23/2.45 (~r(s(s(s(s(s(elem!1))))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[886, 10308, 10295])).
% 2.23/2.45 tff(10310,plain,
% 2.23/2.45 (b(s(s(s(s(s(elem!1))))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[894, 10309])).
% 2.23/2.45 tff(10311,plain,
% 2.23/2.45 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[935, 10310, 10157, 10304, 3044])).
% 2.23/2.45 tff(10312,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[10311, 10300])).
% 2.23/2.45 tff(10313,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[9847, 10312])).
% 2.23/2.45 tff(10314,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10315,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10314, 97, 2])).
% 2.23/2.45 tff(10316,plain,
% 2.23/2.45 (r(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[595, 10315])).
% 2.23/2.45 tff(10317,plain,
% 2.23/2.45 (~r(s(s(z)), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[586, 10316, 2])).
% 2.23/2.45 tff(10318,plain,
% 2.23/2.45 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[442, 10317])).
% 2.23/2.45 tff(10319,plain,
% 2.23/2.45 (~r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1377, 10316, 97])).
% 2.23/2.45 tff(10320,plain,
% 2.23/2.45 (b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[381, 10319])).
% 2.23/2.45 tff(10321,plain,
% 2.23/2.45 (~r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2611, 10316, 97])).
% 2.23/2.45 tff(10322,plain,
% 2.23/2.45 (b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[295, 10321])).
% 2.23/2.45 tff(10323,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[7999, 10322, 10320, 3044, 10258, 10318])).
% 2.23/2.45 tff(10324,plain,((~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10325,plain,
% 2.23/2.45 (~r(z, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10324, 2])).
% 2.23/2.45 tff(10326,plain,
% 2.23/2.45 (b(z, s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[117, 10325])).
% 2.23/2.45 tff(10327,plain,
% 2.23/2.45 ((~b(s(z), z)) | (~b(s(s(s(z))), z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8634, 162, 121, 537, 6735, 600])).
% 2.23/2.45 tff(10328,plain,
% 2.23/2.45 (~b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10327, 152])).
% 2.23/2.45 tff(10329,plain,
% 2.23/2.45 (r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[381, 10328])).
% 2.23/2.45 tff(10330,plain,
% 2.23/2.45 (~r(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2028, 10329, 273])).
% 2.23/2.45 tff(10331,plain,
% 2.23/2.45 (b(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[245, 10330])).
% 2.23/2.45 tff(10332,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8655, 162, 152, 121, 10331, 537, 6735])).
% 2.23/2.45 tff(10333,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10334,plain,
% 2.23/2.45 (~b(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10333, 273, 10157, 10326, 8551])).
% 2.23/2.45 tff(10335,plain,
% 2.23/2.45 (r(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[175, 10334])).
% 2.23/2.45 tff(10336,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5582, 10335, 2, 10157, 9847])).
% 2.23/2.45 tff(10337,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[149, 10336])).
% 2.23/2.45 tff(10338,plain,
% 2.23/2.45 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[202, 194, 2, 193])).
% 2.23/2.45 tff(10339,plain,
% 2.23/2.45 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[216, 10338])).
% 2.23/2.45 tff(10340,plain,
% 2.23/2.45 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[503, 194, 193])).
% 2.23/2.45 tff(10341,plain,
% 2.23/2.45 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[83, 10340])).
% 2.23/2.45 tff(10342,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2637, 2563, 10341, 9847, 10157, 10339])).
% 2.23/2.45 tff(10343,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10344,plain,
% 2.23/2.45 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10343, 10335, 2])).
% 2.23/2.45 tff(10345,plain,
% 2.23/2.45 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[191, 10344])).
% 2.23/2.45 tff(10346,plain,
% 2.23/2.45 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10033, 162, 10326, 9847, 6735, 8551])).
% 2.23/2.45 tff(10347,plain,
% 2.23/2.45 (~b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10346, 10345])).
% 2.23/2.45 tff(10348,plain,
% 2.23/2.45 (r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[381, 10347])).
% 2.23/2.45 tff(10349,plain,
% 2.23/2.45 (~r(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2271, 10348, 10335])).
% 2.23/2.45 tff(10350,plain,
% 2.23/2.45 (b(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[493, 10349])).
% 2.23/2.45 tff(10351,plain,
% 2.23/2.45 (~r(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[238, 10335, 2])).
% 2.23/2.45 tff(10352,plain,
% 2.23/2.45 (b(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[245, 10351])).
% 2.23/2.45 tff(10353,plain,
% 2.23/2.45 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[9972, 162, 10326, 9847, 6735, 8551])).
% 2.23/2.45 tff(10354,plain,
% 2.23/2.45 (~b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10353, 10345])).
% 2.23/2.45 tff(10355,plain,
% 2.23/2.45 (r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[295, 10354])).
% 2.23/2.45 tff(10356,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5777, 10355, 9847, 10157, 10352])).
% 2.23/2.45 tff(10357,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[360, 10356])).
% 2.23/2.45 tff(10358,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5771, 10357, 10350, 10326, 8551, 10345, 10337])).
% 2.23/2.45 tff(10359,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10360,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10359, 2])).
% 2.23/2.45 tff(10361,plain,
% 2.23/2.45 (b(s(s(s(z))), s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[459, 10360])).
% 2.23/2.45 tff(10362,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2549, 340, 385])).
% 2.23/2.45 tff(10363,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[149, 10362])).
% 2.23/2.45 tff(10364,plain,
% 2.23/2.45 (~r(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[9928, 1, 121, 340])).
% 2.23/2.45 tff(10365,plain,
% 2.23/2.45 (b(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[493, 10364])).
% 2.23/2.45 tff(10366,plain,
% 2.23/2.45 ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[6831, 162, 121, 151, 445, 6735])).
% 2.23/2.45 tff(10367,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10366, 2719, 10365])).
% 2.23/2.45 tff(10368,plain,((~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10369,plain,
% 2.23/2.45 (~r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10368, 10363, 121, 445, 340])).
% 2.23/2.45 tff(10370,plain,
% 2.23/2.45 (b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[295, 10369])).
% 2.23/2.45 tff(10371,plain,
% 2.23/2.45 (~b(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1465, 10370, 537, 445, 444])).
% 2.23/2.45 tff(10372,plain,
% 2.23/2.45 (r(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[245, 10371])).
% 2.23/2.45 tff(10373,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[453, 6106, 9847, 445, 444])).
% 2.23/2.45 tff(10374,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[360, 10373])).
% 2.23/2.45 tff(10375,plain,
% 2.23/2.45 (~r(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[413, 10374, 193])).
% 2.23/2.45 tff(10376,plain,
% 2.23/2.45 (b(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[493, 10375])).
% 2.23/2.45 tff(10377,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10119, 162, 9847, 444, 6106, 445, 6735, 10376])).
% 2.23/2.45 tff(10378,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10379,plain,
% 2.23/2.45 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10378, 444, 445, 385])).
% 2.23/2.45 tff(10380,plain,
% 2.23/2.45 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[191, 10379])).
% 2.23/2.45 tff(10381,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3122, 10363, 121, 10380, 152])).
% 2.23/2.45 tff(10382,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[95, 10381])).
% 2.23/2.45 tff(10383,plain,
% 2.23/2.45 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4631, 65, 10382, 10372])).
% 2.23/2.45 tff(10384,plain,
% 2.23/2.45 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[216, 10383])).
% 2.23/2.45 tff(10385,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10137, 162, 9847, 10380, 10363, 10384, 6735])).
% 2.23/2.45 tff(10386,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10387,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10386, 152, 10361, 588, 10326, 10157, 385])).
% 2.23/2.45 tff(10388,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[360, 10387])).
% 2.23/2.45 tff(10389,plain,
% 2.23/2.45 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[453, 10388, 9847, 10361, 588])).
% 2.23/2.45 tff(10390,plain,
% 2.23/2.45 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[338, 10389])).
% 2.23/2.45 tff(10391,plain,
% 2.23/2.45 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10378, 588, 10361, 385])).
% 2.23/2.45 tff(10392,plain,
% 2.23/2.45 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[191, 10391])).
% 2.23/2.45 tff(10393,plain,
% 2.23/2.45 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2986, 10388, 9847, 10361, 588])).
% 2.23/2.45 tff(10394,plain,
% 2.23/2.45 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[216, 10393])).
% 2.23/2.45 tff(10395,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[131, 10394, 2])).
% 2.23/2.45 tff(10396,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[149, 10395])).
% 2.23/2.45 tff(10397,plain,
% 2.23/2.45 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4610, 10396, 10326, 10392, 152])).
% 2.23/2.45 tff(10398,plain,
% 2.23/2.45 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[83, 10397])).
% 2.23/2.45 tff(10399,plain,
% 2.23/2.45 (~r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2507, 10398, 10390])).
% 2.23/2.45 tff(10400,plain,
% 2.23/2.45 (b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[295, 10399])).
% 2.23/2.45 tff(10401,plain,
% 2.23/2.45 (~b(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1465, 10400, 10157, 10361, 588])).
% 2.23/2.45 tff(10402,plain,
% 2.23/2.45 (r(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[245, 10401])).
% 2.23/2.45 tff(10403,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3122, 10396, 10326, 10392, 152])).
% 2.23/2.45 tff(10404,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[95, 10403])).
% 2.23/2.45 tff(10405,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[4631, 65, 10404, 10394, 10402])).
% 2.23/2.45 tff(10406,plain,((~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10407,plain,
% 2.23/2.45 (~b(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10406, 385, 2])).
% 2.23/2.45 tff(10408,plain,
% 2.23/2.45 (r(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[175, 10407])).
% 2.23/2.45 tff(10409,plain,
% 2.23/2.45 (~r(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[238, 10408, 2])).
% 2.23/2.45 tff(10410,plain,
% 2.23/2.45 (b(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[245, 10409])).
% 2.23/2.45 tff(10411,plain,
% 2.23/2.45 (~r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8647, 10408, 385])).
% 2.23/2.45 tff(10412,plain,
% 2.23/2.45 (b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[381, 10411])).
% 2.23/2.45 tff(10413,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[3150, 10412, 10410, 10157, 588, 10361])).
% 2.23/2.45 tff(10414,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10415,plain,
% 2.23/2.45 (~r(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10414, 2])).
% 2.23/2.45 tff(10416,plain,
% 2.23/2.45 (b(s(s(s(z))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[595, 10415])).
% 2.23/2.45 tff(10417,plain,
% 2.23/2.45 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10343, 194, 2])).
% 2.23/2.45 tff(10418,plain,
% 2.23/2.45 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[191, 10417])).
% 2.23/2.45 tff(10419,plain,
% 2.23/2.45 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10033, 162, 10326, 9847, 6735, 10416])).
% 2.23/2.45 tff(10420,plain,
% 2.23/2.45 (~b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10419, 10418])).
% 2.23/2.45 tff(10421,plain,
% 2.23/2.45 (r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[381, 10420])).
% 2.23/2.45 tff(10422,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8607, 10421, 10157, 10361, 10416, 10159])).
% 2.23/2.45 tff(10423,plain,
% 2.23/2.45 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[9972, 162, 10326, 9847, 6735, 10416])).
% 2.23/2.45 tff(10424,plain,
% 2.23/2.45 (~b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10423, 10418])).
% 2.23/2.45 tff(10425,plain,
% 2.23/2.45 (r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[295, 10424])).
% 2.23/2.45 tff(10426,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5777, 10425, 9847, 10157, 5571])).
% 2.23/2.45 tff(10427,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[360, 10426, 10422])).
% 2.23/2.45 tff(10428,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10429,plain,
% 2.23/2.45 (~r(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10428, 2])).
% 2.23/2.45 tff(10430,plain,
% 2.23/2.45 (b(s(z), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[175, 10429])).
% 2.23/2.45 tff(10431,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(10432,plain,
% 2.23/2.45 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(10433,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[10432])).
% 2.23/2.45 tff(10434,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[10433, 10431])).
% 2.23/2.45 tff(10435,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(10436,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[10435, 10434])).
% 2.23/2.45 tff(10437,plain,
% 2.23/2.45 ((~b(s(z), z)) | (~b(z, s(s(s(z)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10436, 162, 10326, 10157, 6735, 10416])).
% 2.23/2.45 tff(10438,plain,
% 2.23/2.45 (~b(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10437, 10430])).
% 2.23/2.45 tff(10439,plain,
% 2.23/2.45 (r(z, s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[295, 10438])).
% 2.23/2.45 tff(10440,plain,
% 2.23/2.45 ((~b(s(z), z)) | (~b(s(s(s(z))), z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8634, 162, 10326, 10157, 6735, 10416])).
% 2.23/2.45 tff(10441,plain,
% 2.23/2.45 (~b(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10440, 10430])).
% 2.23/2.45 tff(10442,plain,
% 2.23/2.45 (r(s(s(s(z))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[381, 10441])).
% 2.23/2.45 tff(10443,plain,
% 2.23/2.45 (~b(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8672, 444, 10361, 10416])).
% 2.23/2.45 tff(10444,plain,
% 2.23/2.45 (r(s(z), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[493, 10443])).
% 2.23/2.45 tff(10445,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[9928, 10444, 10326, 10439])).
% 2.23/2.45 tff(10446,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[360, 10445])).
% 2.23/2.45 tff(10447,plain,
% 2.23/2.45 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2986, 10446, 9847, 10361, 444])).
% 2.23/2.45 tff(10448,plain,
% 2.23/2.45 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[216, 10447])).
% 2.23/2.45 tff(10449,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8607, 10446, 10157, 10361, 10416, 10442])).
% 2.23/2.45 tff(10450,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[149, 10449])).
% 2.23/2.45 tff(10451,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[131, 10450, 10448, 2])).
% 2.23/2.45 tff(10452,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(10453,plain,
% 2.23/2.45 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10452, 2])).
% 2.23/2.45 tff(10454,plain,
% 2.23/2.45 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[442, 10453])).
% 2.23/2.45 tff(10455,plain,
% 2.23/2.45 (~r(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8456, 10454, 10442])).
% 2.23/2.45 tff(10456,plain,
% 2.23/2.45 (b(s(s(z)), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[245, 10455])).
% 2.23/2.45 tff(10457,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5777, 10456, 9847, 10157, 10439])).
% 2.23/2.45 tff(10458,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[360, 10457])).
% 2.23/2.45 tff(10459,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8607, 10458, 10157, 10361, 10416, 10442])).
% 2.23/2.45 tff(10460,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[149, 10459])).
% 2.23/2.45 tff(10461,plain,
% 2.23/2.45 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[131, 10460, 2])).
% 2.23/2.45 tff(10462,plain,
% 2.23/2.45 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[216, 10461])).
% 2.23/2.45 tff(10463,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(10464,plain,
% 2.23/2.45 (((~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(10465,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[10464])).
% 2.23/2.45 tff(10466,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[10465, 10463])).
% 2.23/2.45 tff(10467,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(10468,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[10467, 10466])).
% 2.23/2.46 tff(10469,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10468, 162, 416, 120, 538, 363, 445, 526])).
% 2.23/2.46 tff(10470,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10471,plain,
% 2.23/2.46 (~b(z, s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10470, 10462, 9847, 10361, 10456, 10458])).
% 2.23/2.46 tff(10472,plain,
% 2.23/2.46 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[83, 10471])).
% 2.23/2.46 tff(10473,plain,
% 2.23/2.46 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[620, 10462, 9847, 10361, 10458])).
% 2.23/2.46 tff(10474,plain,
% 2.23/2.46 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[338, 10473])).
% 2.23/2.46 tff(10475,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2507, 10474, 10472, 10439])).
% 2.23/2.46 tff(10476,plain,(~r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10477,plain,
% 2.23/2.46 (b(s(s(z)), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[271, 10476])).
% 2.23/2.46 tff(10478,plain,
% 2.23/2.46 ((~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9053, 6735])).
% 2.23/2.46 tff(10479,plain,
% 2.23/2.46 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10478, 97, 9847, 10477])).
% 2.23/2.46 tff(10480,plain,
% 2.23/2.46 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[83, 10479])).
% 2.23/2.46 tff(10481,plain,
% 2.23/2.46 ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9051, 6735])).
% 2.23/2.46 tff(10482,plain,
% 2.23/2.46 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10481, 9030, 9847, 10477])).
% 2.23/2.46 tff(10483,plain,
% 2.23/2.46 (r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[191, 10482])).
% 2.23/2.46 tff(10484,plain,
% 2.23/2.46 (~r(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2561, 10483, 2252])).
% 2.23/2.46 tff(10485,plain,
% 2.23/2.46 (b(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[175, 10484])).
% 2.23/2.46 tff(10486,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10487,plain,
% 2.23/2.46 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10488,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[10487])).
% 2.23/2.46 tff(10489,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[10488, 10486])).
% 2.23/2.46 tff(10490,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(10491,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[10490, 10489])).
% 2.23/2.46 tff(10492,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10491, 162, 10485, 9847, 9030, 538, 10477, 6735])).
% 2.23/2.46 tff(10493,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10494,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10493, 538, 97])).
% 2.23/2.46 tff(10495,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[95, 10494])).
% 2.23/2.46 tff(10496,plain,
% 2.23/2.46 (~b(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9471, 230, 273, 97, 10477])).
% 2.23/2.46 tff(10497,plain,
% 2.23/2.46 (r(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[295, 10496])).
% 2.23/2.46 tff(10498,plain,
% 2.23/2.46 (~r(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2611, 10497, 97])).
% 2.23/2.46 tff(10499,plain,
% 2.23/2.46 (~r(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6781, 55, 97])).
% 2.23/2.46 tff(10500,plain,
% 2.23/2.46 (b(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[295, 10499])).
% 2.23/2.46 tff(10501,plain,
% 2.23/2.46 (~r(s(s(s(z))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9849, 55, 273])).
% 2.23/2.46 tff(10502,plain,
% 2.23/2.46 (b(s(s(s(z))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[381, 10501])).
% 2.23/2.46 tff(10503,plain,
% 2.23/2.46 (~r(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9471, 10500, 273, 97, 10477])).
% 2.23/2.46 tff(10504,plain,
% 2.23/2.46 (b(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[245, 10503])).
% 2.23/2.46 tff(10505,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10493, 10504, 97])).
% 2.23/2.46 tff(10506,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[95, 10505])).
% 2.23/2.46 tff(10507,plain,
% 2.23/2.46 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6271, 10506, 10502, 10480, 10500])).
% 2.23/2.46 tff(10508,plain,
% 2.23/2.46 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[338, 10507])).
% 2.23/2.46 tff(10509,plain,
% 2.23/2.46 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6509, 10508, 273])).
% 2.23/2.46 tff(10510,plain,
% 2.23/2.46 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[216, 10509])).
% 2.23/2.46 tff(10511,plain,
% 2.23/2.46 ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9115, 6735])).
% 2.23/2.46 tff(10512,plain,
% 2.23/2.46 (~b(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10511, 10506, 9847, 10477, 10502, 10500, 10480])).
% 2.23/2.46 tff(10513,plain,
% 2.23/2.46 (r(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[175, 10512])).
% 2.23/2.46 tff(10514,plain,
% 2.23/2.46 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6271, 122, 298, 10480, 297])).
% 2.23/2.46 tff(10515,plain,
% 2.23/2.46 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[338, 10514])).
% 2.23/2.46 tff(10516,plain,
% 2.23/2.46 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6509, 10515, 273])).
% 2.23/2.46 tff(10517,plain,
% 2.23/2.46 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[216, 10516])).
% 2.23/2.46 tff(10518,plain,
% 2.23/2.46 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9079, 6735])).
% 2.23/2.46 tff(10519,plain,
% 2.23/2.46 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10518, 10517, 9847, 10477])).
% 2.23/2.46 tff(10520,plain,
% 2.23/2.46 (r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[191, 10519])).
% 2.23/2.46 tff(10521,plain,
% 2.23/2.46 (~r(s(z), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9940, 10520, 10515])).
% 2.23/2.46 tff(10522,plain,
% 2.23/2.46 (b(s(z), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[493, 10521])).
% 2.23/2.46 tff(10523,plain,
% 2.23/2.46 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8721, 10522, 10477, 600])).
% 2.23/2.46 tff(10524,plain,
% 2.23/2.46 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[442, 10523])).
% 2.23/2.46 tff(10525,plain,
% 2.23/2.46 (~b(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10511, 122, 9847, 10477, 298, 297, 10480])).
% 2.23/2.46 tff(10526,plain,
% 2.23/2.46 (r(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[175, 10525])).
% 2.23/2.46 tff(10527,plain,
% 2.23/2.46 ((~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9429, 6735])).
% 2.23/2.46 tff(10528,plain,
% 2.23/2.46 (~b(s(z), s(s(s(s(z)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10527, 10522, 10477, 273, 600, 10515])).
% 2.23/2.46 tff(10529,plain,
% 2.23/2.46 (r(s(z), s(s(s(s(z)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6862, 10528])).
% 2.23/2.46 tff(10530,plain,
% 2.23/2.46 (~r(z, s(s(s(s(z)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[5603, 10529, 10526])).
% 2.23/2.46 tff(10531,plain,
% 2.23/2.46 (b(z, s(s(s(s(z)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[823, 10530])).
% 2.23/2.46 tff(10532,plain,
% 2.23/2.46 (~r(s(s(s(s(z)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[5600, 10529, 10526])).
% 2.23/2.46 tff(10533,plain,
% 2.23/2.46 (b(s(s(s(s(z)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1089, 10532])).
% 2.23/2.46 tff(10534,plain,
% 2.23/2.46 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8176, 10533, 298, 297, 10531])).
% 2.23/2.46 tff(10535,plain,
% 2.23/2.46 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6804, 10534])).
% 2.23/2.46 tff(10536,plain,
% 2.23/2.46 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[796, 10535, 10524])).
% 2.23/2.46 tff(10537,plain,
% 2.23/2.46 (b(s(s(z)), s(s(s(s(z)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8314, 10536])).
% 2.23/2.46 tff(10538,plain,
% 2.23/2.46 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8718, 10522, 273, 97, 600, 298])).
% 2.23/2.46 tff(10539,plain,
% 2.23/2.46 (b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6873, 10538])).
% 2.23/2.46 tff(10540,plain,
% 2.23/2.46 (~r(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9471, 297, 273, 97, 10477])).
% 2.23/2.46 tff(10541,plain,
% 2.23/2.46 (b(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[245, 10540])).
% 2.23/2.46 tff(10542,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10543,plain,
% 2.23/2.46 (((~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)))))) | (~b(s(s(z)), 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)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10544,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[10543])).
% 2.23/2.46 tff(10545,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[10544, 10542])).
% 2.23/2.46 tff(10546,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))))) | (~b(s(s(z)), z)))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(10547,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[10546, 10545])).
% 2.23/2.46 tff(10548,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10547, 162, 10541, 10533, 10539, 10531, 10537])).
% 2.23/2.46 tff(10549,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10550,plain,
% 2.23/2.46 (~b(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10549, 10506, 10500, 273, 10502, 97])).
% 2.23/2.46 tff(10551,plain,
% 2.23/2.46 (r(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[595, 10550])).
% 2.23/2.46 tff(10552,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8395, 10551, 10500, 10502, 10480, 10513])).
% 2.23/2.46 tff(10553,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[149, 10552])).
% 2.23/2.46 tff(10554,plain,
% 2.23/2.46 ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9038, 6735])).
% 2.23/2.46 tff(10555,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10554, 10553, 10510, 9847, 10477])).
% 2.23/2.46 tff(10556,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10557,plain,
% 2.23/2.46 (~r(z, s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10556, 97, 273])).
% 2.23/2.46 tff(10558,plain,
% 2.23/2.46 (b(z, s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[524, 10557])).
% 2.23/2.46 tff(10559,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9724, 230, 10477, 97])).
% 2.23/2.46 tff(10560,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[95, 10559])).
% 2.23/2.46 tff(10561,plain,
% 2.23/2.46 (~r(s(s(z)), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2577, 416, 122, 97, 120])).
% 2.23/2.46 tff(10562,plain,
% 2.23/2.46 (b(s(s(z)), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[271, 10561])).
% 2.23/2.46 tff(10563,plain,
% 2.23/2.46 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6608, 162, 416, 120, 537, 10562, 600])).
% 2.23/2.46 tff(10564,plain,
% 2.23/2.46 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[442, 10563])).
% 2.23/2.46 tff(10565,plain,
% 2.23/2.46 (~b(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2573, 537, 122, 416, 120])).
% 2.23/2.46 tff(10566,plain,
% 2.23/2.46 (r(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[245, 10565])).
% 2.23/2.46 tff(10567,plain,
% 2.23/2.46 (((~![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(s(z))))) | (~r(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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10568,plain,
% 2.23/2.46 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10569,plain,
% 2.23/2.46 (((~![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(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(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[10568])).
% 2.23/2.46 tff(10570,plain,
% 2.23/2.46 (((~![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(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(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[10569, 10567])).
% 2.23/2.46 tff(10571,plain,
% 2.23/2.46 ((~![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(z))) | (~r(s(s(z)), z)))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(10572,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[10571, 10570])).
% 2.23/2.46 tff(10573,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10572, 65, 97, 1, 10566, 10564])).
% 2.23/2.46 tff(10574,plain,((~b(z, s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10575,plain,
% 2.23/2.46 (~b(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10574, 10560, 9847, 97, 10497, 10558, 10480])).
% 2.23/2.46 tff(10576,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[595, 10575, 10498])).
% 2.23/2.46 tff(10577,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10578,plain,
% 2.23/2.46 (~r(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10577, 97, 273])).
% 2.23/2.46 tff(10579,plain,
% 2.23/2.46 (b(s(s(z)), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[245, 10578])).
% 2.23/2.46 tff(10580,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10493, 10579, 97])).
% 2.23/2.46 tff(10581,plain,
% 2.23/2.46 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2573, 10579, 9847, 10480, 10558])).
% 2.23/2.46 tff(10582,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[95, 10581, 10580])).
% 2.23/2.46 tff(10583,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10584,plain,
% 2.23/2.46 (~r(z, s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10583, 273])).
% 2.23/2.46 tff(10585,plain,
% 2.23/2.46 (b(z, s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[117, 10584])).
% 2.23/2.46 tff(10586,plain,
% 2.23/2.46 (~r(s(s(s(z))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6754, 10585, 10477, 273])).
% 2.23/2.46 tff(10587,plain,
% 2.23/2.46 (b(s(s(s(z))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[381, 10586])).
% 2.23/2.46 tff(10588,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 2.23/2.46 tff(10589,plain,
% 2.23/2.46 (r(s(s(s(z))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[595, 10588])).
% 2.23/2.46 tff(10590,plain,
% 2.23/2.46 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6166, 495, 55])).
% 2.23/2.46 tff(10591,plain,
% 2.23/2.46 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[216, 10590])).
% 2.23/2.46 tff(10592,plain,
% 2.23/2.46 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[503, 495, 194])).
% 2.23/2.46 tff(10593,plain,
% 2.23/2.46 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[191, 10592])).
% 2.23/2.46 tff(10594,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10518, 10593, 10591, 9847, 10477])).
% 2.23/2.46 tff(10595,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10596,plain,
% 2.23/2.46 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10595, 194, 55])).
% 2.23/2.46 tff(10597,plain,
% 2.23/2.46 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[83, 10596])).
% 2.23/2.46 tff(10598,plain,
% 2.23/2.46 (~r(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[281, 55, 273])).
% 2.23/2.46 tff(10599,plain,
% 2.23/2.46 (b(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[295, 10598])).
% 2.23/2.46 tff(10600,plain,
% 2.23/2.46 ((~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9131, 333])).
% 2.23/2.46 tff(10601,plain,
% 2.23/2.46 ((~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10600, 6735])).
% 2.23/2.46 tff(10602,plain,
% 2.23/2.46 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10601, 10597, 273, 230, 385, 10587, 10599, 194])).
% 2.23/2.46 tff(10603,plain,
% 2.23/2.46 (r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[191, 10602])).
% 2.23/2.46 tff(10604,plain,
% 2.23/2.46 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2517, 10603, 385])).
% 2.23/2.46 tff(10605,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[338, 10604])).
% 2.23/2.46 tff(10606,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2561, 10603, 194])).
% 2.23/2.46 tff(10607,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[95, 10606])).
% 2.23/2.46 tff(10608,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[6271, 10607, 10605, 10587, 10599, 10597])).
% 2.23/2.46 tff(10609,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10610,plain,
% 2.23/2.46 (~r(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10609, 3020, 273, 230, 10589])).
% 2.23/2.46 tff(10611,plain,
% 2.23/2.46 (b(s(z), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[175, 10610])).
% 2.23/2.46 tff(10612,plain,
% 2.23/2.46 (~r(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[281, 3020, 273])).
% 2.23/2.46 tff(10613,plain,
% 2.23/2.46 (b(z, s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[295, 10612])).
% 2.23/2.46 tff(10614,plain,
% 2.23/2.46 (b(s(s(s(z))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[381, 375])).
% 2.23/2.46 tff(10615,plain,
% 2.23/2.46 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[2517, 193, 10589])).
% 2.23/2.46 tff(10616,plain,
% 2.23/2.46 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[338, 10615])).
% 2.23/2.46 tff(10617,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10618,plain,
% 2.23/2.46 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(10619,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[10618])).
% 2.23/2.46 tff(10620,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[10619, 10617])).
% 2.23/2.46 tff(10621,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(10622,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[10621, 10620])).
% 2.23/2.46 tff(10623,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10622, 162, 152, 121, 298, 599, 297])).
% 2.23/2.46 tff(10624,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(10625,plain,
% 2.23/2.46 (~b(s(z), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10624, 152, 121, 10614, 297])).
% 2.23/2.46 tff(10626,plain,
% 2.23/2.46 (r(s(z), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[493, 10625])).
% 2.23/2.46 tff(10627,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[413, 193, 10626])).
% 2.23/2.46 tff(10628,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[360, 10627])).
% 2.23/2.46 tff(10629,plain,
% 2.23/2.46 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[371, 10628, 10616, 297, 10614])).
% 2.23/2.46 tff(10630,plain,
% 2.23/2.46 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[95, 10629])).
% 2.23/2.46 tff(10631,plain,
% 2.23/2.46 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[4631, 65, 10630, 230])).
% 2.23/2.46 tff(10632,plain,
% 2.23/2.46 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[216, 10631])).
% 2.23/2.46 tff(10633,plain,
% 2.23/2.46 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[720, 10632, 9847, 10628, 10616])).
% 2.23/2.46 tff(10634,plain,
% 2.23/2.46 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[442, 10633])).
% 2.23/2.47 tff(10635,plain,
% 2.23/2.47 (~r(z, s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8022, 694, 10477, 230, 55])).
% 2.23/2.47 tff(10636,plain,
% 2.23/2.47 (b(z, s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[823, 10635])).
% 2.23/2.47 tff(10637,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2657, 10636, 121, 152, 694])).
% 2.23/2.47 tff(10638,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6793, 10637])).
% 2.23/2.47 tff(10639,plain,
% 2.23/2.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6858, 10638, 385])).
% 2.23/2.47 tff(10640,plain,
% 2.23/2.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6855, 10639])).
% 2.23/2.47 tff(10641,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(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))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10642,plain,
% 2.23/2.47 (((~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)))), 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(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))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10643,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(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)))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10642])).
% 2.23/2.47 tff(10644,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(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))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[10643, 10641])).
% 2.23/2.47 tff(10645,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(10646,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[10645, 10644])).
% 2.23/2.47 tff(10647,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10646, 162, 298, 693, 1075, 297, 692])).
% 2.23/2.47 tff(10648,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(10649,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10648, 10640, 298, 297, 10636])).
% 2.23/2.47 tff(10650,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6804, 10649])).
% 2.23/2.47 tff(10651,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8333, 65, 230, 417, 787, 644])).
% 2.23/2.47 tff(10652,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(10653,plain,
% 2.23/2.47 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10652, 10650, 230, 417])).
% 2.23/2.47 tff(10654,plain,
% 2.23/2.47 (b(s(s(s(s(z)))), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6873, 10653])).
% 2.23/2.47 tff(10655,plain,
% 2.23/2.47 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[796, 10650, 417])).
% 2.23/2.47 tff(10656,plain,
% 2.23/2.47 (b(s(s(z)), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8314, 10655])).
% 2.23/2.47 tff(10657,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8312, 10656, 10654, 10477, 694])).
% 2.23/2.47 tff(10658,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(10659,plain,
% 2.23/2.47 (~b(s(z), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10658, 10634, 230, 10614, 297, 10589, 121, 152, 3020])).
% 2.23/2.47 tff(10660,plain,
% 2.23/2.47 (r(s(z), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6862, 10659])).
% 2.23/2.47 tff(10661,plain,
% 2.23/2.47 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6804, 7982])).
% 2.23/2.47 tff(10662,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3934, 162, 298, 1076, 693, 297, 692])).
% 2.23/2.47 tff(10663,plain,((~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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(10664,plain,
% 2.23/2.47 (~b(s(s(s(s(z)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10663, 693, 10614, 297, 692])).
% 2.23/2.47 tff(10665,plain,
% 2.23/2.47 (r(s(s(s(s(z)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1089, 10664])).
% 2.23/2.47 tff(10666,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[371, 363, 362, 297, 10614])).
% 2.23/2.47 tff(10667,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[95, 10666])).
% 2.23/2.47 tff(10668,plain,
% 2.23/2.47 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[4681, 65, 10667, 10665])).
% 2.23/2.47 tff(10669,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[8835, 693, 362, 363, 692])).
% 2.23/2.47 tff(10670,plain,
% 2.23/2.47 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[763, 47, 10669])).
% 2.23/2.47 tff(10671,plain,
% 2.23/2.47 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10670, 10668])).
% 2.23/2.47 tff(10672,plain,
% 2.23/2.47 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10671])).
% 2.23/2.47 tff(10673,plain,
% 2.23/2.47 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[20, 10672, 630])).
% 2.23/2.47 tff(10674,plain,
% 2.23/2.47 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10673])).
% 2.23/2.47 tff(10675,plain,
% 2.23/2.47 (s(s(elem!1)) = s(s(z))),
% 2.23/2.47 inference(transitivity,[status(thm)],[25, 10674, 312])).
% 2.23/2.47 tff(10676,plain,
% 2.23/2.47 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10675])).
% 2.23/2.47 tff(10677,plain,
% 2.23/2.47 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.23/2.47 inference(symmetry,[status(thm)],[10676])).
% 2.23/2.47 tff(10678,plain,
% 2.23/2.47 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10675])).
% 2.23/2.47 tff(10679,plain,
% 2.23/2.47 (s(elem!1) = s(z)),
% 2.23/2.47 inference(transitivity,[status(thm)],[325, 10678, 15])).
% 2.23/2.47 tff(10680,plain,
% 2.23/2.47 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10679])).
% 2.23/2.47 tff(10681,plain,
% 2.23/2.47 (elem!1 = z),
% 2.23/2.47 inference(transitivity,[status(thm)],[1171, 10680, 13])).
% 2.23/2.47 tff(10682,plain,
% 2.23/2.47 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10681])).
% 2.23/2.47 tff(10683,plain,
% 2.23/2.47 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.23/2.47 inference(symmetry,[status(thm)],[10682])).
% 2.23/2.47 tff(10684,plain,
% 2.23/2.47 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[10683, 10677])).
% 2.23/2.47 tff(10685,plain,
% 2.23/2.47 ((~b(z, s(s(z)))) <=> (~b(elem!1, s(s(elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10684])).
% 2.23/2.47 tff(10686,plain,
% 2.23/2.47 (~b(elem!1, s(s(elem!1)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[3019, 10685])).
% 2.23/2.47 tff(10687,plain,
% 2.23/2.47 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[4631, 65, 10667, 230])).
% 2.23/2.47 tff(10688,plain,
% 2.23/2.47 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[216, 10687])).
% 2.23/2.47 tff(10689,plain,
% 2.23/2.47 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10554, 10688, 9847, 10477])).
% 2.23/2.47 tff(10690,plain,
% 2.23/2.47 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[149, 10689])).
% 2.23/2.47 tff(10691,plain,
% 2.23/2.47 ((elem!1 = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10671])).
% 2.23/2.47 tff(10692,plain,
% 2.23/2.47 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[10691])).
% 2.23/2.47 tff(10693,plain,
% 2.23/2.47 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10681])).
% 2.23/2.47 tff(10694,plain,
% 2.23/2.47 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.23/2.47 inference(transitivity,[status(thm)],[10693, 813])).
% 2.23/2.47 tff(10695,plain,
% 2.23/2.47 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[10694])).
% 2.23/2.47 tff(10696,plain,
% 2.23/2.47 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[10695, 10692])).
% 2.23/2.47 tff(10697,plain,
% 2.23/2.47 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10696])).
% 2.23/2.47 tff(10698,plain,
% 2.23/2.47 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[817, 10697])).
% 2.23/2.47 tff(10699,plain,
% 2.23/2.47 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10671])).
% 2.23/2.47 tff(10700,plain,
% 2.23/2.47 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[10699])).
% 2.23/2.47 tff(10701,plain,
% 2.23/2.47 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10681])).
% 2.23/2.47 tff(10702,plain,
% 2.23/2.47 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[10701])).
% 2.23/2.47 tff(10703,plain,
% 2.23/2.47 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[10702, 10700])).
% 2.23/2.47 tff(10704,plain,
% 2.23/2.47 ((~b(z, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10703])).
% 2.23/2.47 tff(10705,plain,
% 2.23/2.47 (~b(z, s(s(s(s(z)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10648, 693, 10614, 297, 692])).
% 2.23/2.47 tff(10706,plain,
% 2.23/2.47 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[10705, 10704])).
% 2.23/2.47 tff(10707,plain,
% 2.23/2.47 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(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(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10708,plain,
% 2.23/2.47 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10709,plain,
% 2.23/2.47 (((~![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(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10708])).
% 2.23/2.47 tff(10710,plain,
% 2.23/2.47 (((~![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(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[10709, 10707])).
% 2.23/2.47 tff(10711,plain,
% 2.23/2.47 ((~![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(elem!1)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(10712,plain,
% 2.23/2.47 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[10711, 10710])).
% 2.23/2.47 tff(10713,plain,
% 2.23/2.47 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10712, 65, 123, 1230, 230])).
% 2.23/2.47 tff(10714,plain,
% 2.23/2.47 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[214, 47, 10713, 209])).
% 2.23/2.47 tff(10715,plain,
% 2.23/2.47 (b(s(z), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3713, 1323])).
% 2.23/2.47 tff(10716,plain,
% 2.23/2.47 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[6251, 65, 123, 10589])).
% 2.23/2.47 tff(10717,plain,
% 2.23/2.47 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[338, 10716])).
% 2.23/2.47 tff(10718,plain,
% 2.23/2.47 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2547, 65, 123, 10589])).
% 2.23/2.47 tff(10719,plain,
% 2.23/2.47 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[360, 10718])).
% 2.23/2.47 tff(10720,plain,
% 2.23/2.47 (~b(s(s(z)), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[720, 10719, 416, 10717, 10714])).
% 2.23/2.47 tff(10721,plain,
% 2.23/2.47 (r(s(s(z)), s(s(s(z))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[442, 10720])).
% 2.23/2.47 tff(10722,plain,
% 2.23/2.47 (~r(s(s(z)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[586, 10721, 10589])).
% 2.23/2.47 tff(10723,plain,
% 2.23/2.47 (b(s(s(z)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[271, 10722])).
% 2.23/2.47 tff(10724,plain,
% 2.23/2.47 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[9079, 10723, 416, 10715, 10714])).
% 2.23/2.47 tff(10725,plain,
% 2.23/2.47 (r(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[191, 10724])).
% 2.23/2.47 tff(10726,assumption,(~b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.47 tff(10727,plain,
% 2.23/2.47 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3975, 1538, 10726])).
% 2.23/2.47 tff(10728,plain,
% 2.23/2.47 (~r(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3613, 10727, 10725])).
% 2.23/2.47 tff(10729,plain,
% 2.23/2.47 (~r(s(z), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2260, 123, 1230])).
% 2.23/2.47 tff(10730,plain,
% 2.23/2.47 (b(s(z), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[175, 10729])).
% 2.23/2.47 tff(10731,plain,
% 2.23/2.47 (((~![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(z, s(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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10732,plain,
% 2.23/2.47 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10733,plain,
% 2.23/2.47 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10732])).
% 2.23/2.47 tff(10734,plain,
% 2.23/2.47 (((~![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(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(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(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[10733, 10731])).
% 2.23/2.47 tff(10735,plain,
% 2.23/2.47 ((~![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(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1)))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(10736,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[10735, 10734])).
% 2.23/2.47 tff(10737,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10736, 65, 4891, 3532, 495])).
% 2.23/2.47 tff(10738,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(10739,plain,
% 2.23/2.47 (~r(z, elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10738, 10727, 495])).
% 2.23/2.47 tff(10740,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 2.23/2.47 tff(10741,plain,
% 2.23/2.47 (s(z) = elem!1),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1682, 6919, 10740])).
% 2.23/2.47 tff(10742,plain,
% 2.23/2.47 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10741])).
% 2.23/2.47 tff(10743,plain,
% 2.23/2.47 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 2.23/2.47 inference(symmetry,[status(thm)],[10742])).
% 2.23/2.47 tff(10744,assumption,(~r(z, elem!1)), introduced(assumption)).
% 2.23/2.47 tff(10745,assumption,(s(z) = elem!1), introduced(assumption)).
% 2.23/2.47 tff(10746,plain,
% 2.23/2.47 (s(s(z)) = s(elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10745])).
% 2.23/2.47 tff(10747,plain,
% 2.23/2.47 (s(s(s(z))) = s(s(elem!1))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10746])).
% 2.23/2.47 tff(10748,plain,
% 2.23/2.47 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10747])).
% 2.23/2.47 tff(10749,plain,
% 2.23/2.47 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.23/2.47 inference(symmetry,[status(thm)],[10748])).
% 2.23/2.47 tff(10750,plain,
% 2.23/2.47 (r(s(s(s(z))), z)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[3375, 10749])).
% 2.23/2.47 tff(10751,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[375, 10750])).
% 2.23/2.47 tff(10752,plain,((~r(s(s(elem!1)), z)) | r(s(s(s(z))), z) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(10753,plain,
% 2.23/2.47 (~r(s(s(elem!1)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10752, 10741, 375])).
% 2.23/2.47 tff(10754,plain,
% 2.23/2.47 (b(s(s(elem!1)), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2783, 10753])).
% 2.23/2.47 tff(10755,plain,
% 2.23/2.47 (r(elem!1, s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3637, 4753, 3632])).
% 2.23/2.47 tff(10756,plain,
% 2.23/2.47 (~(s(s(elem!1)) = elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1561, 1559])).
% 2.23/2.47 tff(10757,plain,
% 2.23/2.47 (r(s(z), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1682, 1247, 6919])).
% 2.23/2.47 tff(10758,plain,
% 2.23/2.47 (~r(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[1663, 10757, 385])).
% 2.23/2.47 tff(10759,plain,
% 2.23/2.47 (s(s(s(z))) = elem!1),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3664, 10758, 6915])).
% 2.23/2.47 tff(10760,plain,
% 2.23/2.47 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10759])).
% 2.23/2.47 tff(10761,plain,
% 2.23/2.47 (r(elem!1, s(z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[385, 10760])).
% 2.23/2.47 tff(10762,plain,
% 2.23/2.47 (~r(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[4762, 10761, 3621])).
% 2.23/2.47 tff(10763,plain,
% 2.23/2.47 (b(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3591, 10762])).
% 2.23/2.47 tff(10764,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10765,plain,
% 2.23/2.47 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(10766,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[10765])).
% 2.23/2.47 tff(10767,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[10766, 10764])).
% 2.23/2.47 tff(10768,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(10769,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[10768, 10767])).
% 2.23/2.47 tff(10770,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10769, 162, 3577, 3576, 152, 121, 1148])).
% 2.23/2.47 tff(10771,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(10772,plain,
% 2.23/2.47 (~b(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[10771, 10763, 152, 121, 1148])).
% 2.23/2.47 tff(10773,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[3824, 10772])).
% 2.23/2.47 tff(10774,plain,
% 2.23/2.47 (((~![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(z), 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)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10775,plain,
% 2.23/2.48 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10776,plain,
% 2.23/2.48 (((~![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(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(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(z), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10775])).
% 2.23/2.48 tff(10777,plain,
% 2.23/2.48 (((~![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(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 2.23/2.48 inference(transitivity,[status(thm)],[10776, 10774])).
% 2.23/2.48 tff(10778,plain,
% 2.23/2.48 ((~![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(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(10779,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10778, 10777])).
% 2.23/2.48 tff(10780,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10779, 65, 3367, 1655, 1571])).
% 2.23/2.48 tff(10781,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(10782,plain,
% 2.23/2.48 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10781, 10773, 10757])).
% 2.23/2.48 tff(10783,plain,
% 2.23/2.48 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10759])).
% 2.23/2.48 tff(10784,plain,
% 2.23/2.48 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 2.23/2.48 inference(transitivity,[status(thm)],[10783, 1202])).
% 2.23/2.48 tff(10785,plain,
% 2.23/2.48 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10784])).
% 2.23/2.48 tff(10786,plain,
% 2.23/2.48 (~(z = elem!1)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[286, 10785])).
% 2.23/2.48 tff(10787,plain,
% 2.23/2.48 (b(z, elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[4889, 10786, 10744])).
% 2.23/2.48 tff(10788,plain,
% 2.23/2.48 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 2.23/2.48 inference(transitivity,[status(thm)],[10784, 1203])).
% 2.23/2.48 tff(10789,plain,
% 2.23/2.48 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10788])).
% 2.23/2.48 tff(10790,plain,
% 2.23/2.48 (~(elem!1 = z)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[286, 10789])).
% 2.23/2.48 tff(10791,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10792,plain,
% 2.23/2.48 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10793,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10792])).
% 2.23/2.48 tff(10794,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[10793, 10791])).
% 2.23/2.48 tff(10795,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(10796,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10795, 10794])).
% 2.23/2.48 tff(10797,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10796, 162, 1149, 3576, 152, 121, 1148])).
% 2.23/2.48 tff(10798,plain,((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(10799,plain,
% 2.23/2.48 (~b(z, s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10798, 10763, 121, 152, 1148])).
% 2.23/2.48 tff(10800,plain,
% 2.23/2.48 (r(z, s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3401, 10799])).
% 2.23/2.48 tff(10801,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, 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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10802,plain,
% 2.23/2.48 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10803,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, 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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10802])).
% 2.23/2.48 tff(10804,plain,
% 2.23/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, 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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.23/2.48 inference(transitivity,[status(thm)],[10803, 10801])).
% 2.23/2.48 tff(10805,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(10806,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10805, 10804])).
% 2.23/2.48 tff(10807,plain,
% 2.23/2.48 (~r(elem!1, z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10806, 65, 10800, 3621])).
% 2.23/2.48 tff(10808,plain,
% 2.23/2.48 (b(elem!1, z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3486, 10807, 10790])).
% 2.23/2.48 tff(10809,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10810,plain,
% 2.23/2.48 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10811,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10810])).
% 2.23/2.48 tff(10812,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(transitivity,[status(thm)],[10811, 10809])).
% 2.23/2.48 tff(10813,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(10814,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10813, 10812])).
% 2.23/2.48 tff(10815,plain,
% 2.23/2.48 ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10814, 162])).
% 2.23/2.48 tff(10816,plain,
% 2.23/2.48 (~b(elem!1, s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10815, 4882, 7114, 1148, 1600])).
% 2.23/2.48 tff(10817,plain,
% 2.23/2.48 (r(elem!1, s(s(elem!1)))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3637, 10816, 1559])).
% 2.23/2.48 tff(10818,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10819,plain,
% 2.23/2.48 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10820,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10819])).
% 2.23/2.48 tff(10821,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(transitivity,[status(thm)],[10820, 10818])).
% 2.23/2.48 tff(10822,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(10823,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10822, 10821])).
% 2.23/2.48 tff(10824,plain,
% 2.23/2.48 (~b(elem!1, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10823, 162, 4882, 7114, 152, 1148, 1600])).
% 2.23/2.48 tff(10825,plain,
% 2.23/2.48 (r(elem!1, s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1651, 10824, 7030])).
% 2.23/2.48 tff(10826,plain,
% 2.23/2.48 (((~![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(s(elem!1)))) | (~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(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10827,plain,
% 2.23/2.48 (((~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(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10828,plain,
% 2.23/2.48 (((~![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(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10827])).
% 2.23/2.48 tff(10829,plain,
% 2.23/2.48 (((~![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(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[10828, 10826])).
% 2.23/2.48 tff(10830,plain,
% 2.23/2.48 ((~![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)))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(10831,plain,
% 2.23/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10830, 10829])).
% 2.23/2.48 tff(10832,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10831, 65, 3367, 10825, 10817])).
% 2.23/2.48 tff(10833,plain,((~b(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(10834,plain,
% 2.23/2.48 (~b(s(s(elem!1)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10833, 10773, 1615, 10808, 10787, 1148, 152, 1559])).
% 2.23/2.48 tff(10835,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1569, 10834, 10782, 10756])).
% 2.23/2.48 tff(10836,plain,((s(z) = elem!1) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~r(elem!1, s(s(elem!1)))) | r(z, elem!1) | (~r(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(10837,plain,
% 2.23/2.48 (s(z) = elem!1),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10836, 4753, 152, 1148, 121, 10755, 10744, 385, 6915, 6919])).
% 2.23/2.48 tff(10838,plain,
% 2.23/2.48 (s(s(z)) = s(elem!1)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10837])).
% 2.23/2.48 tff(10839,plain,
% 2.23/2.48 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10838])).
% 2.23/2.48 tff(10840,plain,
% 2.23/2.48 (~b(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[5089, 383, 121, 152, 10715])).
% 2.23/2.48 tff(10841,plain,
% 2.23/2.48 (r(s(s(z)), z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[245, 10840])).
% 2.23/2.48 tff(10842,plain,
% 2.23/2.48 (r(s(elem!1), z)),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10841, 10839])).
% 2.23/2.48 tff(10843,plain,
% 2.23/2.48 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1493, 1489, 4773])).
% 2.23/2.48 tff(10844,plain,
% 2.23/2.48 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3629, 10843, 3621])).
% 2.23/2.48 tff(10845,plain,
% 2.23/2.48 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3975, 10844, 1538])).
% 2.23/2.48 tff(10846,plain,
% 2.23/2.48 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[4845, 10800, 1495])).
% 2.23/2.48 tff(10847,plain,
% 2.23/2.48 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[83, 10846])).
% 2.23/2.48 tff(10848,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10849,plain,
% 2.23/2.48 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(rewrite,[status(thm)],[])).
% 2.23/2.48 tff(10850,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10849])).
% 2.23/2.48 tff(10851,plain,
% 2.23/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.23/2.48 inference(transitivity,[status(thm)],[10850, 10848])).
% 2.23/2.48 tff(10852,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.23/2.48 inference(quant_inst,[status(thm)],[])).
% 2.23/2.48 tff(10853,plain,
% 2.23/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10852, 10851])).
% 2.23/2.48 tff(10854,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10853, 162, 4882, 3577, 152, 1148, 3990, 120])).
% 2.23/2.48 tff(10855,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(10856,plain,
% 2.23/2.48 (~b(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10855, 10847, 152, 10787, 1148, 3990])).
% 2.23/2.48 tff(10857,plain,
% 2.23/2.48 (r(s(s(elem!1)), s(z))),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3824, 10856])).
% 2.23/2.48 tff(10858,plain,
% 2.23/2.48 (~r(s(s(elem!1)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10781, 10857, 10757])).
% 2.23/2.48 tff(10859,plain,
% 2.23/2.48 (b(s(s(elem!1)), elem!1)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[1569, 10858, 10756])).
% 2.23/2.48 tff(10860,plain,
% 2.23/2.48 (~b(elem!1, z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10833, 10859, 1615, 10857, 10787, 1148, 152, 1559])).
% 2.23/2.48 tff(10861,plain,
% 2.23/2.48 (r(elem!1, z)),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[3486, 10860, 10790])).
% 2.23/2.48 tff(10862,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10806, 65, 10861, 10800, 3621])).
% 2.23/2.48 tff(10863,plain,((s(z) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (elem!1 = s(s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | r(z, elem!1) | (~r(s(s(s(z))), s(z))) | b(s(s(s(z))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.48 tff(10864,plain,
% 2.23/2.48 (s(z) = elem!1),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[10863, 10845, 1148, 152, 4753, 3621, 10843, 121, 10744, 385, 6915, 6919])).
% 2.23/2.48 tff(10865,plain,
% 2.23/2.48 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10745])).
% 2.23/2.48 tff(10866,plain,
% 2.23/2.48 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 2.23/2.48 inference(symmetry,[status(thm)],[10865])).
% 2.23/2.48 tff(10867,plain,
% 2.23/2.48 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(z)))),
% 2.23/2.48 inference(monotonicity,[status(thm)],[10866])).
% 2.23/2.48 tff(10868,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 2.23/2.48 tff(10869,plain,
% 2.23/2.48 (~b(s(s(z)), s(z))),
% 2.23/2.48 inference(modus_ponens,[status(thm)],[10868, 10867])).
% 2.23/2.48 tff(10870,plain,
% 2.23/2.48 ($false),
% 2.23/2.48 inference(unit_resolution,[status(thm)],[383, 10869])).
% 2.23/2.48 tff(10871,plain,((~(s(z) = elem!1)) | (~b(s(s(z)), s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10872,plain,
% 2.23/2.49 (b(s(s(z)), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10871, 10745, 383])).
% 2.23/2.49 tff(10873,plain,
% 2.23/2.49 (s(elem!1) = s(s(z))),
% 2.23/2.49 inference(symmetry,[status(thm)],[10746])).
% 2.23/2.49 tff(10874,plain,
% 2.23/2.49 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10873])).
% 2.23/2.49 tff(10875,plain,
% 2.23/2.49 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 2.23/2.49 inference(symmetry,[status(thm)],[10874])).
% 2.23/2.49 tff(10876,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 2.23/2.49 tff(10877,plain,
% 2.23/2.49 (b(s(elem!1), elem!1)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10876, 10875])).
% 2.23/2.49 tff(10878,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[3466, 10877])).
% 2.23/2.49 tff(10879,plain,((~b(s(s(z)), elem!1)) | b(s(elem!1), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10880,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10879, 10872, 10745, 3466])).
% 2.23/2.49 tff(10881,plain,((~(s(z) = elem!1)) | b(s(elem!1), elem!1) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10882,plain,
% 2.23/2.49 (b(s(elem!1), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10881, 10864, 383])).
% 2.23/2.49 tff(10883,plain,
% 2.23/2.49 (b(s(z), z) <=> b(elem!1, z)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10745])).
% 2.23/2.49 tff(10884,plain,
% 2.23/2.49 (b(elem!1, z) <=> b(s(z), z)),
% 2.23/2.49 inference(symmetry,[status(thm)],[10883])).
% 2.23/2.49 tff(10885,plain,
% 2.23/2.49 ((~b(elem!1, z)) <=> (~b(s(z), z))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10884])).
% 2.23/2.49 tff(10886,plain,
% 2.23/2.49 (~b(s(z), z)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[3442, 10885])).
% 2.23/2.49 tff(10887,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[152, 10886])).
% 2.23/2.49 tff(10888,plain,((~(s(z) = elem!1)) | (~b(s(z), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10889,plain,
% 2.23/2.49 (b(elem!1, z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10888, 10864, 152])).
% 2.23/2.49 tff(10890,plain,
% 2.23/2.49 (b(z, s(z)) <=> b(z, elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10745])).
% 2.23/2.49 tff(10891,plain,
% 2.23/2.49 (b(z, elem!1) <=> b(z, s(z))),
% 2.23/2.49 inference(symmetry,[status(thm)],[10890])).
% 2.23/2.49 tff(10892,plain,
% 2.23/2.49 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10891])).
% 2.23/2.49 tff(10893,assumption,(~b(z, elem!1)), introduced(assumption)).
% 2.23/2.49 tff(10894,plain,
% 2.23/2.49 (~b(z, s(z))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10893, 10892])).
% 2.23/2.49 tff(10895,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[121, 10894])).
% 2.23/2.49 tff(10896,plain,((~(s(z) = elem!1)) | (~b(z, s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10897,plain,
% 2.23/2.49 (b(z, elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10896, 10864, 121])).
% 2.23/2.49 tff(10898,plain,
% 2.23/2.49 (~(elem!1 = s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[3463, 4753])).
% 2.23/2.49 tff(10899,plain,
% 2.23/2.49 (elem!1 = s(z)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10745, 1179])).
% 2.23/2.49 tff(10900,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[7030, 10899])).
% 2.23/2.49 tff(10901,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10902,plain,
% 2.23/2.49 (elem!1 = s(z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10901, 10864])).
% 2.23/2.49 tff(10903,plain,
% 2.23/2.49 (s(elem!1) = s(s(z))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[1611])).
% 2.23/2.49 tff(10904,plain,
% 2.23/2.49 (s(s(z)) = s(elem!1)),
% 2.23/2.49 inference(symmetry,[status(thm)],[10903])).
% 2.23/2.49 tff(10905,plain,
% 2.23/2.49 (s(z) = elem!1),
% 2.23/2.49 inference(symmetry,[status(thm)],[1611])).
% 2.23/2.49 tff(10906,plain,
% 2.23/2.49 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10905, 10904])).
% 2.23/2.49 tff(10907,plain,
% 2.23/2.49 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.23/2.49 inference(symmetry,[status(thm)],[10906])).
% 2.23/2.49 tff(10908,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10909,plain,
% 2.23/2.49 (r(s(z), s(s(z)))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10908, 10907])).
% 2.23/2.49 tff(10910,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1323, 10909])).
% 2.23/2.49 tff(10911,plain,(r(s(z), s(s(z))) | (~r(elem!1, s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10912,plain,
% 2.23/2.49 (~r(elem!1, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10911, 10902, 1323])).
% 2.23/2.49 tff(10913,plain,
% 2.23/2.49 (((~![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)))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10914,plain,
% 2.23/2.49 ((~![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)))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(10915,plain,
% 2.23/2.49 ((~![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))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10914, 10913])).
% 2.23/2.49 tff(10916,plain,
% 2.23/2.49 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10915, 47])).
% 2.23/2.49 tff(10917,plain,
% 2.23/2.49 (b(elem!1, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10916, 10912, 10898])).
% 2.23/2.49 tff(10918,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10919,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 2.23/2.49 tff(10920,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10921,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10922,plain,
% 2.23/2.49 (((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10923,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10922])).
% 2.23/2.49 tff(10924,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[10923, 10921])).
% 2.23/2.49 tff(10925,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(10926,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10925, 10924])).
% 2.23/2.49 tff(10927,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10926, 162, 4882, 7114, 10920, 10919, 10918])).
% 2.23/2.49 tff(10928,plain,((~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10929,plain,
% 2.23/2.49 (~b(z, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10928, 10917, 10897, 10889, 10882])).
% 2.23/2.49 tff(10930,plain,
% 2.23/2.49 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10873])).
% 2.23/2.49 tff(10931,plain,
% 2.23/2.49 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 2.23/2.49 inference(symmetry,[status(thm)],[10930])).
% 2.23/2.49 tff(10932,plain,
% 2.23/2.49 (b(z, s(elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[537, 10931])).
% 2.23/2.49 tff(10933,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10934,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10933, 10932])).
% 2.23/2.49 tff(10935,plain,(b(z, s(elem!1)) | (~b(z, s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10936,plain,
% 2.23/2.49 (~b(z, s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10935, 10929, 10864])).
% 2.23/2.49 tff(10937,plain,
% 2.23/2.49 (r(z, s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[524, 10936])).
% 2.23/2.49 tff(10938,plain,
% 2.23/2.49 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10746])).
% 2.23/2.49 tff(10939,plain,
% 2.23/2.49 (r(z, s(elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[55, 10938])).
% 2.23/2.49 tff(10940,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10941,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10940, 10939])).
% 2.23/2.49 tff(10942,plain,((~r(z, s(s(z)))) | r(z, s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10943,plain,
% 2.23/2.49 (r(z, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10942, 10937, 10864])).
% 2.23/2.49 tff(10944,plain,
% 2.23/2.49 (s(s(z)) = s(elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10864])).
% 2.23/2.49 tff(10945,plain,
% 2.23/2.49 (s(s(s(z))) = s(s(elem!1))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10944])).
% 2.23/2.49 tff(10946,plain,
% 2.23/2.49 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10945])).
% 2.23/2.49 tff(10947,plain,
% 2.23/2.49 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10946])).
% 2.23/2.49 tff(10948,plain,
% 2.23/2.49 (~b(s(s(elem!1)), elem!1)),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[6915, 10947])).
% 2.23/2.49 tff(10949,plain,
% 2.23/2.49 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[1582, 10948, 1489, 4794])).
% 2.23/2.49 tff(10950,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10951,plain,
% 2.23/2.49 (elem!1 = s(z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10901, 10745])).
% 2.23/2.49 tff(10952,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.23/2.49 tff(10953,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(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(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10954,plain,
% 2.23/2.49 (((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10955,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(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(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10954])).
% 2.23/2.49 tff(10956,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(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(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[10955, 10953])).
% 2.23/2.49 tff(10957,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(10958,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10957, 10956])).
% 2.23/2.49 tff(10959,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10958, 65, 495, 10950, 10952])).
% 2.23/2.49 tff(10960,plain,((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10961,plain,
% 2.23/2.49 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10960, 495, 10950])).
% 2.23/2.49 tff(10962,plain,
% 2.23/2.49 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.23/2.49 inference(symmetry,[status(thm)],[5067])).
% 2.23/2.49 tff(10963,plain,
% 2.23/2.49 (s(s(s(s(elem!1)))) = s(s(z))),
% 2.23/2.49 inference(transitivity,[status(thm)],[10962, 10873])).
% 2.23/2.49 tff(10964,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[37, 10963])).
% 2.23/2.49 tff(10965,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10966,plain,
% 2.23/2.49 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10965, 10745])).
% 2.23/2.49 tff(10967,plain,
% 2.23/2.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10968,plain,
% 2.23/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(10969,plain,
% 2.23/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10968, 10967])).
% 2.23/2.49 tff(10970,plain,
% 2.23/2.49 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10969, 47, 10966, 10961])).
% 2.23/2.49 tff(10971,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10972,plain,
% 2.23/2.49 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(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(s(s(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(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10973,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(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(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10972])).
% 2.23/2.49 tff(10974,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(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(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[10973, 10971])).
% 2.23/2.49 tff(10975,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(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(s(s(s(elem!1)))), elem!1)))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(10976,plain,
% 2.23/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10975, 10974])).
% 2.23/2.49 tff(10977,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10976, 162, 1240, 10920, 5305, 5312, 10919])).
% 2.23/2.49 tff(10978,plain,((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10979,plain,
% 2.23/2.49 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10978, 10970, 10919, 10920, 1240])).
% 2.23/2.49 tff(10980,plain,
% 2.23/2.49 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10903])).
% 2.23/2.49 tff(10981,plain,
% 2.23/2.49 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(symmetry,[status(thm)],[10980])).
% 2.23/2.49 tff(10982,plain,
% 2.23/2.49 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[416, 10981])).
% 2.23/2.49 tff(10983,assumption,(~b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10984,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10983, 10982])).
% 2.23/2.49 tff(10985,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(s(elem!1)))), s(elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10986,plain,
% 2.23/2.49 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10985, 10979, 10951])).
% 2.23/2.49 tff(10987,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[52, 10986])).
% 2.23/2.49 tff(10988,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10746])).
% 2.23/2.49 tff(10989,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[54, 10988])).
% 2.23/2.49 tff(10990,assumption,(~r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(10991,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10990, 10989])).
% 2.23/2.49 tff(10992,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | r(s(s(s(s(elem!1)))), s(elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(10993,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10992, 10987, 10745])).
% 2.23/2.49 tff(10994,plain,
% 2.23/2.49 (((~![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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10995,plain,
% 2.23/2.49 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(10996,plain,
% 2.23/2.49 (((~![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(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), 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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10995])).
% 2.23/2.49 tff(10997,plain,
% 2.23/2.49 (((~![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(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), 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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[10996, 10994])).
% 2.23/2.49 tff(10998,plain,
% 2.23/2.49 ((~![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(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(10999,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[10998, 10997])).
% 2.23/2.49 tff(11000,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10999, 65, 495, 10993, 10950])).
% 2.23/2.49 tff(11001,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(11002,plain,
% 2.23/2.49 (~r(z, s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[11001, 10949, 10864, 10882, 10917, 10943])).
% 2.23/2.49 tff(11003,plain,
% 2.23/2.49 (b(z, s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[83, 11002])).
% 2.23/2.49 tff(11004,plain,
% 2.23/2.49 (b(s(z), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10745])).
% 2.23/2.49 tff(11005,plain,
% 2.23/2.49 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(symmetry,[status(thm)],[11004])).
% 2.23/2.49 tff(11006,plain,
% 2.23/2.49 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[3990, 11005])).
% 2.23/2.49 tff(11007,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[7521, 11006])).
% 2.23/2.49 tff(11008,plain,((~(s(z) = elem!1)) | b(s(z), s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(11009,plain,
% 2.23/2.49 (b(s(z), s(s(s(s(elem!1)))))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[11008, 10864, 10845])).
% 2.23/2.49 tff(11010,plain,
% 2.23/2.49 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[5497, 11003, 152, 11009, 121])).
% 2.23/2.49 tff(11011,plain,
% 2.23/2.49 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[95, 11010])).
% 2.23/2.49 tff(11012,plain,
% 2.23/2.49 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[10873])).
% 2.23/2.49 tff(11013,plain,
% 2.23/2.49 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.23/2.49 inference(symmetry,[status(thm)],[11012])).
% 2.23/2.49 tff(11014,plain,
% 2.23/2.49 (r(z, s(elem!1))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[55, 11013])).
% 2.23/2.49 tff(11015,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 2.23/2.49 tff(11016,plain,
% 2.23/2.49 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(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(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(11017,plain,
% 2.23/2.49 (((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.23/2.49 tff(11018,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.23/2.49 inference(monotonicity,[status(thm)],[11017])).
% 2.23/2.49 tff(11019,plain,
% 2.23/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, 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)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.23/2.49 inference(transitivity,[status(thm)],[11018, 11016])).
% 2.23/2.49 tff(11020,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.23/2.49 inference(quant_inst,[status(thm)],[])).
% 2.23/2.49 tff(11021,plain,
% 2.23/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.23/2.49 inference(modus_ponens,[status(thm)],[11020, 11019])).
% 2.23/2.49 tff(11022,plain,
% 2.23/2.49 (~r(z, s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[11021, 65, 2252, 11015])).
% 2.23/2.49 tff(11023,plain,
% 2.23/2.49 ($false),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[11022, 11014])).
% 2.23/2.49 tff(11024,plain,((~r(z, s(s(z)))) | (~(s(z) = elem!1)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.49 tff(11025,plain,
% 2.23/2.49 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[11024, 11011, 10864, 10937])).
% 2.23/2.49 tff(11026,plain,
% 2.23/2.49 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10992, 11025, 10864])).
% 2.23/2.49 tff(11027,plain,
% 2.23/2.49 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[52, 11026])).
% 2.23/2.49 tff(11028,plain,
% 2.23/2.49 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.49 inference(unit_resolution,[status(thm)],[10985, 11027, 10902])).
% 2.23/2.49 tff(11029,plain,
% 2.23/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.23/2.49 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11030,plain,
% 2.33/2.50 (((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~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, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11031,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1))))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11030])).
% 2.33/2.50 tff(11032,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[11031, 11029])).
% 2.33/2.50 tff(11033,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, z)) | (~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))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(11034,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(s(elem!1))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11033, 11032])).
% 2.33/2.50 tff(11035,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11034, 162, 10889, 10845, 10949, 11028, 10882, 11003])).
% 2.33/2.50 tff(11036,plain,(b(s(s(elem!1)), s(s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | b(s(s(s(z))), elem!1) | r(s(z), s(s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | r(z, elem!1) | (~r(s(s(s(z))), s(z))) | b(s(z), elem!1) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(11037,plain,
% 2.33/2.50 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11036, 10755, 121, 6915, 1323, 383, 1148, 152, 10744, 385, 6919, 1538])).
% 2.33/2.50 tff(11038,plain,
% 2.33/2.50 (elem!1 = s(z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10901, 10837])).
% 2.33/2.50 tff(11039,plain,
% 2.33/2.50 (~r(elem!1, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10911, 11038, 1323])).
% 2.33/2.50 tff(11040,plain,
% 2.33/2.50 (b(elem!1, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10916, 11039, 10898])).
% 2.33/2.50 tff(11041,plain,
% 2.33/2.50 (b(s(elem!1), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10881, 10837, 383])).
% 2.33/2.50 tff(11042,plain,
% 2.33/2.50 (b(elem!1, z)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10888, 10745, 152])).
% 2.33/2.50 tff(11043,plain,
% 2.33/2.50 (b(z, elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10896, 10745, 121])).
% 2.33/2.50 tff(11044,plain,
% 2.33/2.50 (~b(z, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10928, 10920, 11043, 11042, 10919])).
% 2.33/2.50 tff(11045,plain,
% 2.33/2.50 (~b(z, s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10935, 11044, 10745])).
% 2.33/2.50 tff(11046,plain,
% 2.33/2.50 (r(z, s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[524, 11045])).
% 2.33/2.50 tff(11047,plain,
% 2.33/2.50 (r(z, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10942, 11046, 10745])).
% 2.33/2.50 tff(11048,plain,
% 2.33/2.50 (((~![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(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)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11049,plain,
% 2.33/2.50 (((~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)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11050,plain,
% 2.33/2.50 (((~![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)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11049])).
% 2.33/2.50 tff(11051,plain,
% 2.33/2.50 (((~![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)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.33/2.50 inference(transitivity,[status(thm)],[11050, 11048])).
% 2.33/2.50 tff(11052,plain,
% 2.33/2.50 ((~![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)))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(11053,plain,
% 2.33/2.50 ((~![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(s(s(s(s(elem!1)))), elem!1))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11052, 11051])).
% 2.33/2.50 tff(11054,plain,
% 2.33/2.50 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11053, 65, 3621, 2084])).
% 2.33/2.50 tff(11055,plain,
% 2.33/2.50 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[1529, 11054, 1245])).
% 2.33/2.50 tff(11056,plain,
% 2.33/2.50 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11001, 11055, 10745, 10919, 10920, 11047])).
% 2.33/2.50 tff(11057,plain,
% 2.33/2.50 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[10745])).
% 2.33/2.50 tff(11058,plain,
% 2.33/2.50 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.33/2.50 inference(symmetry,[status(thm)],[11057])).
% 2.33/2.50 tff(11059,plain,
% 2.33/2.50 (r(s(z), s(s(elem!1)))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[3621, 11058])).
% 2.33/2.50 tff(11060,plain,
% 2.33/2.50 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[2092, 2084, 11059])).
% 2.33/2.50 tff(11061,plain,
% 2.33/2.50 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[191, 11060])).
% 2.33/2.50 tff(11062,plain,
% 2.33/2.50 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11061, 11004])).
% 2.33/2.50 tff(11063,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 2.33/2.50 tff(11064,plain,
% 2.33/2.50 (((~![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(elem!1)))))) | (~r(s(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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11065,plain,
% 2.33/2.50 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11066,plain,
% 2.33/2.50 (((~![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(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11065])).
% 2.33/2.50 tff(11067,plain,
% 2.33/2.50 (((~![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(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~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(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)))),
% 2.33/2.50 inference(transitivity,[status(thm)],[11066, 11064])).
% 2.33/2.50 tff(11068,plain,
% 2.33/2.50 ((~![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(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(11069,plain,
% 2.33/2.50 ((~![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(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11068, 11067])).
% 2.33/2.50 tff(11070,plain,
% 2.33/2.50 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11069, 65, 2252, 3443])).
% 2.33/2.50 tff(11071,plain,
% 2.33/2.50 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10969, 47, 10966, 11070])).
% 2.33/2.50 tff(11072,plain,
% 2.33/2.50 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.33/2.50 inference(symmetry,[status(thm)],[10988])).
% 2.33/2.50 tff(11073,plain,
% 2.33/2.50 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11072])).
% 2.33/2.50 tff(11074,plain,
% 2.33/2.50 (((~![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(elem!1)))), z)) | (~r(s(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(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11075,plain,
% 2.33/2.50 (((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11076,plain,
% 2.33/2.50 (((~![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(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~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(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), z))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11075])).
% 2.33/2.50 tff(11077,plain,
% 2.33/2.50 (((~![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(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~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(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), z)))),
% 2.33/2.50 inference(transitivity,[status(thm)],[11076, 11074])).
% 2.33/2.50 tff(11078,plain,
% 2.33/2.50 ((~![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(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(11079,plain,
% 2.33/2.50 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(elem!1), z))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11078, 11077])).
% 2.33/2.50 tff(11080,plain,
% 2.33/2.50 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11079, 65, 2252, 3443])).
% 2.33/2.50 tff(11081,plain,
% 2.33/2.50 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11080, 11073])).
% 2.33/2.50 tff(11082,plain,
% 2.33/2.50 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[52, 11081])).
% 2.33/2.50 tff(11083,plain,
% 2.33/2.50 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10985, 11082, 10951])).
% 2.33/2.50 tff(11084,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11085,plain,
% 2.33/2.50 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11086,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11085])).
% 2.33/2.50 tff(11087,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[11086, 11084])).
% 2.33/2.50 tff(11088,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(11089,plain,
% 2.33/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11088, 11087])).
% 2.33/2.50 tff(11090,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11089, 162, 3990, 10920, 5312, 5305, 10919])).
% 2.33/2.50 tff(11091,plain,((~b(elem!1, s(elem!1))) | (~b(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(s(elem!1)))))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(11092,plain,
% 2.33/2.50 (~b(elem!1, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11091, 11083, 3990, 11071, 10919])).
% 2.33/2.50 tff(11093,plain,
% 2.33/2.50 (r(elem!1, s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[10916, 11092, 3514])).
% 2.33/2.50 tff(11094,plain,
% 2.33/2.50 (s(s(elem!1)) = s(s(s(z)))),
% 2.33/2.50 inference(symmetry,[status(thm)],[10747])).
% 2.33/2.50 tff(11095,plain,
% 2.33/2.50 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11094, 10873])).
% 2.33/2.50 tff(11096,plain,
% 2.33/2.50 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 2.33/2.50 inference(symmetry,[status(thm)],[11095])).
% 2.33/2.50 tff(11097,plain,
% 2.33/2.50 (r(s(s(elem!1)), s(elem!1))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[273, 11096])).
% 2.33/2.50 tff(11098,plain,
% 2.33/2.50 (((~![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(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(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11099,plain,
% 2.33/2.50 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11100,plain,
% 2.33/2.50 (((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), 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(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11099])).
% 2.33/2.50 tff(11101,plain,
% 2.33/2.50 (((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), 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(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.33/2.50 inference(transitivity,[status(thm)],[11100, 11098])).
% 2.33/2.50 tff(11102,plain,
% 2.33/2.50 ((~![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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 2.33/2.50 inference(quant_inst,[status(thm)],[])).
% 2.33/2.50 tff(11103,plain,
% 2.33/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[11102, 11101])).
% 2.33/2.50 tff(11104,plain,
% 2.33/2.50 (~r(s(s(elem!1)), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11103, 65, 3621, 10908])).
% 2.33/2.50 tff(11105,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11104, 11097])).
% 2.33/2.50 tff(11106,plain,((~r(s(s(s(z))), s(s(z)))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(11107,plain,
% 2.33/2.50 (~r(s(s(s(z))), s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11106, 11093, 3621, 10745])).
% 2.33/2.50 tff(11108,plain,
% 2.33/2.50 (b(s(s(s(z))), s(s(z)))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[458, 11107, 11063])).
% 2.33/2.50 tff(11109,plain,
% 2.33/2.50 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 2.33/2.50 inference(monotonicity,[status(thm)],[11094, 10873])).
% 2.33/2.50 tff(11110,plain,
% 2.33/2.50 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.33/2.50 inference(symmetry,[status(thm)],[11109])).
% 2.33/2.50 tff(11111,plain,
% 2.33/2.50 (b(s(s(elem!1)), s(elem!1))),
% 2.33/2.50 inference(modus_ponens,[status(thm)],[445, 11110])).
% 2.33/2.50 tff(11112,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.33/2.50 tff(11113,plain,
% 2.33/2.50 ($false),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11112, 11111])).
% 2.33/2.50 tff(11114,plain,(b(s(s(elem!1)), s(elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.50 tff(11115,plain,
% 2.33/2.50 (b(s(s(elem!1)), s(elem!1))),
% 2.33/2.50 inference(unit_resolution,[status(thm)],[11114, 11108, 10745])).
% 2.33/2.50 tff(11116,plain,
% 2.33/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.33/2.50 inference(rewrite,[status(thm)],[])).
% 2.33/2.50 tff(11117,plain,
% 2.33/2.50 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11118,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11117])).
% 2.33/2.51 tff(11119,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[11118, 11116])).
% 2.33/2.51 tff(11120,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(11121,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11120, 11119])).
% 2.33/2.51 tff(11122,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11121, 162, 3990, 1147, 11083, 11071, 10919, 11115])).
% 2.33/2.51 tff(11123,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (s(s(s(z))) = s(s(z))) | (~r(elem!1, s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11124,plain,
% 2.33/2.51 ((~r(s(elem!1), z)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11123, 436])).
% 2.33/2.51 tff(11125,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11124, 11062, 1147, 10919, 3621, 10745, 3514, 3443])).
% 2.33/2.51 tff(11126,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[95, 11125])).
% 2.33/2.51 tff(11127,plain,
% 2.33/2.51 (~b(z, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[5497, 11126, 152, 11061, 121])).
% 2.33/2.51 tff(11128,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[83, 11127, 11056])).
% 2.33/2.51 tff(11129,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~(s(z) = elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11130,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11129, 10837, 121, 152, 11041, 11040, 4794, 11037, 10755, 10898, 10842])).
% 2.33/2.51 tff(11131,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2101, 11130, 4960])).
% 2.33/2.51 tff(11132,plain,
% 2.33/2.51 (b(elem!1, z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10888, 10837, 152])).
% 2.33/2.51 tff(11133,plain,
% 2.33/2.51 (b(z, elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10896, 10837, 121])).
% 2.33/2.51 tff(11134,plain,
% 2.33/2.51 (~b(z, s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10928, 11040, 11133, 11132, 11041])).
% 2.33/2.51 tff(11135,plain,
% 2.33/2.51 (~b(z, s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10935, 11134, 10837])).
% 2.33/2.51 tff(11136,plain,
% 2.33/2.51 (r(z, s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[524, 11135])).
% 2.33/2.51 tff(11137,plain,
% 2.33/2.51 (r(z, s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10942, 11136, 10837])).
% 2.33/2.51 tff(11138,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11079, 65, 2252, 3443, 11015])).
% 2.33/2.51 tff(11139,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11140,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11139, 11015, 3443])).
% 2.33/2.51 tff(11141,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[95, 11140])).
% 2.33/2.51 tff(11142,plain,
% 2.33/2.51 (~b(z, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2778, 11141, 1148, 1146, 1147])).
% 2.33/2.51 tff(11143,plain,
% 2.33/2.51 (r(z, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[83, 11142])).
% 2.33/2.51 tff(11144,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10999, 65, 11143, 11015, 10950])).
% 2.33/2.51 tff(11145,plain,((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11146,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11145, 11131, 1148, 11137, 11037, 10842])).
% 2.33/2.51 tff(11147,plain,
% 2.33/2.51 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[10992, 11146, 10837])).
% 2.33/2.51 tff(11148,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[52, 11147])).
% 2.33/2.51 tff(11149,plain,
% 2.33/2.51 (s(s(s(z))) = s(s(elem!1))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[10838])).
% 2.33/2.51 tff(11150,plain,
% 2.33/2.51 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11149])).
% 2.33/2.51 tff(11151,plain,
% 2.33/2.51 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(symmetry,[status(thm)],[11150])).
% 2.33/2.51 tff(11152,plain,
% 2.33/2.51 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11037, 11151])).
% 2.33/2.51 tff(11153,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11149])).
% 2.33/2.51 tff(11154,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(symmetry,[status(thm)],[11153])).
% 2.33/2.51 tff(11155,plain,
% 2.33/2.51 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11131, 11154])).
% 2.33/2.51 tff(11156,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11157,plain,
% 2.33/2.51 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11158,plain,
% 2.33/2.51 (((~![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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), 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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11157])).
% 2.33/2.51 tff(11159,plain,
% 2.33/2.51 (((~![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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), 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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[11158, 11156])).
% 2.33/2.51 tff(11160,plain,
% 2.33/2.51 ((~![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(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(11161,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11160, 11159])).
% 2.33/2.51 tff(11162,plain,
% 2.33/2.51 (~r(s(s(elem!1)), s(elem!1))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11161, 65, 3998, 10950])).
% 2.33/2.51 tff(11163,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11162, 11097])).
% 2.33/2.51 tff(11164,plain,((~r(s(s(s(z))), s(s(z)))) | (~(s(z) = elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11165,plain,
% 2.33/2.51 (~r(s(s(s(z))), s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11164, 3998, 10745, 10950])).
% 2.33/2.51 tff(11166,plain,
% 2.33/2.51 (b(s(s(s(z))), s(s(z)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[459, 11165])).
% 2.33/2.51 tff(11167,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 2.33/2.51 tff(11168,plain,
% 2.33/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11169,plain,
% 2.33/2.51 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11170,plain,
% 2.33/2.51 (((~![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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11169])).
% 2.33/2.51 tff(11171,plain,
% 2.33/2.51 (((~![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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[11170, 11168])).
% 2.33/2.51 tff(11172,plain,
% 2.33/2.51 ((~![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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(11173,plain,
% 2.33/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11172, 11171])).
% 2.33/2.51 tff(11174,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11173, 65, 3998, 11167, 10950])).
% 2.33/2.51 tff(11175,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11176,plain,
% 2.33/2.51 (~r(s(elem!1), s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11175, 3998, 10950])).
% 2.33/2.51 tff(11177,plain,
% 2.33/2.51 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[10746, 10747])).
% 2.33/2.51 tff(11178,plain,
% 2.33/2.51 (r(s(elem!1), s(s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[417, 11177])).
% 2.33/2.51 tff(11179,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 2.33/2.51 tff(11180,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11179, 11178])).
% 2.33/2.51 tff(11181,plain,((~r(s(s(z)), s(s(s(z))))) | r(s(elem!1), s(s(elem!1))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11182,plain,
% 2.33/2.51 (~r(s(s(z)), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11181, 11176, 10745])).
% 2.33/2.51 tff(11183,plain,
% 2.33/2.51 (b(s(s(z)), s(s(s(z))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[442, 11182])).
% 2.33/2.51 tff(11184,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[453, 11183, 11166, 362, 363, 416])).
% 2.33/2.51 tff(11185,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~(s(z) = elem!1)) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11186,plain,
% 2.33/2.51 (~r(z, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11185, 11155, 10837, 11152, 11148, 11137])).
% 2.33/2.51 tff(11187,plain,
% 2.33/2.51 (b(z, s(s(elem!1)))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[3401, 11186])).
% 2.33/2.51 tff(11188,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11189,plain,
% 2.33/2.51 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11190,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11189])).
% 2.33/2.51 tff(11191,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[11190, 11188])).
% 2.33/2.51 tff(11192,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(11193,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11192, 11191])).
% 2.33/2.51 tff(11194,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11193, 162, 1149, 1148, 1147, 120, 1146])).
% 2.33/2.51 tff(11195,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11196,plain,
% 2.33/2.51 (~b(z, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11195, 11187, 11131, 1148, 11037])).
% 2.33/2.51 tff(11197,plain,
% 2.33/2.51 (r(z, s(s(s(s(elem!1)))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[83, 11196])).
% 2.33/2.51 tff(11198,plain,
% 2.33/2.51 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[10837])).
% 2.33/2.51 tff(11199,plain,
% 2.33/2.51 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.33/2.51 inference(symmetry,[status(thm)],[11198])).
% 2.33/2.51 tff(11200,plain,
% 2.33/2.51 (r(s(z), s(s(elem!1)))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[10755, 11199])).
% 2.33/2.51 tff(11201,plain,
% 2.33/2.51 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[10837])).
% 2.33/2.51 tff(11202,plain,
% 2.33/2.51 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 2.33/2.51 inference(symmetry,[status(thm)],[11201])).
% 2.33/2.51 tff(11203,plain,
% 2.33/2.51 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11149])).
% 2.33/2.51 tff(11204,plain,
% 2.33/2.51 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), s(z))),
% 2.33/2.51 inference(transitivity,[status(thm)],[11203, 11202])).
% 2.33/2.51 tff(11205,plain,
% 2.33/2.51 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[10837])).
% 2.33/2.51 tff(11206,plain,
% 2.33/2.51 (r(s(s(s(z))), elem!1)),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[385, 11205])).
% 2.33/2.51 tff(11207,plain,
% 2.33/2.51 (r(s(s(elem!1)), s(z))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11206, 11204])).
% 2.33/2.51 tff(11208,plain,
% 2.33/2.51 (s(z) = s(s(s(elem!1)))),
% 2.33/2.51 inference(transitivity,[status(thm)],[10745, 4877])).
% 2.33/2.51 tff(11209,plain,
% 2.33/2.51 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11208])).
% 2.33/2.51 tff(11210,plain,
% 2.33/2.51 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 2.33/2.51 inference(symmetry,[status(thm)],[11209])).
% 2.33/2.51 tff(11211,plain,
% 2.33/2.51 (s(s(elem!1)) = z),
% 2.33/2.51 inference(transitivity,[status(thm)],[25, 11210, 13])).
% 2.33/2.51 tff(11212,plain,
% 2.33/2.51 ($false),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[35, 11211])).
% 2.33/2.51 tff(11213,plain,((~(elem!1 = s(s(s(elem!1))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.51 tff(11214,plain,
% 2.33/2.51 (~(elem!1 = s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11213, 10837])).
% 2.33/2.51 tff(11215,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.51 inference(monotonicity,[status(thm)],[10837])).
% 2.33/2.51 tff(11216,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.51 inference(symmetry,[status(thm)],[11215])).
% 2.33/2.51 tff(11217,plain,
% 2.33/2.51 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11001, 11197, 10837, 11041, 11040, 11137])).
% 2.33/2.51 tff(11218,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[1529, 11217, 4794])).
% 2.33/2.51 tff(11219,plain,
% 2.33/2.51 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11218, 11216])).
% 2.33/2.51 tff(11220,plain,
% 2.33/2.51 (~r(s(s(s(elem!1))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[7676, 2112, 1147, 1146, 123, 1253])).
% 2.33/2.51 tff(11221,plain,
% 2.33/2.51 (b(s(s(s(elem!1))), s(z))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[7638, 11220])).
% 2.33/2.51 tff(11222,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11223,plain,
% 2.33/2.51 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11224,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11223])).
% 2.33/2.51 tff(11225,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.33/2.51 inference(transitivity,[status(thm)],[11224, 11222])).
% 2.33/2.51 tff(11226,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.51 inference(quant_inst,[status(thm)],[])).
% 2.33/2.51 tff(11227,plain,
% 2.33/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 2.33/2.51 inference(modus_ponens,[status(thm)],[11226, 11225])).
% 2.33/2.51 tff(11228,plain,
% 2.33/2.51 (~b(z, s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[11227, 162, 152, 121, 741, 11221])).
% 2.33/2.51 tff(11229,plain,
% 2.33/2.51 (r(z, s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2296, 11228])).
% 2.33/2.51 tff(11230,plain,
% 2.33/2.51 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.51 inference(unit_resolution,[status(thm)],[2116, 2112, 1253])).
% 2.33/2.51 tff(11231,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11232,plain,
% 2.33/2.51 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(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(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.51 inference(rewrite,[status(thm)],[])).
% 2.33/2.51 tff(11233,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.33/2.51 inference(monotonicity,[status(thm)],[11232])).
% 2.33/2.51 tff(11234,plain,
% 2.33/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[11233, 11231])).
% 2.33/2.52 tff(11235,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(11236,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11235, 11234])).
% 2.33/2.52 tff(11237,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11236, 162, 152, 741, 2219, 3883, 1146, 740])).
% 2.33/2.52 tff(11238,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11239,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11238, 11230, 741, 152, 1146, 11221])).
% 2.33/2.52 tff(11240,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1304, 11239, 1275])).
% 2.33/2.52 tff(11241,plain,
% 2.33/2.52 (((~![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(s(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(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))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11242,plain,
% 2.33/2.52 (((~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(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))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11243,plain,
% 2.33/2.52 (((~![X0: $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(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)))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[11242])).
% 2.33/2.52 tff(11244,plain,
% 2.33/2.52 (((~![X0: $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(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))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[11243, 11241])).
% 2.33/2.52 tff(11245,plain,
% 2.33/2.52 ((~![X0: $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)))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(11246,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11245, 11244])).
% 2.33/2.52 tff(11247,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11246, 65, 11240, 11229, 495])).
% 2.33/2.52 tff(11248,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11249,plain,
% 2.33/2.52 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11248, 741, 152, 1275, 495, 1146, 121, 1147, 123, 1253])).
% 2.33/2.52 tff(11250,plain,
% 2.33/2.52 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[10905])).
% 2.33/2.52 tff(11251,plain,
% 2.33/2.52 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(symmetry,[status(thm)],[11250])).
% 2.33/2.52 tff(11252,plain,
% 2.33/2.52 (r(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[1507, 11251])).
% 2.33/2.52 tff(11253,plain,
% 2.33/2.52 (((~![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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11254,plain,
% 2.33/2.52 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11255,plain,
% 2.33/2.52 (((~![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(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[11254])).
% 2.33/2.52 tff(11256,plain,
% 2.33/2.52 (((~![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(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[11255, 11253])).
% 2.33/2.52 tff(11257,plain,
% 2.33/2.52 ((~![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(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(11258,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11257, 11256])).
% 2.33/2.52 tff(11259,plain,
% 2.33/2.52 (~r(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11258, 65, 1246, 2313])).
% 2.33/2.52 tff(11260,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11259, 11252])).
% 2.33/2.52 tff(11261,plain,((~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11262,plain,
% 2.33/2.52 (~r(elem!1, s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11261, 11249, 1611, 1246])).
% 2.33/2.52 tff(11263,plain,
% 2.33/2.52 (b(elem!1, s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1483, 11262, 7589])).
% 2.33/2.52 tff(11264,plain,
% 2.33/2.52 (~r(s(s(s(elem!1))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[3751, 11249, 3367])).
% 2.33/2.52 tff(11265,plain,
% 2.33/2.52 (b(s(s(s(elem!1))), s(z))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[7638, 11264])).
% 2.33/2.52 tff(11266,plain,
% 2.33/2.52 (~b(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[749, 11265, 152, 741, 121])).
% 2.33/2.52 tff(11267,plain,
% 2.33/2.52 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[10905])).
% 2.33/2.52 tff(11268,plain,
% 2.33/2.52 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(symmetry,[status(thm)],[11267])).
% 2.33/2.52 tff(11269,plain,
% 2.33/2.52 (b(s(z), s(s(s(elem!1))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[3884, 11268])).
% 2.33/2.52 tff(11270,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 2.33/2.52 tff(11271,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11270, 11269])).
% 2.33/2.52 tff(11272,plain,(b(s(z), s(s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11273,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11272, 11266, 11263, 1611])).
% 2.33/2.52 tff(11274,plain,((~b(s(s(s(elem!1))), z)) | (~(elem!1 = s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11275,plain,
% 2.33/2.52 (~b(s(s(s(elem!1))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11274, 11219, 152, 121, 11214, 11038, 11207, 4774, 11200, 11131, 11037, 11197, 4959])).
% 2.33/2.52 tff(11276,plain,
% 2.33/2.52 (r(s(s(s(elem!1))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[5193, 11275])).
% 2.33/2.52 tff(11277,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11278,plain,
% 2.33/2.52 (((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11279,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~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), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[11278])).
% 2.33/2.52 tff(11280,plain,
% 2.33/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~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), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[11279, 11277])).
% 2.33/2.52 tff(11281,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(11282,plain,
% 2.33/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11281, 11280])).
% 2.33/2.52 tff(11283,plain,
% 2.33/2.52 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11282, 65, 11276, 10842])).
% 2.33/2.52 tff(11284,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 2.33/2.52 tff(11285,plain,
% 2.33/2.52 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[11284])).
% 2.33/2.52 tff(11286,plain,
% 2.33/2.52 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.33/2.52 inference(symmetry,[status(thm)],[11285])).
% 2.33/2.52 tff(11287,plain,
% 2.33/2.52 (elem!1 = s(s(elem!1))),
% 2.33/2.52 inference(transitivity,[status(thm)],[1171, 11286, 24])).
% 2.33/2.52 tff(11288,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1559, 11287])).
% 2.33/2.52 tff(11289,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11290,plain,
% 2.33/2.52 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11289, 4753])).
% 2.33/2.52 tff(11291,plain,
% 2.33/2.52 (((~![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)))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11292,plain,
% 2.33/2.52 ((~![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)))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(11293,plain,
% 2.33/2.52 ((~![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))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11292, 11291])).
% 2.33/2.52 tff(11294,plain,
% 2.33/2.52 (b(s(s(s(elem!1))), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11293, 47, 11290, 11283])).
% 2.33/2.52 tff(11295,plain,
% 2.33/2.52 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[4774, 2104])).
% 2.33/2.52 tff(11296,plain,
% 2.33/2.52 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1157, 11187, 1148, 11037, 11131])).
% 2.33/2.52 tff(11297,plain,
% 2.33/2.52 (r(s(s(s(s(elem!1)))), z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[95, 11296])).
% 2.33/2.52 tff(11298,plain,
% 2.33/2.52 (((~![X0: $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(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(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(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11299,plain,
% 2.33/2.52 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11300,plain,
% 2.33/2.52 (((~![X0: $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(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[11299])).
% 2.33/2.52 tff(11301,plain,
% 2.33/2.52 (((~![X0: $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(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)))),
% 2.33/2.52 inference(transitivity,[status(thm)],[11300, 11298])).
% 2.33/2.52 tff(11302,plain,
% 2.33/2.52 ((~![X0: $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(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(11303,plain,
% 2.33/2.52 ((~![X0: $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(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11302, 11301])).
% 2.33/2.52 tff(11304,plain,
% 2.33/2.52 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11303, 65, 11218, 11276, 11297])).
% 2.33/2.52 tff(11305,plain,
% 2.33/2.52 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[2109, 47, 11304])).
% 2.33/2.52 tff(11306,plain,
% 2.33/2.52 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11305, 11295])).
% 2.33/2.52 tff(11307,plain,
% 2.33/2.52 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1299, 65, 11276, 11297])).
% 2.33/2.52 tff(11308,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1304, 11307, 4774])).
% 2.33/2.52 tff(11309,plain,
% 2.33/2.52 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10960, 11197, 11137])).
% 2.33/2.52 tff(11310,plain,
% 2.33/2.52 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10965, 10837])).
% 2.33/2.52 tff(11311,plain,
% 2.33/2.52 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10969, 47, 11310, 11309])).
% 2.33/2.52 tff(11312,plain,
% 2.33/2.52 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10985, 11148, 11038])).
% 2.33/2.52 tff(11313,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11314,plain,
% 2.33/2.52 (((~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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(rewrite,[status(thm)],[])).
% 2.33/2.52 tff(11315,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[11314])).
% 2.33/2.52 tff(11316,plain,
% 2.33/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(transitivity,[status(thm)],[11315, 11313])).
% 2.33/2.52 tff(11317,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, 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(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.33/2.52 inference(quant_inst,[status(thm)],[])).
% 2.33/2.52 tff(11318,plain,
% 2.33/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11317, 11316])).
% 2.33/2.52 tff(11319,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11318, 162, 11312, 11311, 11308, 11306, 11294])).
% 2.33/2.52 tff(11320,plain,((elem!1 = s(s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(z))) | r(s(z), s(s(z))) | (~b(s(s(z)), s(z))) | r(z, elem!1) | b(s(s(s(z))), elem!1) | b(s(z), elem!1) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11321,plain,
% 2.33/2.52 (b(s(s(s(z))), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11320, 10754, 10589, 152, 1323, 121, 383, 3632, 10744, 1538, 6919])).
% 2.33/2.52 tff(11322,plain,
% 2.33/2.52 (b(s(s(s(z))), s(z))),
% 2.33/2.52 inference(modus_ponens,[status(thm)],[11321, 10743])).
% 2.33/2.52 tff(11323,plain,
% 2.33/2.52 ($false),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[10588, 11322])).
% 2.33/2.52 tff(11324,plain,(b(s(z), elem!1) | b(s(s(s(z))), s(z)) | (~b(s(z), z)) | r(s(z), s(s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | b(elem!1, s(s(elem!1))) | r(z, elem!1) | (elem!1 = s(s(s(s(elem!1))))) | r(s(s(s(z))), z) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.52 tff(11325,plain,
% 2.33/2.52 (b(s(z), elem!1)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[11324, 10739, 10730, 1323, 121, 10723, 3632, 10588, 1538, 375, 10728])).
% 2.33/2.52 tff(11326,plain,
% 2.33/2.52 (~r(elem!1, z)),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[4809, 10727, 1230])).
% 2.33/2.52 tff(11327,plain,
% 2.33/2.52 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1524, 4773])).
% 2.33/2.52 tff(11328,plain,
% 2.33/2.52 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 2.33/2.52 inference(unit_resolution,[status(thm)],[1517, 4774])).
% 2.33/2.52 tff(11329,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[1705])).
% 2.33/2.52 tff(11330,plain,
% 2.33/2.52 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.52 inference(symmetry,[status(thm)],[11329])).
% 2.33/2.52 tff(11331,plain,
% 2.33/2.52 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 2.33/2.52 inference(monotonicity,[status(thm)],[1827])).
% 2.33/2.52 tff(11332,plain,
% 2.33/2.52 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(elem!1))))), z)),
% 2.33/2.52 inference(monotonicity,[status(thm)],[1705])).
% 2.33/2.52 tff(11333,plain,
% 2.33/2.52 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(symmetry,[status(thm)],[11332])).
% 2.33/2.52 tff(11334,plain,
% 2.33/2.52 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 2.33/2.52 inference(transitivity,[status(thm)],[1830, 11333])).
% 2.33/2.53 tff(11335,plain,
% 2.33/2.53 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1529, 1244, 1245])).
% 2.33/2.53 tff(11336,plain,
% 2.33/2.53 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2547, 65, 123, 385])).
% 2.33/2.53 tff(11337,plain,
% 2.33/2.53 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[360, 11336])).
% 2.33/2.53 tff(11338,plain,
% 2.33/2.53 (~b(s(s(z)), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[720, 11337, 416, 6281, 10714])).
% 2.33/2.53 tff(11339,plain,
% 2.33/2.53 (r(s(s(z)), s(s(s(z))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[442, 11338])).
% 2.33/2.53 tff(11340,plain,
% 2.33/2.53 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11339, 3741])).
% 2.33/2.53 tff(11341,plain,
% 2.33/2.53 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 2.33/2.53 inference(monotonicity,[status(thm)],[1211])).
% 2.33/2.53 tff(11342,plain,
% 2.33/2.53 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.33/2.53 inference(symmetry,[status(thm)],[11341])).
% 2.33/2.53 tff(11343,plain,
% 2.33/2.53 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 2.33/2.53 inference(monotonicity,[status(thm)],[1213])).
% 2.33/2.53 tff(11344,plain,
% 2.33/2.53 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.33/2.53 inference(symmetry,[status(thm)],[11343])).
% 2.33/2.53 tff(11345,plain,
% 2.33/2.53 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.33/2.53 inference(transitivity,[status(thm)],[11344, 11342])).
% 2.33/2.53 tff(11346,plain,
% 2.33/2.53 (r(s(s(elem!1)), elem!1)),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[230, 11345])).
% 2.33/2.53 tff(11347,assumption,(s(s(elem!1)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.33/2.53 tff(11348,plain,
% 2.33/2.53 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 2.33/2.53 inference(symmetry,[status(thm)],[11347])).
% 2.33/2.53 tff(11349,plain,
% 2.33/2.53 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11348])).
% 2.33/2.53 tff(11350,plain,
% 2.33/2.53 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(symmetry,[status(thm)],[11349])).
% 2.33/2.53 tff(11351,plain,
% 2.33/2.53 (s(elem!1) = s(s(s(s(elem!1))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[325, 11350, 909])).
% 2.33/2.53 tff(11352,plain,
% 2.33/2.53 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11351])).
% 2.33/2.53 tff(11353,plain,
% 2.33/2.53 (elem!1 = s(s(s(elem!1)))),
% 2.33/2.53 inference(transitivity,[status(thm)],[1171, 11352, 19])).
% 2.33/2.53 tff(11354,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[7589, 11353])).
% 2.33/2.53 tff(11355,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(11356,plain,
% 2.33/2.53 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11355, 1473])).
% 2.33/2.53 tff(11357,plain,
% 2.33/2.53 (((~![X0: $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)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(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(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11358,plain,
% 2.33/2.53 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11359,plain,
% 2.33/2.53 (((~![X0: $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)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(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(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11358])).
% 2.33/2.53 tff(11360,plain,
% 2.33/2.53 (((~![X0: $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)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(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(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[11359, 11357])).
% 2.33/2.53 tff(11361,plain,
% 2.33/2.53 ((~![X0: $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)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(11362,plain,
% 2.33/2.53 ((~![X0: $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)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11361, 11360])).
% 2.33/2.53 tff(11363,plain,
% 2.33/2.53 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11362, 65, 1572, 1862])).
% 2.33/2.53 tff(11364,plain,
% 2.33/2.53 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[2214, 11363, 2378])).
% 2.33/2.53 tff(11365,assumption,(~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.33/2.53 tff(11366,plain,
% 2.33/2.53 (((~![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(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), 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(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11367,plain,
% 2.33/2.53 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11368,plain,
% 2.33/2.53 (((~![X0: $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(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), 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(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11367])).
% 2.33/2.53 tff(11369,plain,
% 2.33/2.53 (((~![X0: $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(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), 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(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[11368, 11366])).
% 2.33/2.53 tff(11370,plain,
% 2.33/2.53 ((~![X0: $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(elem!1))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(11371,plain,
% 2.33/2.53 ((~![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(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11370, 11369])).
% 2.33/2.53 tff(11372,plain,
% 2.33/2.53 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11371, 65, 1862, 1571])).
% 2.33/2.53 tff(11373,plain,
% 2.33/2.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), 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(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11374,plain,
% 2.33/2.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(11375,plain,
% 2.33/2.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11374, 11373])).
% 2.33/2.53 tff(11376,plain,
% 2.33/2.53 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11375, 47])).
% 2.33/2.53 tff(11377,plain,
% 2.33/2.53 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11376, 11372, 11365])).
% 2.33/2.53 tff(11378,plain,
% 2.33/2.53 (((~![X0: $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)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11379,plain,
% 2.33/2.53 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11380,plain,
% 2.33/2.53 (((~![X0: $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(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11379])).
% 2.33/2.53 tff(11381,plain,
% 2.33/2.53 (((~![X0: $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(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[11380, 11378])).
% 2.33/2.53 tff(11382,plain,
% 2.33/2.53 ((~![X0: $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(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(11383,plain,
% 2.33/2.53 ((~![X0: $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)))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11382, 11381])).
% 2.33/2.53 tff(11384,plain,
% 2.33/2.53 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11383, 65, 1572, 1862])).
% 2.33/2.53 tff(11385,plain,
% 2.33/2.53 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1789, 11384, 1692])).
% 2.33/2.53 tff(11386,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))), introduced(assumption)).
% 2.33/2.53 tff(11387,plain,
% 2.33/2.53 (((~![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(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11388,plain,
% 2.33/2.53 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11389,plain,
% 2.33/2.53 (((~![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(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11388])).
% 2.33/2.53 tff(11390,plain,
% 2.33/2.53 (((~![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(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[11389, 11387])).
% 2.33/2.53 tff(11391,plain,
% 2.33/2.53 ((~![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(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(11392,plain,
% 2.33/2.53 ((~![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(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11391, 11390])).
% 2.33/2.53 tff(11393,plain,
% 2.33/2.53 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11392, 65, 2313, 1862, 1571])).
% 2.33/2.53 tff(11394,plain,
% 2.33/2.53 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1760, 11393, 11386])).
% 2.33/2.53 tff(11395,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11396,plain,
% 2.33/2.53 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(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(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11397,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11396])).
% 2.33/2.53 tff(11398,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[11397, 11395])).
% 2.33/2.53 tff(11399,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(11400,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11399, 11398])).
% 2.33/2.53 tff(11401,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11400, 162, 1146, 11394, 11385, 11377, 11364])).
% 2.33/2.53 tff(11402,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.53 tff(11403,plain,
% 2.33/2.53 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11402, 11356, 1701, 11346, 1692, 11340, 2303, 11335])).
% 2.33/2.53 tff(11404,plain,
% 2.33/2.53 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1858, 11403, 1834])).
% 2.33/2.53 tff(11405,plain,
% 2.33/2.53 (b(s(s(s(s(s(z))))), z)),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11404, 11334])).
% 2.33/2.53 tff(11406,plain,
% 2.33/2.53 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11329])).
% 2.33/2.53 tff(11407,plain,
% 2.33/2.53 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[1705])).
% 2.33/2.53 tff(11408,plain,
% 2.33/2.53 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.53 inference(symmetry,[status(thm)],[11407])).
% 2.33/2.53 tff(11409,plain,
% 2.33/2.53 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[1705])).
% 2.33/2.53 tff(11410,plain,
% 2.33/2.53 ((~r(s(z), s(s(s(s(s(z))))))) <=> (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11409])).
% 2.33/2.53 tff(11411,plain,
% 2.33/2.53 (~r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[5358, 5350, 385])).
% 2.33/2.53 tff(11412,plain,
% 2.33/2.53 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11411, 11410])).
% 2.33/2.53 tff(11413,plain,
% 2.33/2.53 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[1050, 11412])).
% 2.33/2.53 tff(11414,plain,
% 2.33/2.53 (b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11413, 11408])).
% 2.33/2.53 tff(11415,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11416,plain,
% 2.33/2.53 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(rewrite,[status(thm)],[])).
% 2.33/2.53 tff(11417,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.33/2.53 inference(monotonicity,[status(thm)],[11416])).
% 2.33/2.53 tff(11418,plain,
% 2.33/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.33/2.53 inference(transitivity,[status(thm)],[11417, 11415])).
% 2.33/2.53 tff(11419,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.33/2.53 inference(quant_inst,[status(thm)],[])).
% 2.33/2.53 tff(11420,plain,
% 2.33/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.33/2.53 inference(modus_ponens,[status(thm)],[11419, 11418])).
% 2.33/2.53 tff(11421,plain,
% 2.33/2.53 ($false),
% 2.33/2.53 inference(unit_resolution,[status(thm)],[11420, 162, 152, 121, 7321, 7363, 2903])).
% 2.33/2.54 tff(11422,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(11423,plain,
% 2.33/2.54 (~b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11422, 11414, 121, 7321, 152])).
% 2.33/2.54 tff(11424,plain,
% 2.33/2.54 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11423, 11406])).
% 2.33/2.54 tff(11425,plain,
% 2.33/2.54 (r(s(s(s(s(s(elem!1))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[968, 11424])).
% 2.33/2.54 tff(11426,plain,
% 2.33/2.54 (r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11425, 1828])).
% 2.33/2.54 tff(11427,plain,
% 2.33/2.54 (((~![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(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11428,plain,
% 2.33/2.54 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11429,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[11428])).
% 2.33/2.54 tff(11430,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[11429, 11427])).
% 2.33/2.54 tff(11431,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(11432,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11431, 11430])).
% 2.33/2.54 tff(11433,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11432, 65, 385, 5350, 11426])).
% 2.33/2.54 tff(11434,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(11435,plain,
% 2.33/2.54 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11434, 1211, 385, 121, 11405, 10730])).
% 2.33/2.54 tff(11436,plain,
% 2.33/2.54 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[5347, 11435, 1211])).
% 2.33/2.54 tff(11437,plain,
% 2.33/2.54 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1001, 11436])).
% 2.33/2.54 tff(11438,plain,
% 2.33/2.54 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11437, 2169])).
% 2.33/2.54 tff(11439,plain,
% 2.33/2.54 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11337, 4052])).
% 2.33/2.54 tff(11440,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 2.33/2.54 tff(11441,plain,
% 2.33/2.54 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[5400, 65, 385, 11440])).
% 2.33/2.54 tff(11442,plain,
% 2.33/2.54 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11441, 2183])).
% 2.33/2.54 tff(11443,plain,
% 2.33/2.54 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1731, 11442, 1691])).
% 2.33/2.54 tff(11444,plain,
% 2.33/2.54 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[2046])).
% 2.33/2.54 tff(11445,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11446,plain,
% 2.33/2.54 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11447,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[11446])).
% 2.33/2.54 tff(11448,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[11447, 11445])).
% 2.33/2.54 tff(11449,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(11450,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11449, 11448])).
% 2.33/2.54 tff(11451,plain,
% 2.33/2.54 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11450, 65, 1131, 11440])).
% 2.33/2.54 tff(11452,plain,
% 2.33/2.54 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11451, 11444])).
% 2.33/2.54 tff(11453,plain,
% 2.33/2.54 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1789, 11452, 1692])).
% 2.33/2.54 tff(11454,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(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(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11455,plain,
% 2.33/2.54 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11456,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[11455])).
% 2.33/2.54 tff(11457,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[11456, 11454])).
% 2.33/2.54 tff(11458,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(11459,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11458, 11457])).
% 2.33/2.54 tff(11460,plain,
% 2.33/2.54 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11459, 65, 1131, 11440])).
% 2.33/2.54 tff(11461,plain,
% 2.33/2.54 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11460, 2200])).
% 2.33/2.54 tff(11462,plain,
% 2.33/2.54 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2214, 11461, 2378])).
% 2.33/2.54 tff(11463,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[2227, 11462, 11453, 2219, 2216, 11443])).
% 2.33/2.54 tff(11464,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~(elem!1 = z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(11465,plain,
% 2.33/2.54 (~r(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11464, 11439, 11438, 1691, 1692, 1211, 3542, 385])).
% 2.33/2.54 tff(11466,plain,
% 2.33/2.54 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11465, 11331])).
% 2.33/2.54 tff(11467,plain,
% 2.33/2.54 (b(s(s(s(s(s(elem!1))))), s(z))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[968, 11466])).
% 2.33/2.54 tff(11468,plain,
% 2.33/2.54 (b(s(s(s(s(s(z))))), s(z))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11467, 11330])).
% 2.33/2.54 tff(11469,plain,
% 2.33/2.54 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11437, 1843])).
% 2.33/2.54 tff(11470,plain,
% 2.33/2.54 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11337, 1339])).
% 2.33/2.54 tff(11471,plain,
% 2.33/2.54 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[1705])).
% 2.33/2.54 tff(11472,plain,
% 2.33/2.54 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(symmetry,[status(thm)],[11471])).
% 2.33/2.54 tff(11473,plain,
% 2.33/2.54 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[1793, 11472])).
% 2.33/2.54 tff(11474,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11475,plain,
% 2.33/2.54 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11476,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[11475])).
% 2.33/2.54 tff(11477,plain,
% 2.33/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[11476, 11474])).
% 2.33/2.54 tff(11478,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(11479,plain,
% 2.33/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11478, 11477])).
% 2.33/2.54 tff(11480,plain,
% 2.33/2.54 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11479, 162, 152, 692, 7321, 2904, 2903])).
% 2.33/2.54 tff(11481,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11480, 11473])).
% 2.33/2.54 tff(11482,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~(elem!1 = z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(11483,plain,
% 2.33/2.54 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11482, 1211, 10730, 11470, 11405, 11469, 11468])).
% 2.33/2.54 tff(11484,plain,
% 2.33/2.54 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11483, 2049])).
% 2.33/2.54 tff(11485,plain,
% 2.33/2.54 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1789, 11484, 1692])).
% 2.33/2.54 tff(11486,plain,
% 2.33/2.54 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11485, 2047])).
% 2.33/2.54 tff(11487,plain,
% 2.33/2.54 (r(s(z), s(s(s(s(s(elem!1)))))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(symmetry,[status(thm)],[11409])).
% 2.33/2.54 tff(11488,plain,
% 2.33/2.54 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[11407])).
% 2.33/2.54 tff(11489,plain,
% 2.33/2.54 (~b(s(z), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11420, 162, 10730, 121, 11405, 11468])).
% 2.33/2.54 tff(11490,plain,
% 2.33/2.54 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11489, 11488])).
% 2.33/2.54 tff(11491,plain,
% 2.33/2.54 (r(s(z), s(s(s(s(s(elem!1))))))),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1050, 11490])).
% 2.33/2.54 tff(11492,plain,
% 2.33/2.54 (r(s(z), s(s(s(s(s(z))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11491, 11487])).
% 2.33/2.54 tff(11493,plain,
% 2.33/2.54 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(z)))))),
% 2.33/2.54 inference(symmetry,[status(thm)],[2067])).
% 2.33/2.54 tff(11494,plain,
% 2.33/2.54 (r(s(z), s(s(s(s(z)))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[193, 11493])).
% 2.33/2.54 tff(11495,plain,
% 2.33/2.54 (((~![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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), 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(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11496,plain,
% 2.33/2.54 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(rewrite,[status(thm)],[])).
% 2.33/2.54 tff(11497,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(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(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.33/2.54 inference(monotonicity,[status(thm)],[11496])).
% 2.33/2.54 tff(11498,plain,
% 2.33/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(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(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.33/2.54 inference(transitivity,[status(thm)],[11497, 11495])).
% 2.33/2.54 tff(11499,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.33/2.54 inference(quant_inst,[status(thm)],[])).
% 2.33/2.54 tff(11500,plain,
% 2.33/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.33/2.54 inference(modus_ponens,[status(thm)],[11499, 11498])).
% 2.33/2.54 tff(11501,plain,
% 2.33/2.54 ($false),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11500, 65, 11494, 11492, 11486])).
% 2.33/2.54 tff(11502,plain,((~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(s(elem!1)))), z)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.54 tff(11503,plain,
% 2.33/2.54 (~(elem!1 = z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[11502, 11328, 121, 11327, 10589, 123, 10725, 230, 4794, 416, 1229])).
% 2.33/2.54 tff(11504,plain,
% 2.33/2.54 (b(elem!1, z)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[3486, 11503, 11326])).
% 2.33/2.54 tff(11505,plain,
% 2.33/2.54 (~(z = elem!1)),
% 2.33/2.54 inference(unit_resolution,[status(thm)],[1208, 11503])).
% 2.33/2.55 tff(11506,plain,
% 2.33/2.55 (b(z, elem!1)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[4889, 11505, 10739])).
% 2.33/2.55 tff(11507,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[7122, 11506, 11504, 10730, 121, 11325])).
% 2.33/2.55 tff(11508,plain,((elem!1 = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(s(elem!1)))), z) | r(s(z), s(s(z))) | b(elem!1, s(s(elem!1))) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), z) | (~r(z, s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11509,plain,
% 2.33/2.55 ((elem!1 = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(s(elem!1)))), z) | b(elem!1, s(s(elem!1))) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), z) | (~r(z, s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11508, 6734])).
% 2.33/2.55 tff(11510,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11509, 10706, 10698, 10690, 230, 9847, 10666, 10686, 10588, 375, 495, 121])).
% 2.33/2.55 tff(11511,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), z) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | b(z, s(s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(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)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11512,plain,
% 2.33/2.55 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11511, 10661, 10588, 375, 495, 121, 3019, 297, 230, 362, 363])).
% 2.33/2.55 tff(11513,plain,
% 2.33/2.55 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[6855, 11512])).
% 2.33/2.55 tff(11514,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[7991, 65, 395, 11513, 645])).
% 2.33/2.55 tff(11515,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), z) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | b(z, s(s(z))) | (~b(z, s(s(s(z))))) | (~r(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)))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11516,plain,
% 2.33/2.55 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11515, 10660, 10588, 375, 10626, 121, 3019, 297, 230, 10616, 10628])).
% 2.33/2.55 tff(11517,plain,
% 2.33/2.55 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[83, 11516])).
% 2.33/2.55 tff(11518,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11519,plain,
% 2.33/2.55 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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(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))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11520,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[11519])).
% 2.33/2.55 tff(11521,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[11520, 11518])).
% 2.33/2.55 tff(11522,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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)))))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(11523,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[11522, 11521])).
% 2.33/2.55 tff(11524,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11523, 162, 11517, 10628, 10616, 10614, 297])).
% 2.33/2.55 tff(11525,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), z) | (~b(z, s(z))) | b(z, s(s(z))) | (~r(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11526,plain,
% 2.33/2.55 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11525, 10613, 10588, 10586, 10585, 3019, 230, 10611])).
% 2.33/2.55 tff(11527,plain,
% 2.33/2.55 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[191, 11526])).
% 2.33/2.55 tff(11528,plain,
% 2.33/2.55 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[10518, 11527, 9847, 10477])).
% 2.33/2.55 tff(11529,plain,
% 2.33/2.55 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[216, 11528])).
% 2.33/2.55 tff(11530,plain,
% 2.33/2.55 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[6166, 11529, 3020])).
% 2.33/2.55 tff(11531,plain,
% 2.33/2.55 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[83, 11530])).
% 2.33/2.55 tff(11532,plain,
% 2.33/2.55 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[10511, 11531, 9847, 10477, 10587, 10613, 10611])).
% 2.33/2.55 tff(11533,plain,
% 2.33/2.55 (r(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[95, 11532])).
% 2.33/2.55 tff(11534,plain,
% 2.33/2.55 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[10481, 11527, 9847, 10477])).
% 2.33/2.55 tff(11535,plain,
% 2.33/2.55 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[149, 11534])).
% 2.33/2.55 tff(11536,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[10712, 65, 11535, 11533, 11529, 230])).
% 2.33/2.55 tff(11537,plain,(b(z, s(s(z))) | (~r(s(s(z)), z)) | b(s(s(s(z))), s(z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11538,plain,
% 2.33/2.55 (b(z, s(s(z)))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11537, 10588, 230, 273])).
% 2.33/2.55 tff(11539,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11540,plain,
% 2.33/2.55 (((~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(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11541,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[11540])).
% 2.33/2.55 tff(11542,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[11541, 11539])).
% 2.33/2.55 tff(11543,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(11544,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[11543, 11542])).
% 2.33/2.55 tff(11545,plain,
% 2.33/2.55 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11544, 162, 10585, 9847, 10477, 6735])).
% 2.33/2.55 tff(11546,plain,
% 2.33/2.55 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11545, 11538])).
% 2.33/2.55 tff(11547,plain,
% 2.33/2.55 (r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[191, 11546])).
% 2.33/2.55 tff(11548,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2517, 11547, 10589])).
% 2.33/2.55 tff(11549,plain,
% 2.33/2.55 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[338, 11548])).
% 2.33/2.55 tff(11550,plain,
% 2.33/2.55 (~b(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[8929, 11538, 10477, 10585])).
% 2.33/2.55 tff(11551,plain,
% 2.33/2.55 (r(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[175, 11550])).
% 2.33/2.55 tff(11552,plain,
% 2.33/2.55 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[503, 11551, 11547])).
% 2.33/2.55 tff(11553,plain,
% 2.33/2.55 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[83, 11552])).
% 2.33/2.55 tff(11554,plain,
% 2.33/2.55 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2561, 11551, 11547])).
% 2.33/2.55 tff(11555,plain,
% 2.33/2.55 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[95, 11554])).
% 2.33/2.55 tff(11556,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11557,plain,
% 2.33/2.55 (((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11558,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[11557])).
% 2.33/2.55 tff(11559,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[11558, 11556])).
% 2.33/2.55 tff(11560,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(11561,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[11560, 11559])).
% 2.33/2.55 tff(11562,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11561, 162, 9847, 11555, 11553, 11538, 11549, 10587])).
% 2.33/2.55 tff(11563,plain,(b(s(s(s(z))), s(z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11564,plain,
% 2.33/2.55 (b(s(s(s(z))), s(z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11563, 230, 273])).
% 2.33/2.55 tff(11565,plain,
% 2.33/2.55 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[10033, 162, 10585, 9847, 6735, 10587, 11564])).
% 2.33/2.55 tff(11566,plain,
% 2.33/2.55 (r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[191, 11565])).
% 2.33/2.55 tff(11567,plain,
% 2.33/2.55 (~b(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[8929, 537, 10477, 10585])).
% 2.33/2.55 tff(11568,plain,
% 2.33/2.55 (r(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[175, 11567])).
% 2.33/2.55 tff(11569,plain,
% 2.33/2.55 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[503, 11568, 193])).
% 2.33/2.55 tff(11570,plain,
% 2.33/2.55 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[83, 11569])).
% 2.33/2.55 tff(11571,plain,
% 2.33/2.55 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2561, 11568, 193])).
% 2.33/2.55 tff(11572,plain,
% 2.33/2.55 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[95, 11571])).
% 2.33/2.55 tff(11573,plain,
% 2.33/2.55 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2637, 11572, 9847, 11570, 537])).
% 2.33/2.55 tff(11574,plain,
% 2.33/2.55 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[216, 11573])).
% 2.33/2.55 tff(11575,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[6509, 11574, 273])).
% 2.33/2.55 tff(11576,plain,
% 2.33/2.55 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[338, 11575])).
% 2.33/2.55 tff(11577,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11561, 162, 9847, 11572, 11570, 537, 11576, 10587])).
% 2.33/2.55 tff(11578,plain,((~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11579,plain,
% 2.33/2.55 (~b(z, s(s(z)))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11578, 11566, 273])).
% 2.33/2.55 tff(11580,plain,
% 2.33/2.55 (r(z, s(s(z)))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[524, 11579])).
% 2.33/2.55 tff(11581,plain,
% 2.33/2.55 (~r(z, s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[281, 11580, 273])).
% 2.33/2.55 tff(11582,plain,
% 2.33/2.55 (b(z, s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[295, 11581])).
% 2.33/2.55 tff(11583,plain,
% 2.33/2.55 (~b(s(z), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[5781, 11582, 10585, 10587, 11564])).
% 2.33/2.55 tff(11584,plain,
% 2.33/2.55 (r(s(z), s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[493, 11583])).
% 2.33/2.55 tff(11585,plain,
% 2.33/2.55 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[9940, 11584, 11566])).
% 2.33/2.55 tff(11586,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[5513, 9045, 296, 121, 600, 152])).
% 2.33/2.55 tff(11587,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11588,plain,
% 2.33/2.55 (~b(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11587, 11580, 273, 230, 10585, 11564])).
% 2.33/2.55 tff(11589,plain,
% 2.33/2.55 (r(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[175, 11588])).
% 2.33/2.55 tff(11590,plain,
% 2.33/2.55 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[503, 11589, 11566])).
% 2.33/2.55 tff(11591,plain,
% 2.33/2.55 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[83, 11590])).
% 2.33/2.55 tff(11592,plain,
% 2.33/2.55 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[2561, 11589, 11566])).
% 2.33/2.55 tff(11593,plain,
% 2.33/2.55 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[95, 11592])).
% 2.33/2.55 tff(11594,plain,
% 2.33/2.55 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[6271, 11593, 10587, 11582, 11591])).
% 2.33/2.55 tff(11595,plain,
% 2.33/2.55 ($false),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[338, 11594, 11585])).
% 2.33/2.55 tff(11596,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.55 tff(11597,plain,
% 2.33/2.55 (~r(s(s(z)), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11596, 273])).
% 2.33/2.55 tff(11598,plain,
% 2.33/2.55 (b(s(s(z)), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[245, 11597])).
% 2.33/2.55 tff(11599,plain,
% 2.33/2.55 (~b(z, s(s(z)))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[9012, 11598, 10477, 10585])).
% 2.33/2.55 tff(11600,plain,
% 2.33/2.55 (r(z, s(s(z)))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[524, 11599])).
% 2.33/2.55 tff(11601,plain,
% 2.33/2.55 (~r(z, s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[281, 11600, 273])).
% 2.33/2.55 tff(11602,plain,
% 2.33/2.55 (b(z, s(s(s(z))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[295, 11601])).
% 2.33/2.55 tff(11603,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11604,plain,
% 2.33/2.55 (((~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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11605,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.33/2.55 inference(monotonicity,[status(thm)],[11604])).
% 2.33/2.55 tff(11606,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.55 inference(transitivity,[status(thm)],[11605, 11603])).
% 2.33/2.55 tff(11607,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.33/2.55 inference(quant_inst,[status(thm)],[])).
% 2.33/2.55 tff(11608,plain,
% 2.33/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.33/2.55 inference(modus_ponens,[status(thm)],[11607, 11606])).
% 2.33/2.55 tff(11609,plain,
% 2.33/2.55 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), z))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11608, 162, 10585, 9847, 10477, 6735])).
% 2.33/2.55 tff(11610,plain,
% 2.33/2.55 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[11609, 11598])).
% 2.33/2.55 tff(11611,plain,
% 2.33/2.55 (r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[191, 11610])).
% 2.33/2.55 tff(11612,plain,
% 2.33/2.55 (~b(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[6912, 11598, 10477, 10585])).
% 2.33/2.55 tff(11613,plain,
% 2.33/2.55 (r(s(z), z)),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[175, 11612])).
% 2.33/2.55 tff(11614,plain,
% 2.33/2.55 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[503, 11613, 11611])).
% 2.33/2.55 tff(11615,plain,
% 2.33/2.55 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.55 inference(unit_resolution,[status(thm)],[83, 11614])).
% 2.33/2.55 tff(11616,plain,
% 2.33/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.55 inference(rewrite,[status(thm)],[])).
% 2.33/2.55 tff(11617,plain,
% 2.33/2.56 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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(z, 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)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11618,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[11617])).
% 2.33/2.56 tff(11619,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[11618, 11616])).
% 2.33/2.56 tff(11620,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~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))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(11621,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[11620, 11619])).
% 2.33/2.56 tff(11622,plain,
% 2.33/2.56 ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11621, 162, 10585, 9847, 10477, 6735])).
% 2.33/2.56 tff(11623,plain,
% 2.33/2.56 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11622, 11598])).
% 2.33/2.56 tff(11624,plain,
% 2.33/2.56 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[149, 11623])).
% 2.33/2.56 tff(11625,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8395, 11602, 11624, 10587, 11613, 11615])).
% 2.33/2.56 tff(11626,plain,
% 2.33/2.56 (b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[595, 11625])).
% 2.33/2.56 tff(11627,plain,
% 2.33/2.56 (~b(s(z), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[5781, 11626, 10585, 10587, 11602])).
% 2.33/2.56 tff(11628,plain,
% 2.33/2.56 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2561, 11613, 11611])).
% 2.33/2.56 tff(11629,plain,
% 2.33/2.56 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[95, 11628])).
% 2.33/2.56 tff(11630,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6271, 11629, 10587, 11602, 11615])).
% 2.33/2.56 tff(11631,plain,
% 2.33/2.56 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[338, 11630])).
% 2.33/2.56 tff(11632,plain,
% 2.33/2.56 (~r(s(z), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[9940, 11631, 11611])).
% 2.33/2.56 tff(11633,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[493, 11632, 11627])).
% 2.33/2.56 tff(11634,plain,(~r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(11635,plain,
% 2.33/2.56 (b(s(s(s(z))), s(s(z)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[459, 11634])).
% 2.33/2.56 tff(11636,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8491, 97, 10477, 11635, 866])).
% 2.33/2.56 tff(11637,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[595, 11636, 1435])).
% 2.33/2.56 tff(11638,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(11639,plain,
% 2.33/2.56 (~r(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11638, 866])).
% 2.33/2.56 tff(11640,plain,
% 2.33/2.56 (b(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[117, 11639])).
% 2.33/2.56 tff(11641,plain,
% 2.33/2.56 (~r(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8647, 385, 866])).
% 2.33/2.56 tff(11642,plain,
% 2.33/2.56 (b(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[175, 11641])).
% 2.33/2.56 tff(11643,plain,
% 2.33/2.56 (~b(s(s(z)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6912, 11642, 10477, 11640])).
% 2.33/2.56 tff(11644,plain,
% 2.33/2.56 (r(s(s(z)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[245, 11643])).
% 2.33/2.56 tff(11645,plain,
% 2.33/2.56 (~r(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8456, 11644, 866])).
% 2.33/2.56 tff(11646,plain,
% 2.33/2.56 (b(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[442, 11645])).
% 2.33/2.56 tff(11647,plain,
% 2.33/2.56 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10378, 11646, 11635, 385])).
% 2.33/2.56 tff(11648,plain,
% 2.33/2.56 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[191, 11647])).
% 2.33/2.56 tff(11649,plain,
% 2.33/2.56 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10481, 11648, 9847, 10477])).
% 2.33/2.56 tff(11650,plain,
% 2.33/2.56 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[149, 11649])).
% 2.33/2.56 tff(11651,plain,
% 2.33/2.56 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2549, 11650, 385])).
% 2.33/2.56 tff(11652,plain,
% 2.33/2.56 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[360, 11651])).
% 2.33/2.56 tff(11653,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[453, 11652, 9847, 11635, 11646])).
% 2.33/2.56 tff(11654,plain,
% 2.33/2.56 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[338, 11653])).
% 2.33/2.56 tff(11655,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6251, 65, 11650, 385, 11654])).
% 2.33/2.56 tff(11656,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(11657,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11656, 866])).
% 2.33/2.56 tff(11658,plain,
% 2.33/2.56 (b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[595, 11657])).
% 2.33/2.56 tff(11659,plain,
% 2.33/2.56 ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8446, 162, 11640, 11635, 10477, 6735])).
% 2.33/2.56 tff(11660,plain,
% 2.33/2.56 (~b(s(s(z)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11659, 11658])).
% 2.33/2.56 tff(11661,plain,
% 2.33/2.56 (r(s(s(z)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[245, 11660])).
% 2.33/2.56 tff(11662,plain,
% 2.33/2.56 (~r(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8456, 11661, 866])).
% 2.33/2.56 tff(11663,plain,
% 2.33/2.56 (b(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[442, 11662])).
% 2.33/2.56 tff(11664,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8432, 162, 11663, 11635, 10477, 6735, 11658])).
% 2.33/2.56 tff(11665,plain,(~r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(11666,plain,
% 2.33/2.56 (b(s(s(s(z))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[381, 11665])).
% 2.33/2.56 tff(11667,plain,
% 2.33/2.56 (~b(z, s(s(z)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2573, 10495, 9847, 538, 10480])).
% 2.33/2.56 tff(11668,plain,
% 2.33/2.56 (r(z, s(s(z)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[524, 11667])).
% 2.33/2.56 tff(11669,plain,
% 2.33/2.56 (~r(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6781, 1, 55])).
% 2.33/2.56 tff(11670,plain,
% 2.33/2.56 (b(z, s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[117, 11669])).
% 2.33/2.56 tff(11671,plain,
% 2.33/2.56 (~b(s(z), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8367, 6853, 10477, 11635])).
% 2.33/2.56 tff(11672,plain,
% 2.33/2.56 (r(s(z), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[493, 11671])).
% 2.33/2.56 tff(11673,plain,
% 2.33/2.56 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[9928, 11672, 11670, 1])).
% 2.33/2.56 tff(11674,plain,
% 2.33/2.56 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[360, 11673])).
% 2.33/2.56 tff(11675,plain,
% 2.33/2.56 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[2986, 11674, 9847, 11635, 6853])).
% 2.33/2.56 tff(11676,plain,
% 2.33/2.56 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[216, 11675])).
% 2.33/2.56 tff(11677,plain,
% 2.33/2.56 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6166, 11676, 55])).
% 2.33/2.56 tff(11678,plain,
% 2.33/2.56 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[83, 11677])).
% 2.33/2.56 tff(11679,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[453, 11674, 9847, 11635, 6853])).
% 2.33/2.56 tff(11680,plain,
% 2.33/2.56 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[338, 11679])).
% 2.33/2.56 tff(11681,plain,
% 2.33/2.56 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[9940, 11680, 11672])).
% 2.33/2.56 tff(11682,plain,
% 2.33/2.56 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[191, 11681])).
% 2.33/2.56 tff(11683,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11684,plain,
% 2.33/2.56 (((~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(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11685,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(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(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[11684])).
% 2.33/2.56 tff(11686,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(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(s(elem!1)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[11685, 11683])).
% 2.33/2.56 tff(11687,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(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(s(elem!1)))))) | (~b(z, s(z))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(11688,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[11687, 11686])).
% 2.33/2.56 tff(11689,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11688, 162, 11670, 9847, 11682, 11678, 11674, 11635])).
% 2.33/2.56 tff(11690,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(11691,plain,
% 2.33/2.56 (~r(z, s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11690, 11668])).
% 2.33/2.56 tff(11692,plain,
% 2.33/2.56 (b(z, s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[295, 11691])).
% 2.33/2.56 tff(11693,plain,
% 2.33/2.56 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6271, 11692, 11666, 10495, 10480])).
% 2.33/2.56 tff(11694,plain,
% 2.33/2.56 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[338, 11693])).
% 2.33/2.56 tff(11695,plain,
% 2.33/2.56 (~b(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[7999, 11692, 11635, 11666, 538])).
% 2.33/2.56 tff(11696,plain,
% 2.33/2.56 (r(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[442, 11695])).
% 2.33/2.56 tff(11697,plain,
% 2.33/2.56 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[6350, 11696, 11694])).
% 2.33/2.56 tff(11698,plain,
% 2.33/2.56 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[216, 11697])).
% 2.33/2.56 tff(11699,plain,
% 2.33/2.56 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10518, 11698, 9847, 10477])).
% 2.33/2.56 tff(11700,plain,
% 2.33/2.56 (r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[191, 11699])).
% 2.33/2.56 tff(11701,plain,
% 2.33/2.56 (~r(s(z), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[9940, 11700, 11694])).
% 2.33/2.56 tff(11702,plain,
% 2.33/2.56 (b(s(z), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[493, 11701])).
% 2.33/2.56 tff(11703,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11704,plain,
% 2.33/2.56 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~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(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11705,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[11704])).
% 2.33/2.56 tff(11706,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[11705, 11703])).
% 2.33/2.56 tff(11707,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(11708,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[11707, 11706])).
% 2.33/2.56 tff(11709,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11708, 162, 10495, 538, 11635, 11698, 6735, 11702])).
% 2.33/2.56 tff(11710,plain,((~b(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(11711,plain,
% 2.33/2.56 (~b(s(s(z)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11710, 97])).
% 2.33/2.56 tff(11712,plain,
% 2.33/2.56 (r(s(s(z)), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[245, 11711])).
% 2.33/2.56 tff(11713,plain,
% 2.33/2.56 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[9724, 11712, 10477, 97])).
% 2.33/2.56 tff(11714,plain,
% 2.33/2.56 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[95, 11713])).
% 2.33/2.56 tff(11715,plain,
% 2.33/2.56 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10481, 177, 9847, 10477])).
% 2.33/2.56 tff(11716,plain,
% 2.33/2.56 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[149, 11715])).
% 2.33/2.56 tff(11717,plain,
% 2.33/2.56 ((~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[9107, 6735])).
% 2.33/2.56 tff(11718,plain,
% 2.33/2.56 (~b(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11717, 11716, 9847, 10477, 11666, 10480, 11714, 177])).
% 2.33/2.56 tff(11719,plain,
% 2.33/2.56 (r(s(z), z)),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[175, 11718])).
% 2.33/2.56 tff(11720,plain,
% 2.33/2.56 (~r(z, s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[9827, 11719, 10477, 11635, 97])).
% 2.33/2.56 tff(11721,plain,
% 2.33/2.56 (b(z, s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[295, 11720])).
% 2.33/2.56 tff(11722,plain,
% 2.33/2.56 (~r(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[8395, 11721, 11666, 11716, 11719, 10480])).
% 2.33/2.56 tff(11723,plain,
% 2.33/2.56 (b(s(s(s(z))), s(z))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[595, 11722])).
% 2.33/2.56 tff(11724,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11725,plain,
% 2.33/2.56 (((~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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11726,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.33/2.56 inference(monotonicity,[status(thm)],[11725])).
% 2.33/2.56 tff(11727,plain,
% 2.33/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.33/2.56 inference(transitivity,[status(thm)],[11726, 11724])).
% 2.33/2.56 tff(11728,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.33/2.56 inference(quant_inst,[status(thm)],[])).
% 2.33/2.56 tff(11729,plain,
% 2.33/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.33/2.56 inference(modus_ponens,[status(thm)],[11728, 11727])).
% 2.33/2.56 tff(11730,plain,
% 2.33/2.56 ($false),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11729, 162, 9847, 177, 11635, 10477, 6735, 11723])).
% 2.33/2.56 tff(11731,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.56 tff(11732,plain,
% 2.33/2.56 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[11731, 97])).
% 2.33/2.56 tff(11733,plain,
% 2.33/2.56 (r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[191, 11732])).
% 2.33/2.56 tff(11734,plain,
% 2.33/2.56 (~b(z, s(s(z)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[10574, 600, 1, 416, 120, 97, 122])).
% 2.33/2.56 tff(11735,plain,
% 2.33/2.56 (r(z, s(s(z)))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[524, 11734])).
% 2.33/2.56 tff(11736,plain,
% 2.33/2.56 (~r(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[833, 11735, 1])).
% 2.33/2.56 tff(11737,plain,
% 2.33/2.56 (b(s(s(z)), s(s(s(z))))),
% 2.33/2.56 inference(unit_resolution,[status(thm)],[442, 11736])).
% 2.33/2.56 tff(11738,plain,
% 2.33/2.56 (((~![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(z), s(s(s(s(elem!1)))))) | (~r(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(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11739,plain,
% 2.33/2.56 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.33/2.56 inference(rewrite,[status(thm)],[])).
% 2.33/2.56 tff(11740,plain,
% 2.33/2.56 (((~![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(elem!1)))))) | (~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(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[11739])).
% 2.33/2.57 tff(11741,plain,
% 2.33/2.57 (((~![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(elem!1)))))) | (~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(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[11740, 11738])).
% 2.33/2.57 tff(11742,plain,
% 2.33/2.57 ((~![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(elem!1)))))) | (~r(z, s(z))))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(11743,plain,
% 2.33/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[11742, 11741])).
% 2.33/2.57 tff(11744,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11743, 65, 97, 193, 384, 55])).
% 2.33/2.57 tff(11745,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11746,plain,
% 2.33/2.57 (~r(s(z), s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11745, 11735, 193, 97])).
% 2.33/2.57 tff(11747,plain,
% 2.33/2.57 (b(s(z), s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[3713, 11746])).
% 2.33/2.57 tff(11748,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[4145, 11747, 11737, 10562, 6774, 600])).
% 2.33/2.57 tff(11749,plain,((~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11750,plain,
% 2.33/2.57 (~r(z, s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11749, 600, 9847, 97, 11733, 11714, 10480])).
% 2.33/2.57 tff(11751,plain,
% 2.33/2.57 (b(z, s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[295, 11750])).
% 2.33/2.57 tff(11752,plain,
% 2.33/2.57 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[6271, 11751, 11666, 11714, 10480])).
% 2.33/2.57 tff(11753,plain,
% 2.33/2.57 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[338, 11752])).
% 2.33/2.57 tff(11754,plain,
% 2.33/2.57 (~r(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[9940, 11753, 11733])).
% 2.33/2.57 tff(11755,plain,
% 2.33/2.57 (b(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[493, 11754])).
% 2.33/2.57 tff(11756,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[4407, 162, 11635, 10477, 6735, 600, 11755])).
% 2.33/2.57 tff(11757,plain,((~b(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11758,plain,
% 2.33/2.57 (~b(s(s(s(z))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11757, 97])).
% 2.33/2.57 tff(11759,plain,
% 2.33/2.57 (r(s(s(s(z))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[595, 11758])).
% 2.33/2.57 tff(11760,plain,
% 2.33/2.57 (~r(z, s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[2611, 11759, 97])).
% 2.33/2.57 tff(11761,plain,
% 2.33/2.57 (b(z, s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[295, 11760])).
% 2.33/2.57 tff(11762,plain,
% 2.33/2.57 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[2517, 11759, 11733])).
% 2.33/2.57 tff(11763,plain,
% 2.33/2.57 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[338, 11762])).
% 2.33/2.57 tff(11764,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[6271, 11763, 11761, 11666, 11714, 10480])).
% 2.33/2.57 tff(11765,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11766,plain,
% 2.33/2.57 (b(z, s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[117, 11765])).
% 2.33/2.57 tff(11767,plain,
% 2.33/2.57 (~r(z, s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11690, 1])).
% 2.33/2.57 tff(11768,plain,
% 2.33/2.57 (b(z, s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[524, 11767])).
% 2.33/2.57 tff(11769,plain,
% 2.33/2.57 (~b(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[8929, 11768, 10477, 11766])).
% 2.33/2.57 tff(11770,plain,
% 2.33/2.57 (r(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[175, 11769])).
% 2.33/2.57 tff(11771,plain,
% 2.33/2.57 ((~b(z, s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[9769, 162, 11766, 11635, 10477, 6735])).
% 2.33/2.57 tff(11772,plain,
% 2.33/2.57 (~b(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11771, 11768])).
% 2.33/2.57 tff(11773,plain,
% 2.33/2.57 (r(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[493, 11772])).
% 2.33/2.57 tff(11774,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[1966, 11773, 11770, 1])).
% 2.33/2.57 tff(11775,plain,(~r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11776,plain,
% 2.33/2.57 (b(z, s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[295, 11775])).
% 2.33/2.57 tff(11777,plain,
% 2.33/2.57 ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[6721, 162, 11766, 9847, 11635, 10477])).
% 2.33/2.57 tff(11778,plain,
% 2.33/2.57 (~b(s(s(z)), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11777, 10616])).
% 2.33/2.57 tff(11779,plain,
% 2.33/2.57 (r(s(s(z)), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[245, 11778])).
% 2.33/2.57 tff(11780,plain,
% 2.33/2.57 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[10518, 177, 9847, 10477])).
% 2.33/2.57 tff(11781,plain,
% 2.33/2.57 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[216, 11780])).
% 2.33/2.57 tff(11782,plain,
% 2.33/2.57 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11544, 162, 11766, 9847, 10477, 6735])).
% 2.33/2.57 tff(11783,plain,
% 2.33/2.57 (~b(z, s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11782, 177])).
% 2.33/2.57 tff(11784,plain,
% 2.33/2.57 (r(z, s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[524, 11783])).
% 2.33/2.57 tff(11785,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[6166, 11784, 11781, 495])).
% 2.33/2.57 tff(11786,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11787,plain,
% 2.33/2.57 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11786, 495])).
% 2.33/2.57 tff(11788,plain,
% 2.33/2.57 (r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[191, 11787])).
% 2.33/2.57 tff(11789,plain,
% 2.33/2.57 (~r(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[503, 11788, 495])).
% 2.33/2.57 tff(11790,plain,
% 2.33/2.57 (b(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[175, 11789])).
% 2.33/2.57 tff(11791,plain,
% 2.33/2.57 (~b(z, s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[8929, 11790, 10477, 11766])).
% 2.33/2.57 tff(11792,plain,
% 2.33/2.57 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[2517, 11788, 10589])).
% 2.33/2.57 tff(11793,plain,
% 2.33/2.57 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[338, 11792])).
% 2.33/2.57 tff(11794,plain,
% 2.33/2.57 (~b(s(s(z)), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11777, 11793])).
% 2.33/2.57 tff(11795,plain,
% 2.33/2.57 (r(s(s(z)), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[245, 11794])).
% 2.33/2.57 tff(11796,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11525, 11795, 11791, 11665, 11766, 10588, 11788, 11776, 11790])).
% 2.33/2.57 tff(11797,plain,((~r(z, s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11798,plain,
% 2.33/2.57 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11797, 10588])).
% 2.33/2.57 tff(11799,plain,
% 2.33/2.57 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[83, 11798])).
% 2.33/2.57 tff(11800,plain,
% 2.33/2.57 (~b(s(s(s(s(elem!1)))), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[6271, 10616, 11666, 11776, 11799])).
% 2.33/2.57 tff(11801,plain,
% 2.33/2.57 (r(s(s(s(s(elem!1)))), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[95, 11800])).
% 2.33/2.57 tff(11802,plain,
% 2.33/2.57 (~r(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[2561, 11801, 193])).
% 2.33/2.57 tff(11803,plain,
% 2.33/2.57 (b(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[175, 11802])).
% 2.33/2.57 tff(11804,plain,
% 2.33/2.57 (~b(z, s(s(z)))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[8929, 11803, 10477, 11766])).
% 2.33/2.57 tff(11805,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11525, 11804, 11803, 11665, 11766, 10588, 193, 11776, 11779])).
% 2.33/2.57 tff(11806,plain,((~r(s(z), s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11807,plain,
% 2.33/2.57 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11806, 10588])).
% 2.33/2.57 tff(11808,plain,
% 2.33/2.57 (b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[191, 11807])).
% 2.33/2.57 tff(11809,plain,
% 2.33/2.57 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[10481, 11808, 9847, 10477])).
% 2.33/2.57 tff(11810,plain,
% 2.33/2.57 (r(s(s(s(s(elem!1)))), s(z))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[149, 11809])).
% 2.33/2.57 tff(11811,plain,
% 2.33/2.57 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[2549, 11810, 10589])).
% 2.33/2.57 tff(11812,plain,
% 2.33/2.57 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[360, 11811])).
% 2.33/2.57 tff(11813,plain,
% 2.33/2.57 (~r(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[8395, 11810, 11666, 11776, 10589, 11799])).
% 2.33/2.57 tff(11814,plain,
% 2.33/2.57 (b(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[175, 11813])).
% 2.33/2.57 tff(11815,plain,
% 2.33/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(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(z)))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(11816,plain,
% 2.33/2.57 (((~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(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(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(z)))))),
% 2.33/2.57 inference(rewrite,[status(thm)],[])).
% 2.33/2.57 tff(11817,plain,
% 2.33/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(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(z))))))),
% 2.33/2.57 inference(monotonicity,[status(thm)],[11816])).
% 2.33/2.57 tff(11818,plain,
% 2.33/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(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(z)))))),
% 2.33/2.57 inference(transitivity,[status(thm)],[11817, 11815])).
% 2.33/2.57 tff(11819,plain,
% 2.33/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(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(s(elem!1)))))) | (~b(s(z), z)))),
% 2.33/2.57 inference(quant_inst,[status(thm)],[])).
% 2.33/2.57 tff(11820,plain,
% 2.33/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.33/2.57 inference(modus_ponens,[status(thm)],[11819, 11818])).
% 2.33/2.57 tff(11821,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[11820, 162, 11814, 9847, 11808, 11799, 11812, 11635])).
% 2.33/2.57 tff(11822,plain,(b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.33/2.57 tff(11823,plain,
% 2.33/2.57 (~b(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[5513, 11822, 11666, 11766, 11776])).
% 2.33/2.57 tff(11824,plain,
% 2.33/2.57 (r(s(z), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[175, 11823])).
% 2.33/2.57 tff(11825,plain,
% 2.33/2.57 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[10033, 162, 11766, 9847, 6735, 11666, 11822])).
% 2.33/2.57 tff(11826,plain,
% 2.33/2.57 (r(s(z), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[191, 11825])).
% 2.33/2.57 tff(11827,plain,
% 2.33/2.57 (~r(z, s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[503, 11826, 11824])).
% 2.33/2.57 tff(11828,plain,
% 2.33/2.57 (b(z, s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[83, 11827])).
% 2.33/2.57 tff(11829,plain,
% 2.33/2.57 (~b(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[8626, 11822, 11635, 11666, 11766])).
% 2.33/2.57 tff(11830,plain,
% 2.33/2.57 (r(s(z), s(s(s(z))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[493, 11829])).
% 2.33/2.57 tff(11831,plain,
% 2.33/2.57 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[9940, 11826, 11830])).
% 2.33/2.57 tff(11832,plain,
% 2.33/2.57 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[338, 11831])).
% 2.33/2.57 tff(11833,plain,
% 2.33/2.57 (~r(s(s(s(s(elem!1)))), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[2561, 11826, 11824])).
% 2.33/2.57 tff(11834,plain,
% 2.33/2.57 (b(s(s(s(s(elem!1)))), z)),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[95, 11833])).
% 2.33/2.57 tff(11835,plain,
% 2.33/2.57 ($false),
% 2.33/2.57 inference(unit_resolution,[status(thm)],[6271, 11834, 11832, 11666, 11776, 11828])).
% 2.33/2.57 % SZS output end Proof
% 2.33/2.58 % E exiting
%------------------------------------------------------------------------------