%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA131-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n024.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 06:33:46 PM UTC 2026
% Result : Unsatisfiable 1.14s 1.30s
% Output : Proof 2.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRA131-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : run_E %s %d THM
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 17:43:58 EDT 2026
% 0.06/0.24 % CPUTime :
% 1.14/1.30 % SZS status Unsatisfiable
% 1.14/1.30 % SZS output start Proof
% 1.14/1.30 tff(b_type, type, (
% 1.14/1.30 b: ( $i * $i ) > $o)).
% 1.14/1.30 tff(z_type, type, (
% 1.14/1.30 z: $i)).
% 1.14/1.30 tff(s_type, type, (
% 1.14/1.30 s: $i > $i)).
% 1.14/1.30 tff(elem_1_type, type, (
% 1.14/1.30 elem_1: $i)).
% 1.14/1.30 tff(r_type, type, (
% 1.14/1.30 r: ( $i * $i ) > $o)).
% 1.14/1.30 tff(inj_0_type, type, (
% 1.14/1.30 inj_0: $i > $i)).
% 1.14/1.30 tff(1,assumption,(r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.30 tff(2,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.30 tff(3,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.14/1.30 tff(4,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.30 tff(5,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.30 tff(6,plain,
% 1.14/1.30 (s(s(s(s(s(z))))) = z),
% 1.14/1.30 inference(symmetry,[status(thm)],[5])).
% 1.14/1.30 tff(7,plain,
% 1.14/1.30 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.14/1.30 inference(bind,[status(th)],[])).
% 1.14/1.30 tff(8,plain,
% 1.14/1.30 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.30 inference(quant_intro,[status(thm)],[7])).
% 1.14/1.30 tff(9,plain,
% 1.14/1.30 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(10,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.14/1.30 tff(11,plain,
% 1.14/1.30 (![X: $i] : (~(s(X) = z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[10, 9])).
% 1.14/1.30 tff(12,plain,(
% 1.14/1.30 ![X: $i] : (~(s(X) = z))),
% 1.14/1.30 inference(skolemize,[status(sab)],[11])).
% 1.14/1.30 tff(13,plain,
% 1.14/1.30 (![X: $i] : (~(s(X) = z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.14/1.30 tff(14,plain,
% 1.14/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(15,plain,
% 1.14/1.30 (~(s(s(s(s(s(z))))) = z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[14, 13])).
% 1.14/1.30 tff(16,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[15, 6])).
% 1.14/1.30 tff(17,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(18,assumption,(b(z, s(z))), introduced(assumption)).
% 1.14/1.30 tff(19,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.14/1.30 tff(20,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.14/1.30 tff(21,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.30 tff(22,plain,
% 1.14/1.30 (^[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))))),
% 1.14/1.30 inference(bind,[status(th)],[])).
% 1.14/1.30 tff(23,plain,
% 1.14/1.30 (![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)))),
% 1.14/1.30 inference(quant_intro,[status(thm)],[22])).
% 1.14/1.30 tff(24,plain,
% 1.14/1.30 (![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)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(25,plain,
% 1.14/1.30 (^[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)))))),
% 1.14/1.30 inference(bind,[status(th)],[])).
% 1.14/1.30 tff(26,plain,
% 1.14/1.30 (![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)))),
% 1.14/1.30 inference(quant_intro,[status(thm)],[25])).
% 1.14/1.30 tff(27,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')).
% 1.14/1.30 tff(28,plain,
% 1.14/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.14/1.30 tff(29,plain,
% 1.14/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.14/1.30 tff(30,plain,(
% 1.14/1.30 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.14/1.30 inference(skolemize,[status(sab)],[29])).
% 1.14/1.30 tff(31,plain,
% 1.14/1.30 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.14/1.30 tff(32,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), 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(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(33,plain,
% 1.14/1.30 (((~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(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(34,plain,
% 1.14/1.30 (((~![X0: $i, 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(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[33])).
% 1.14/1.30 tff(35,plain,
% 1.14/1.30 (((~![X0: $i, 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(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[34, 32])).
% 1.14/1.30 tff(36,plain,
% 1.14/1.30 ((~![X0: $i, 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))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(37,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.14/1.30 tff(38,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[37, 31, 3, 21, 1])).
% 1.14/1.30 tff(39,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(40,plain,
% 1.14/1.30 (~r(s(s(s(z))), s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[39, 1, 21])).
% 1.14/1.30 tff(41,plain,
% 1.14/1.30 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(42,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(43,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(44,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.14/1.30 tff(45,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.14/1.30 tff(46,plain,(
% 1.14/1.30 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.30 inference(skolemize,[status(sab)],[45])).
% 1.14/1.30 tff(47,plain,
% 1.14/1.30 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[46, 42])).
% 1.14/1.30 tff(48,plain,
% 1.14/1.30 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[47, 41])).
% 1.14/1.30 tff(49,plain,
% 1.14/1.30 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(50,plain,
% 1.14/1.30 (inj_0(s(z)) = z),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.14/1.30 tff(51,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.14/1.30 tff(52,plain,
% 1.14/1.30 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[51])).
% 1.14/1.30 tff(53,plain,
% 1.14/1.30 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.14/1.30 inference(symmetry,[status(thm)],[52])).
% 1.14/1.30 tff(54,plain,
% 1.14/1.30 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(55,plain,
% 1.14/1.30 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[54, 48])).
% 1.14/1.30 tff(56,plain,
% 1.14/1.30 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.30 inference(symmetry,[status(thm)],[55])).
% 1.14/1.30 tff(57,plain,
% 1.14/1.30 (s(s(z)) = z),
% 1.14/1.30 inference(transitivity,[status(thm)],[56, 53, 50])).
% 1.14/1.30 tff(58,plain,
% 1.14/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(59,plain,
% 1.14/1.30 (~(s(s(z)) = z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[58, 13])).
% 1.14/1.30 tff(60,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[59, 57])).
% 1.14/1.30 tff(61,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(62,plain,
% 1.14/1.30 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.14/1.30 inference(commutativity,[status(thm)],[])).
% 1.14/1.30 tff(63,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.14/1.30 tff(64,plain,
% 1.14/1.30 (s(z) = s(s(s(z)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.14/1.30 tff(65,assumption,(~(s(z) = s(s(s(z))))), introduced(assumption)).
% 1.14/1.30 tff(66,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[65, 64])).
% 1.14/1.30 tff(67,plain,((~(s(s(s(z))) = s(z))) | (s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(68,plain,
% 1.14/1.30 (~(s(s(s(z))) = s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[67, 61])).
% 1.14/1.30 tff(69,plain,
% 1.14/1.30 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.30 inference(bind,[status(th)],[])).
% 1.14/1.30 tff(70,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.30 inference(quant_intro,[status(thm)],[69])).
% 1.14/1.30 tff(71,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(72,plain,
% 1.14/1.30 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.30 inference(bind,[status(th)],[])).
% 1.14/1.30 tff(73,plain,
% 1.14/1.30 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.30 inference(quant_intro,[status(thm)],[72])).
% 1.14/1.30 tff(74,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.14/1.30 tff(75,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.14/1.30 tff(76,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.14/1.30 tff(77,plain,(
% 1.14/1.30 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.30 inference(skolemize,[status(sab)],[76])).
% 1.14/1.30 tff(78,plain,
% 1.14/1.30 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.14/1.30 tff(79,plain,
% 1.14/1.30 (((~![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)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(80,plain,
% 1.14/1.30 ((~![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)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(81,plain,
% 1.14/1.30 ((~![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))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.14/1.30 tff(82,plain,
% 1.14/1.30 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[81, 78])).
% 1.14/1.30 tff(83,plain,
% 1.14/1.30 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[82, 68])).
% 1.14/1.30 tff(84,plain,
% 1.14/1.30 (b(s(s(s(z))), s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[83, 40])).
% 1.14/1.30 tff(85,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.14/1.30 tff(86,plain,
% 1.14/1.30 (((~![X0: $i, 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(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(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(87,plain,
% 1.14/1.30 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(88,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[87])).
% 1.14/1.30 tff(89,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[88, 86])).
% 1.14/1.30 tff(90,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(91,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.14/1.30 tff(92,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[91, 31, 85, 21, 1])).
% 1.14/1.30 tff(93,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(94,plain,
% 1.14/1.30 (~r(s(z), s(s(s(z))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[93, 1, 21])).
% 1.14/1.30 tff(95,plain,
% 1.14/1.30 (((~![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)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(96,plain,
% 1.14/1.30 ((~![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)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(97,plain,
% 1.14/1.30 ((~![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))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.14/1.30 tff(98,plain,
% 1.14/1.30 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[97, 78])).
% 1.14/1.30 tff(99,plain,
% 1.14/1.30 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[98, 61])).
% 1.14/1.30 tff(100,plain,
% 1.14/1.30 (b(s(z), s(s(s(z))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[99, 94])).
% 1.14/1.30 tff(101,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.14/1.30 tff(102,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.14/1.30 tff(103,plain,
% 1.14/1.30 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 1.14/1.30 inference(bind,[status(th)],[])).
% 1.14/1.30 tff(104,plain,
% 1.14/1.30 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.14/1.30 inference(quant_intro,[status(thm)],[103])).
% 1.14/1.30 tff(105,plain,
% 1.14/1.30 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(106,plain,
% 1.14/1.30 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~b(X0, X1)) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) <=> (((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X4))))), rewrite((((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) <=> (((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))))), rewrite((((~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> (((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 1.14/1.30 inference(bind,[status(th)],[])).
% 1.14/1.30 tff(107,plain,
% 1.14/1.30 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.14/1.30 inference(quant_intro,[status(thm)],[106])).
% 1.14/1.30 tff(108,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.14/1.30 tff(109,plain,
% 1.14/1.30 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.14/1.30 tff(110,plain,
% 1.14/1.30 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[109, 105])).
% 1.14/1.30 tff(111,plain,(
% 1.14/1.30 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.14/1.30 inference(skolemize,[status(sab)],[110])).
% 1.14/1.30 tff(112,plain,
% 1.14/1.30 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[111, 104])).
% 1.14/1.30 tff(113,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(114,plain,
% 1.14/1.30 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(115,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[114])).
% 1.14/1.30 tff(116,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[115, 113])).
% 1.14/1.31 tff(117,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(118,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.14/1.31 tff(119,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[118, 112, 102, 101, 19, 4])).
% 1.14/1.31 tff(120,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(121,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[120, 100, 84, 4, 19])).
% 1.14/1.31 tff(122,plain,((~r(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(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(123,plain,
% 1.14/1.31 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[122, 21, 19, 4])).
% 1.14/1.31 tff(124,plain,
% 1.14/1.31 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(commutativity,[status(thm)],[])).
% 1.14/1.31 tff(125,plain,
% 1.14/1.31 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[124])).
% 1.14/1.31 tff(126,plain,
% 1.14/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(127,plain,
% 1.14/1.31 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[126, 48])).
% 1.14/1.31 tff(128,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 1.14/1.31 tff(129,plain,
% 1.14/1.31 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(z))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[128])).
% 1.14/1.31 tff(130,plain,
% 1.14/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(131,plain,
% 1.14/1.31 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[130, 48])).
% 1.14/1.31 tff(132,plain,
% 1.14/1.31 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[131])).
% 1.14/1.31 tff(133,plain,
% 1.14/1.31 (s(s(s(elem!1))) = s(s(z))),
% 1.14/1.31 inference(transitivity,[status(thm)],[132, 129, 55])).
% 1.14/1.31 tff(134,plain,
% 1.14/1.31 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[133])).
% 1.14/1.31 tff(135,plain,
% 1.14/1.31 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[134])).
% 1.14/1.31 tff(136,plain,
% 1.14/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(137,plain,
% 1.14/1.31 (inj_0(s(s(z))) = s(z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[136, 48])).
% 1.14/1.31 tff(138,plain,
% 1.14/1.31 (s(z) = inj_0(s(s(z)))),
% 1.14/1.31 inference(symmetry,[status(thm)],[137])).
% 1.14/1.31 tff(139,plain,
% 1.14/1.31 (s(z) = s(s(elem!1))),
% 1.14/1.31 inference(transitivity,[status(thm)],[138, 135, 127])).
% 1.14/1.31 tff(140,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.14/1.31 tff(141,plain,
% 1.14/1.31 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[140])).
% 1.14/1.31 tff(142,plain,
% 1.14/1.31 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.14/1.31 inference(symmetry,[status(thm)],[141])).
% 1.14/1.31 tff(143,plain,
% 1.14/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(144,plain,
% 1.14/1.31 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[143, 48])).
% 1.14/1.31 tff(145,plain,
% 1.14/1.31 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.14/1.31 inference(symmetry,[status(thm)],[144])).
% 1.14/1.31 tff(146,plain,
% 1.14/1.31 (s(elem!1) = z),
% 1.14/1.31 inference(transitivity,[status(thm)],[145, 142, 50])).
% 1.14/1.31 tff(147,plain,
% 1.14/1.31 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(148,plain,
% 1.14/1.31 (~(s(elem!1) = z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[147, 13])).
% 1.14/1.31 tff(149,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[148, 146])).
% 1.14/1.31 tff(150,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(151,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[150, 139])).
% 1.14/1.31 tff(152,plain,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(153,plain,
% 1.14/1.31 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[152, 125])).
% 1.14/1.31 tff(154,assumption,(~r(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.31 tff(155,assumption,(~b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.31 tff(156,plain,
% 1.14/1.31 (((~![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))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(157,plain,
% 1.14/1.31 ((~![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))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(158,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.14/1.31 tff(159,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[158, 78, 155, 154, 153])).
% 1.14/1.31 tff(160,plain,(b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(161,plain,
% 1.14/1.31 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[160, 123])).
% 1.14/1.31 tff(162,assumption,(r(z, s(z))), introduced(assumption)).
% 1.14/1.31 tff(163,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(164,plain,
% 1.14/1.31 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(165,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[164])).
% 1.14/1.31 tff(166,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[165, 163])).
% 1.14/1.31 tff(167,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(168,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.14/1.31 tff(169,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[168, 31, 85, 20, 162])).
% 1.14/1.31 tff(170,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(171,plain,
% 1.14/1.31 (~r(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[170, 85, 20])).
% 1.14/1.31 tff(172,plain,
% 1.14/1.31 ((z = s(z)) <=> (s(z) = z)),
% 1.14/1.31 inference(commutativity,[status(thm)],[])).
% 1.14/1.31 tff(173,plain,
% 1.14/1.31 ((s(z) = z) <=> (z = s(z))),
% 1.14/1.31 inference(symmetry,[status(thm)],[172])).
% 1.14/1.31 tff(174,plain,
% 1.14/1.31 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[173])).
% 1.14/1.31 tff(175,plain,
% 1.14/1.31 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(176,plain,
% 1.14/1.31 (~(s(z) = z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[175, 13])).
% 1.14/1.31 tff(177,plain,
% 1.14/1.31 (~(z = s(z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[176, 174])).
% 1.14/1.31 tff(178,plain,
% 1.14/1.31 (((~![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)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(179,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(180,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.14/1.31 tff(181,plain,
% 1.14/1.31 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[180, 78])).
% 1.14/1.31 tff(182,plain,
% 1.14/1.31 (b(z, s(z)) | r(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[181, 177])).
% 1.14/1.31 tff(183,plain,
% 1.14/1.31 (b(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[182, 171])).
% 1.14/1.31 tff(184,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.31 tff(185,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(z))))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(186,plain,
% 1.14/1.31 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(187,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[186])).
% 1.14/1.31 tff(188,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[187, 185])).
% 1.14/1.31 tff(189,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(190,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.14/1.31 tff(191,plain,
% 1.14/1.31 (~b(z, s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[190, 112, 18, 19, 2, 184])).
% 1.14/1.31 tff(192,plain,
% 1.14/1.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(193,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(194,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.14/1.31 tff(195,plain,
% 1.14/1.31 (r(z, s(s(s(s(s(z))))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[194, 78, 191, 17])).
% 1.14/1.31 tff(196,assumption,(b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.31 tff(197,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(198,plain,
% 1.14/1.31 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(199,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[198])).
% 1.14/1.31 tff(200,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[199, 197])).
% 1.14/1.31 tff(201,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(s(z))))), s(s(s(s(elem!1)))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(202,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.14/1.31 tff(203,plain,
% 1.14/1.31 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[202, 112, 4, 196, 184])).
% 1.14/1.31 tff(204,assumption,(~r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.31 tff(205,plain,
% 1.14/1.31 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.14/1.31 inference(commutativity,[status(thm)],[])).
% 1.14/1.31 tff(206,plain,
% 1.14/1.31 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[205])).
% 1.14/1.31 tff(207,plain,
% 1.14/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(208,plain,
% 1.14/1.31 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[207, 48])).
% 1.14/1.31 tff(209,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.31 tff(210,plain,
% 1.14/1.31 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[209])).
% 1.14/1.31 tff(211,plain,
% 1.14/1.31 (s(s(z)) = s(s(s(s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[56, 210, 208])).
% 1.14/1.31 tff(212,plain,
% 1.14/1.31 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[211])).
% 1.14/1.31 tff(213,plain,
% 1.14/1.31 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.14/1.31 inference(symmetry,[status(thm)],[212])).
% 1.14/1.31 tff(214,plain,
% 1.14/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(215,plain,
% 1.14/1.31 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[214, 48])).
% 1.14/1.31 tff(216,plain,
% 1.14/1.31 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.31 inference(symmetry,[status(thm)],[215])).
% 1.14/1.31 tff(217,plain,
% 1.14/1.31 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 1.14/1.31 inference(symmetry,[status(thm)],[209])).
% 1.14/1.31 tff(218,plain,
% 1.14/1.31 (s(s(s(s(s(z))))) = s(z)),
% 1.14/1.31 inference(transitivity,[status(thm)],[217, 216, 213, 137])).
% 1.14/1.31 tff(219,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.14/1.31 tff(220,plain,
% 1.14/1.31 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[219])).
% 1.14/1.32 tff(221,plain,
% 1.14/1.32 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[208])).
% 1.14/1.32 tff(222,plain,
% 1.14/1.32 (s(s(s(s(z)))) = z),
% 1.14/1.32 inference(transitivity,[status(thm)],[221, 220, 50])).
% 1.14/1.32 tff(223,plain,
% 1.14/1.32 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(224,plain,
% 1.14/1.32 (~(s(s(s(s(z)))) = z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[223, 13])).
% 1.14/1.32 tff(225,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[224, 222])).
% 1.14/1.32 tff(226,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(227,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[226, 218])).
% 1.14/1.32 tff(228,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(229,plain,
% 1.14/1.32 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[228, 206])).
% 1.14/1.32 tff(230,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.32 tff(231,plain,
% 1.14/1.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(232,plain,
% 1.14/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(233,plain,
% 1.14/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[232, 231])).
% 1.14/1.32 tff(234,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[233, 78, 230, 229, 204])).
% 1.14/1.32 tff(235,plain,(r(s(s(s(s(s(z))))), s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(236,plain,
% 1.14/1.32 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[235, 203])).
% 1.14/1.32 tff(237,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(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(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(238,plain,
% 1.14/1.32 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(239,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[238])).
% 1.14/1.32 tff(240,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[239, 237])).
% 1.14/1.32 tff(241,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(242,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.14/1.32 tff(243,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[242, 31, 20, 236, 195])).
% 1.14/1.32 tff(244,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, 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(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(245,plain,
% 1.14/1.32 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[244, 183, 4, 161, 20, 19, 2])).
% 1.14/1.32 tff(246,plain,
% 1.14/1.32 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(247,plain,
% 1.14/1.32 (inj_0(s(elem!1)) = elem!1),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[246, 48])).
% 1.14/1.32 tff(248,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.32 tff(249,assumption,(r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.32 tff(250,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.32 tff(251,plain,
% 1.14/1.32 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[250])).
% 1.14/1.32 tff(252,plain,
% 1.14/1.32 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[251])).
% 1.14/1.32 tff(253,plain,
% 1.14/1.32 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[127])).
% 1.14/1.32 tff(254,plain,
% 1.14/1.32 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[253, 252, 131, 251])).
% 1.14/1.32 tff(255,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[248, 254])).
% 1.14/1.32 tff(256,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,[]))).
% 1.14/1.32 tff(257,plain,
% 1.14/1.32 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[256, 248])).
% 1.14/1.32 tff(258,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.32 tff(259,plain,
% 1.14/1.32 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[258])).
% 1.14/1.32 tff(260,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[259])).
% 1.14/1.32 tff(261,plain,
% 1.14/1.32 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(262,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[261, 48])).
% 1.14/1.32 tff(263,plain,
% 1.14/1.32 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[262])).
% 1.14/1.32 tff(264,plain,
% 1.14/1.32 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[263, 260, 131])).
% 1.14/1.32 tff(265,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.32 tff(266,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[265, 264])).
% 1.14/1.32 tff(267,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,[]))).
% 1.14/1.32 tff(268,plain,
% 1.14/1.32 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[267, 257])).
% 1.14/1.32 tff(269,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.32 tff(270,plain,
% 1.14/1.32 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[269])).
% 1.14/1.32 tff(271,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.32 tff(272,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[271, 270])).
% 1.14/1.32 tff(273,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,[]))).
% 1.14/1.32 tff(274,plain,
% 1.14/1.32 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[273, 268])).
% 1.14/1.32 tff(275,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.32 tff(276,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.32 tff(277,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(278,plain,
% 1.14/1.32 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(s(elem!1))))), 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))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(279,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[278])).
% 1.14/1.32 tff(280,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[279, 277])).
% 1.14/1.32 tff(281,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(282,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.14/1.32 tff(283,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[282, 31, 276, 249, 275])).
% 1.14/1.32 tff(284,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(285,plain,
% 1.14/1.32 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[284, 275, 249])).
% 1.14/1.32 tff(286,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(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(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(287,plain,
% 1.14/1.32 (((~r(s(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(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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(288,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(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(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[287])).
% 1.14/1.32 tff(289,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(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(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[288, 286])).
% 1.14/1.32 tff(290,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(291,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.14/1.32 tff(292,plain,
% 1.14/1.32 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[291, 31, 249, 275])).
% 1.14/1.32 tff(293,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.32 tff(294,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.32 tff(295,plain,
% 1.14/1.32 (((~![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)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(296,plain,
% 1.14/1.32 ((~![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)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(297,plain,
% 1.14/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.14/1.32 tff(298,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[297, 78, 271, 294, 293])).
% 1.14/1.32 tff(299,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,[]))).
% 1.14/1.32 tff(300,plain,
% 1.14/1.32 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[299, 292, 271])).
% 1.14/1.32 tff(301,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.32 tff(302,assumption,(r(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.32 tff(303,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(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(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(304,plain,
% 1.14/1.32 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(305,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(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(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[304])).
% 1.14/1.32 tff(306,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(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(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[305, 303])).
% 1.14/1.32 tff(307,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(308,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[307, 306])).
% 1.14/1.32 tff(309,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[308, 31, 20, 302, 275])).
% 1.14/1.32 tff(310,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(311,plain,
% 1.14/1.32 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[310, 20, 275])).
% 1.14/1.32 tff(312,plain,
% 1.14/1.32 ((z = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = z)),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(313,plain,
% 1.14/1.32 ((s(s(s(s(s(elem!1))))) = z) <=> (z = s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[312])).
% 1.14/1.32 tff(314,plain,
% 1.14/1.32 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(z = s(s(s(s(s(elem!1)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[313])).
% 1.14/1.32 tff(315,plain,
% 1.14/1.32 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(316,plain,
% 1.14/1.32 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[315, 13])).
% 1.14/1.32 tff(317,plain,
% 1.14/1.32 (~(z = s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[316, 314])).
% 1.14/1.32 tff(318,plain,
% 1.14/1.32 (((~![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)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(319,plain,
% 1.14/1.32 ((~![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)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(320,plain,
% 1.14/1.32 ((~![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))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.14/1.32 tff(321,plain,
% 1.14/1.32 ((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))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[320, 78])).
% 1.14/1.32 tff(322,plain,
% 1.14/1.32 (b(z, s(s(s(s(s(elem!1)))))) | r(z, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[321, 317])).
% 1.14/1.32 tff(323,plain,
% 1.14/1.32 (b(z, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[322, 311])).
% 1.14/1.32 tff(324,plain,
% 1.14/1.32 ((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))))))),
% 1.14/1.32 inference(commutativity,[status(thm)],[])).
% 1.14/1.32 tff(325,plain,
% 1.14/1.32 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[324])).
% 1.14/1.32 tff(326,plain,
% 1.14/1.32 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[325])).
% 1.14/1.32 tff(327,plain,
% 1.14/1.32 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[271, 326])).
% 1.14/1.32 tff(328,plain,
% 1.14/1.32 (((~![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))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(329,plain,
% 1.14/1.32 ((~![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))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(330,plain,
% 1.14/1.32 ((~![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)))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[329, 328])).
% 1.14/1.32 tff(331,plain,
% 1.14/1.32 ((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)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[330, 78, 301])).
% 1.14/1.32 tff(332,plain,
% 1.14/1.32 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[331, 327])).
% 1.14/1.32 tff(333,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.32 tff(334,assumption,(b(z, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.32 tff(335,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(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(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(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(s(s(s(elem!1))))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(336,plain,
% 1.14/1.33 (((~b(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))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(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(s(s(s(elem!1))))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(337,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(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(s(s(s(elem!1)))))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[336])).
% 1.14/1.33 tff(338,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(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(s(s(s(elem!1))))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[337, 335])).
% 1.14/1.33 tff(339,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(z, s(s(s(s(s(elem!1))))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(340,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.14/1.33 tff(341,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[340, 112, 2, 334, 333, 332])).
% 1.14/1.33 tff(342,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | r(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,[]))).
% 1.14/1.33 tff(343,plain,
% 1.14/1.33 (~b(z, s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[342, 323, 301, 271, 300])).
% 1.14/1.33 tff(344,assumption,(z = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.33 tff(345,plain,
% 1.14/1.33 (s(s(s(s(elem!1)))) = z),
% 1.14/1.33 inference(symmetry,[status(thm)],[344])).
% 1.14/1.33 tff(346,plain,
% 1.14/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(347,plain,
% 1.14/1.33 (~(s(s(s(s(elem!1)))) = z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[346, 13])).
% 1.14/1.33 tff(348,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[347, 345])).
% 1.14/1.33 tff(349,plain,(~(z = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(350,assumption,(~r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.33 tff(351,assumption,(~b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.33 tff(352,plain,
% 1.14/1.33 (((~![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))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(353,plain,
% 1.14/1.33 ((~![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))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(354,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.14/1.33 tff(355,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[354, 78, 351, 350, 349])).
% 1.14/1.33 tff(356,plain,(r(z, s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(357,plain,
% 1.14/1.33 (r(z, s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[356, 343])).
% 1.14/1.33 tff(358,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(359,plain,
% 1.14/1.33 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(360,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[359])).
% 1.14/1.33 tff(361,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[360, 358])).
% 1.14/1.33 tff(362,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(363,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.14/1.33 tff(364,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[363, 31, 20, 357, 249])).
% 1.14/1.33 tff(365,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | r(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(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(366,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[365, 285, 275, 20, 271, 249])).
% 1.14/1.33 tff(367,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (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,[]))).
% 1.14/1.33 tff(368,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[367, 20, 268, 249])).
% 1.14/1.33 tff(369,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.33 tff(370,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.33 tff(371,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(z)))), introduced(assumption)).
% 1.14/1.33 tff(372,plain,
% 1.14/1.33 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(z))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[371])).
% 1.14/1.33 tff(373,plain,
% 1.14/1.33 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.14/1.33 inference(transitivity,[status(thm)],[263, 372, 55])).
% 1.14/1.33 tff(374,plain,
% 1.14/1.33 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[373])).
% 1.14/1.33 tff(375,plain,
% 1.14/1.33 (s(s(s(elem!1))) = s(z)),
% 1.14/1.33 inference(transitivity,[status(thm)],[132, 374, 137])).
% 1.14/1.33 tff(376,plain,
% 1.14/1.33 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[375])).
% 1.14/1.33 tff(377,plain,
% 1.14/1.33 (s(s(elem!1)) = z),
% 1.14/1.33 inference(transitivity,[status(thm)],[253, 376, 50])).
% 1.14/1.33 tff(378,plain,
% 1.14/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(379,plain,
% 1.14/1.33 (~(s(s(elem!1)) = z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[378, 13])).
% 1.14/1.33 tff(380,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[379, 377])).
% 1.14/1.33 tff(381,plain,(~(s(s(s(s(s(elem!1))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(382,plain,
% 1.14/1.33 (((~![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)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(383,plain,
% 1.14/1.33 ((~![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)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(384,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(z)))) | b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.14/1.33 tff(385,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[384, 78, 381, 370, 369])).
% 1.14/1.33 tff(386,plain,(b(s(s(s(s(s(elem!1))))), s(s(s(z)))) | r(s(s(s(s(s(elem!1))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(387,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[386, 368])).
% 1.14/1.33 tff(388,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(389,plain,
% 1.14/1.33 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(390,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[389])).
% 1.14/1.33 tff(391,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[390, 388])).
% 1.14/1.33 tff(392,plain,
% 1.14/1.33 ((~![X0: $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)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(393,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.14/1.33 tff(394,plain,
% 1.14/1.33 (~r(s(s(s(s(elem!1)))), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[393, 31, 20, 249])).
% 1.14/1.33 tff(395,plain,
% 1.14/1.33 (((~![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))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(396,plain,
% 1.14/1.33 ((~![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))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(397,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.14/1.33 tff(398,plain,
% 1.14/1.33 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[397, 78, 347])).
% 1.14/1.33 tff(399,plain,
% 1.14/1.33 (b(s(s(s(s(elem!1)))), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[398, 394])).
% 1.14/1.33 tff(400,plain,
% 1.14/1.33 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[160, 155])).
% 1.14/1.33 tff(401,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.33 tff(402,assumption,(~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.33 tff(403,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[330, 78, 301, 402, 401])).
% 1.14/1.33 tff(404,plain,(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))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(405,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[404, 301, 274])).
% 1.14/1.33 tff(406,assumption,(b(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.33 tff(407,plain,
% 1.14/1.33 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[39, 3, 1])).
% 1.14/1.33 tff(408,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.14/1.33 tff(409,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(410,plain,
% 1.14/1.33 (((~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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(411,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[410])).
% 1.14/1.33 tff(412,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[411, 409])).
% 1.14/1.33 tff(413,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(414,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[413, 412])).
% 1.14/1.33 tff(415,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[414, 31, 3, 408, 1])).
% 1.14/1.33 tff(416,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(417,plain,
% 1.14/1.33 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[416, 3, 1])).
% 1.14/1.33 tff(418,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.14/1.33 tff(419,plain,
% 1.14/1.33 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[418])).
% 1.14/1.33 tff(420,plain,
% 1.14/1.33 (s(s(s(elem!1))) = z),
% 1.14/1.33 inference(transitivity,[status(thm)],[132, 419, 50])).
% 1.14/1.33 tff(421,plain,
% 1.14/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(422,plain,
% 1.14/1.33 (~(s(s(s(elem!1))) = z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[421, 13])).
% 1.14/1.33 tff(423,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[422, 420])).
% 1.14/1.33 tff(424,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(425,plain,
% 1.14/1.33 (((~![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)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(426,plain,
% 1.14/1.33 ((~![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)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(427,plain,
% 1.14/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.14/1.33 tff(428,plain,
% 1.14/1.33 ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[427, 78])).
% 1.14/1.33 tff(429,plain,
% 1.14/1.33 (b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[428, 424])).
% 1.14/1.33 tff(430,plain,
% 1.14/1.33 (b(s(s(s(s(elem!1)))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[429, 417])).
% 1.14/1.33 tff(431,assumption,(~r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.33 tff(432,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.33 tff(433,plain,
% 1.14/1.33 (s(s(s(s(elem!1)))) = s(z)),
% 1.14/1.33 inference(symmetry,[status(thm)],[432])).
% 1.14/1.33 tff(434,assumption,(~(s(s(s(s(elem!1)))) = s(z))), introduced(assumption)).
% 1.14/1.33 tff(435,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[434, 433])).
% 1.14/1.33 tff(436,plain,((~(s(z) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(437,plain,
% 1.14/1.33 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[436, 424])).
% 1.14/1.33 tff(438,plain,
% 1.14/1.33 (((~![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))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(439,plain,
% 1.14/1.33 ((~![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))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(440,plain,
% 1.14/1.33 ((~![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)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.14/1.34 tff(441,plain,
% 1.14/1.34 (b(s(z), s(s(s(s(elem!1)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[440, 78, 437, 431])).
% 1.14/1.34 tff(442,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.34 tff(443,assumption,(b(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.14/1.34 tff(444,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~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(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~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(s(elem!1))))), s(z))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(445,plain,
% 1.14/1.34 (((~b(s(s(s(s(elem!1)))), 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(elem!1)))))) | (~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(s(elem!1))))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~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(s(elem!1))))), s(z))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(446,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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(elem!1)))))) | (~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(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~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(s(elem!1))))), s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[445])).
% 1.14/1.34 tff(447,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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(elem!1)))))) | (~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(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~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(s(elem!1))))), s(z))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[446, 444])).
% 1.14/1.34 tff(448,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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(elem!1)))))) | (~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(s(elem!1))))), s(z))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(449,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.14/1.34 tff(450,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[449, 112, 19, 443, 442, 441])).
% 1.14/1.34 tff(451,plain,((~b(s(s(s(s(s(elem!1))))), 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))) | r(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(452,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[451, 430, 405, 407])).
% 1.14/1.34 tff(453,assumption,(s(s(s(s(s(elem!1))))) = s(z)), introduced(assumption)).
% 1.14/1.34 tff(454,plain,
% 1.14/1.34 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[453])).
% 1.14/1.34 tff(455,plain,
% 1.14/1.34 (s(s(s(s(elem!1)))) = z),
% 1.14/1.34 inference(transitivity,[status(thm)],[263, 454, 50])).
% 1.14/1.34 tff(456,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[347, 455])).
% 1.14/1.34 tff(457,plain,(~(s(s(s(s(s(elem!1))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(458,plain,
% 1.14/1.34 (((~![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)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(459,plain,
% 1.14/1.34 ((~![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)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(460,plain,
% 1.14/1.34 ((~![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))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.14/1.34 tff(461,plain,
% 1.14/1.34 ((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))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[460, 78])).
% 1.14/1.34 tff(462,plain,
% 1.14/1.34 (b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[461, 457])).
% 1.14/1.34 tff(463,plain,
% 1.14/1.34 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[462, 452])).
% 1.14/1.34 tff(464,assumption,(r(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 1.14/1.34 tff(465,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), 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(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(466,plain,
% 1.14/1.34 (((~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(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(467,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[466])).
% 1.14/1.34 tff(468,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[467, 465])).
% 1.14/1.34 tff(469,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(470,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[469, 468])).
% 1.14/1.34 tff(471,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[470, 31, 3, 464, 275])).
% 1.14/1.34 tff(472,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(473,plain,
% 1.14/1.34 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[472, 463, 3])).
% 1.14/1.34 tff(474,plain,
% 1.14/1.34 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[384, 78, 381, 473])).
% 1.14/1.34 tff(475,assumption,(~b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.34 tff(476,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[440, 78, 437, 431, 475])).
% 1.14/1.34 tff(477,plain,(b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(478,plain,
% 1.14/1.34 (b(s(z), s(s(s(s(elem!1)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[477, 407])).
% 1.14/1.34 tff(479,plain,
% 1.14/1.34 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[470, 31, 3, 464])).
% 1.14/1.34 tff(480,plain,
% 1.14/1.34 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[384, 78, 381, 479])).
% 1.14/1.34 tff(481,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(482,plain,
% 1.14/1.34 (((~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))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(483,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[482])).
% 1.14/1.34 tff(484,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[483, 481])).
% 1.14/1.34 tff(485,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(486,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.14/1.34 tff(487,plain,
% 1.14/1.34 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[486, 31, 162, 464])).
% 1.14/1.34 tff(488,assumption,(~r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.14/1.34 tff(489,assumption,(~b(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.14/1.34 tff(490,plain,
% 1.14/1.34 (((~![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))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(491,plain,
% 1.14/1.34 ((~![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))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(492,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.14/1.34 tff(493,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[492, 78, 316, 489, 488])).
% 1.14/1.34 tff(494,plain,(r(s(s(s(s(s(elem!1))))), z) | b(s(s(s(s(s(elem!1))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(495,plain,
% 1.14/1.34 (b(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[494, 487])).
% 1.14/1.34 tff(496,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(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(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(497,plain,
% 1.14/1.34 (((~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(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(498,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[497])).
% 1.14/1.34 tff(499,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[498, 496])).
% 1.14/1.34 tff(500,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(501,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.14/1.34 tff(502,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[501, 31, 20, 3, 162])).
% 1.14/1.34 tff(503,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(504,plain,
% 1.14/1.34 (~r(z, s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[503, 162, 3])).
% 1.14/1.34 tff(505,plain,
% 1.14/1.34 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(506,plain,
% 1.14/1.34 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[505])).
% 1.14/1.34 tff(507,plain,
% 1.14/1.34 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[506])).
% 1.14/1.34 tff(508,plain,
% 1.14/1.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(509,plain,
% 1.14/1.34 (~(s(s(s(z))) = z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[508, 13])).
% 1.14/1.34 tff(510,plain,
% 1.14/1.34 (~(z = s(s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[509, 507])).
% 1.14/1.34 tff(511,plain,
% 1.14/1.34 (((~![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)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(512,plain,
% 1.14/1.34 ((~![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)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(513,plain,
% 1.14/1.34 ((~![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))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.14/1.34 tff(514,plain,
% 1.14/1.34 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[513, 78])).
% 1.14/1.34 tff(515,plain,
% 1.14/1.34 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[514, 510])).
% 1.14/1.34 tff(516,plain,
% 1.14/1.34 (b(z, s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[515, 504])).
% 1.14/1.34 tff(517,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(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(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(518,plain,
% 1.14/1.34 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(519,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[518])).
% 1.14/1.34 tff(520,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[519, 517])).
% 1.14/1.34 tff(521,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(522,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.14/1.34 tff(523,plain,
% 1.14/1.34 (~r(s(s(s(z))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[522, 31, 3, 162])).
% 1.14/1.34 tff(524,plain,
% 1.14/1.34 (((~![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))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(525,plain,
% 1.14/1.34 ((~![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))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(526,plain,
% 1.14/1.34 ((~![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)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.14/1.34 tff(527,plain,
% 1.14/1.34 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[526, 78, 509])).
% 1.14/1.34 tff(528,plain,
% 1.14/1.34 (b(s(s(s(z))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[527, 523])).
% 1.14/1.34 tff(529,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(530,plain,
% 1.14/1.35 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(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)) | (~b(s(s(s(z))), z)) | (~b(s(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(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(531,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(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)) | (~b(s(s(s(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[530])).
% 1.14/1.35 tff(532,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(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)) | (~b(s(s(s(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[531, 529])).
% 1.14/1.35 tff(533,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(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)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(534,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.14/1.35 tff(535,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[534, 112, 528, 516, 495, 480])).
% 1.14/1.35 tff(536,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(537,plain,
% 1.14/1.35 (~r(z, s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[536, 463, 3])).
% 1.14/1.35 tff(538,plain,
% 1.14/1.35 (b(z, s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[182, 537])).
% 1.14/1.35 tff(539,assumption,(b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.35 tff(540,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(541,plain,
% 1.14/1.35 (((~b(s(z), s(s(s(s(elem!1)))))) | (~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))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(542,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~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))) | (~b(z, s(z))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[541])).
% 1.14/1.35 tff(543,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~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))) | (~b(z, s(z))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[542, 540])).
% 1.14/1.35 tff(544,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~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))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(545,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[544, 543])).
% 1.14/1.35 tff(546,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[545, 112, 18, 19, 2, 539])).
% 1.14/1.35 tff(547,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(548,plain,
% 1.14/1.35 (~b(z, s(s(s(s(elem!1)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[547, 538, 478, 430])).
% 1.14/1.35 tff(549,plain,
% 1.14/1.35 (r(z, s(s(s(s(elem!1)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[356, 548])).
% 1.14/1.35 tff(550,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, 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(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(551,plain,
% 1.14/1.35 (((~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(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(552,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[551])).
% 1.14/1.35 tff(553,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[552, 550])).
% 1.14/1.35 tff(554,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(555,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[554, 553])).
% 1.14/1.35 tff(556,plain,
% 1.14/1.35 (~r(z, s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[555, 31, 3, 549, 1])).
% 1.14/1.35 tff(557,plain,
% 1.14/1.35 (b(z, s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[515, 556])).
% 1.14/1.35 tff(558,plain,
% 1.14/1.35 (((~![X0: $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))), 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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(559,plain,
% 1.14/1.35 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(560,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[559])).
% 1.14/1.35 tff(561,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[560, 558])).
% 1.14/1.35 tff(562,plain,
% 1.14/1.35 ((~![X0: $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)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(563,plain,
% 1.14/1.35 ((~![X0: $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))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.14/1.35 tff(564,plain,
% 1.14/1.35 (~r(s(s(s(z))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[563, 31, 549, 1])).
% 1.14/1.35 tff(565,plain,
% 1.14/1.35 (b(s(s(s(z))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[527, 564])).
% 1.14/1.35 tff(566,plain,
% 1.14/1.35 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[534, 112, 565, 557, 474])).
% 1.14/1.35 tff(567,plain,
% 1.14/1.35 (r(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[494, 566])).
% 1.14/1.35 tff(568,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.14/1.35 tff(569,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.35 tff(570,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(571,plain,
% 1.14/1.35 (((~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(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(572,plain,
% 1.14/1.35 (((~![X0: $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(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(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[571])).
% 1.14/1.35 tff(573,plain,
% 1.14/1.35 (((~![X0: $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(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(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[572, 570])).
% 1.14/1.35 tff(574,plain,
% 1.14/1.35 ((~![X0: $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(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(575,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.14/1.35 tff(576,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[575, 31, 20, 568, 569, 249])).
% 1.14/1.35 tff(577,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(578,plain,
% 1.14/1.35 (~r(z, s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[577, 569, 568, 249])).
% 1.14/1.35 tff(579,plain,
% 1.14/1.35 (b(z, s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[515, 578])).
% 1.14/1.35 tff(580,assumption,(~b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.14/1.35 tff(581,plain,
% 1.14/1.35 (r(s(s(s(s(elem!1)))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[429, 580])).
% 1.14/1.35 tff(582,plain,
% 1.14/1.35 (((~![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(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(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(583,plain,
% 1.14/1.35 (((~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(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(584,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[583])).
% 1.14/1.36 tff(585,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(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(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[584, 582])).
% 1.14/1.36 tff(586,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(587,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[586, 585])).
% 1.14/1.36 tff(588,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[587, 31, 162, 408, 569])).
% 1.14/1.36 tff(589,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,[]))).
% 1.14/1.36 tff(590,plain,
% 1.14/1.36 (~r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[589, 581, 569])).
% 1.14/1.36 tff(591,plain,
% 1.14/1.36 (b(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[182, 590])).
% 1.14/1.36 tff(592,assumption,(r(s(z), z)), introduced(assumption)).
% 1.14/1.36 tff(593,plain,
% 1.14/1.36 (((~![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)))), 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(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(594,plain,
% 1.14/1.36 (((~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)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(595,plain,
% 1.14/1.36 (((~![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)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[594])).
% 1.14/1.36 tff(596,plain,
% 1.14/1.36 (((~![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)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[595, 593])).
% 1.14/1.36 tff(597,plain,
% 1.14/1.36 ((~![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))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(598,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[597, 596])).
% 1.14/1.36 tff(599,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[598, 31, 592, 408, 568])).
% 1.14/1.36 tff(600,plain,((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(601,plain,
% 1.14/1.36 (~r(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[600, 581, 568])).
% 1.14/1.36 tff(602,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.14/1.36 tff(603,assumption,(~r(s(z), z)), introduced(assumption)).
% 1.14/1.36 tff(604,plain,
% 1.14/1.36 (((~![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))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(605,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(606,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.14/1.36 tff(607,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[606, 78, 176, 603, 602])).
% 1.14/1.36 tff(608,plain,(b(s(z), z) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(609,plain,
% 1.14/1.36 (b(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[608, 601])).
% 1.14/1.36 tff(610,plain,
% 1.14/1.36 (~r(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[600, 408, 568])).
% 1.14/1.36 tff(611,plain,
% 1.14/1.36 (b(s(z), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[608, 610])).
% 1.14/1.36 tff(612,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.14/1.36 tff(613,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), 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(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(614,plain,
% 1.14/1.36 (((~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(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(615,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[614])).
% 1.14/1.36 tff(616,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[615, 613])).
% 1.14/1.36 tff(617,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(618,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.14/1.36 tff(619,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[618, 31, 612, 568, 249])).
% 1.14/1.36 tff(620,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(621,plain,
% 1.14/1.36 (~r(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[620, 249, 568])).
% 1.14/1.36 tff(622,plain,
% 1.14/1.36 (b(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[527, 621])).
% 1.14/1.36 tff(623,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(624,plain,
% 1.14/1.36 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(625,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[624])).
% 1.14/1.36 tff(626,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[625, 623])).
% 1.14/1.36 tff(627,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(628,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[627, 626])).
% 1.14/1.36 tff(629,plain,
% 1.14/1.36 (~b(s(s(s(z))), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[628, 112, 622, 18, 611])).
% 1.14/1.36 tff(630,plain,
% 1.14/1.36 (r(s(s(s(z))), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[83, 629])).
% 1.14/1.36 tff(631,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(632,plain,
% 1.14/1.36 (((~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(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(633,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[632])).
% 1.14/1.36 tff(634,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[633, 631])).
% 1.14/1.36 tff(635,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(636,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.14/1.36 tff(637,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[636, 31, 630, 408, 249])).
% 1.14/1.36 tff(638,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(639,plain,
% 1.14/1.36 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[638, 581, 591, 568])).
% 1.14/1.36 tff(640,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.36 tff(641,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.36 tff(642,plain,
% 1.14/1.36 (((~![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)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(643,plain,
% 1.14/1.36 ((~![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)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(644,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.14/1.36 tff(645,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[644, 78, 641, 640, 152])).
% 1.14/1.36 tff(646,plain,(b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(647,plain,
% 1.14/1.36 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[646, 639])).
% 1.14/1.36 tff(648,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(649,plain,
% 1.14/1.36 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(650,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[649])).
% 1.14/1.36 tff(651,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[650, 648])).
% 1.14/1.36 tff(652,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(653,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[652, 651])).
% 1.14/1.36 tff(654,plain,
% 1.14/1.36 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[653, 112, 591, 443, 609])).
% 1.14/1.36 tff(655,plain,
% 1.14/1.36 (r(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[494, 654])).
% 1.14/1.36 tff(656,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(657,plain,
% 1.14/1.36 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(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(s(s(elem!1))))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(658,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), 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(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[657])).
% 1.14/1.36 tff(659,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), 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(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[658, 656])).
% 1.14/1.36 tff(660,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(661,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.14/1.37 tff(662,plain,
% 1.14/1.37 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[661, 31, 568, 655])).
% 1.14/1.37 tff(663,plain,
% 1.14/1.37 ((~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[324])).
% 1.14/1.37 tff(664,plain,
% 1.14/1.37 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[269])).
% 1.14/1.37 tff(665,plain,
% 1.14/1.37 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.37 inference(symmetry,[status(thm)],[664])).
% 1.14/1.37 tff(666,plain,
% 1.14/1.37 ((~b(s(s(s(s(elem!1)))), s(z))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[665])).
% 1.14/1.37 tff(667,plain,
% 1.14/1.37 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[580, 666])).
% 1.14/1.37 tff(668,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[443, 667])).
% 1.14/1.37 tff(669,plain,((~(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(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(670,plain,
% 1.14/1.37 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[669, 580, 443])).
% 1.14/1.37 tff(671,plain,
% 1.14/1.37 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[670, 663])).
% 1.14/1.37 tff(672,plain,
% 1.14/1.37 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[299, 671, 662])).
% 1.14/1.37 tff(673,assumption,(b(s(z), z)), introduced(assumption)).
% 1.14/1.37 tff(674,plain,
% 1.14/1.37 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[653, 112, 18, 443, 673])).
% 1.14/1.37 tff(675,plain,
% 1.14/1.37 (r(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[494, 674])).
% 1.14/1.37 tff(676,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(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(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(677,plain,
% 1.14/1.37 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(678,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[677])).
% 1.14/1.37 tff(679,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[678, 676])).
% 1.14/1.37 tff(680,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(681,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[680, 679])).
% 1.14/1.37 tff(682,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[681, 31, 276, 569, 675])).
% 1.14/1.37 tff(683,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(684,plain,
% 1.14/1.37 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[683, 591, 569, 443, 609])).
% 1.14/1.37 tff(685,plain,
% 1.14/1.37 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[404, 670, 684])).
% 1.14/1.37 tff(686,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(687,plain,
% 1.14/1.37 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(688,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[687])).
% 1.14/1.37 tff(689,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[688, 686])).
% 1.14/1.37 tff(690,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(691,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[690, 689])).
% 1.14/1.37 tff(692,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[691, 31, 612, 568, 1])).
% 1.14/1.37 tff(693,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(694,plain,
% 1.14/1.37 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[693, 612, 568])).
% 1.14/1.37 tff(695,plain,
% 1.14/1.37 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[160, 694])).
% 1.14/1.37 tff(696,assumption,(s(s(s(z))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.37 tff(697,plain,
% 1.14/1.37 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 1.14/1.37 inference(symmetry,[status(thm)],[696])).
% 1.14/1.37 tff(698,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[381, 697])).
% 1.14/1.37 tff(699,plain,(~(s(s(s(z))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(700,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(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(s(s(elem!1))))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(701,plain,
% 1.14/1.37 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(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(z))))) | (~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(702,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(s(s(elem!1)))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[701])).
% 1.14/1.37 tff(703,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(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(s(s(elem!1))))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[702, 700])).
% 1.14/1.37 tff(704,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(705,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(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(s(s(elem!1)))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[704, 703])).
% 1.14/1.37 tff(706,plain,
% 1.14/1.37 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[705, 112, 4, 196, 333, 442])).
% 1.14/1.37 tff(707,assumption,(~r(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.37 tff(708,plain,
% 1.14/1.37 (((~![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)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(709,plain,
% 1.14/1.37 ((~![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)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(710,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[709, 708])).
% 1.14/1.37 tff(711,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[710, 78, 707, 706, 699])).
% 1.14/1.37 tff(712,plain,(r(s(s(s(z))), s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(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,[]))).
% 1.14/1.37 tff(713,plain,
% 1.14/1.37 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[712, 695, 442, 333, 4])).
% 1.14/1.37 tff(714,assumption,(r(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.14/1.37 tff(715,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(716,plain,
% 1.14/1.37 (((~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))))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(717,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[716])).
% 1.14/1.37 tff(718,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[717, 715])).
% 1.14/1.37 tff(719,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(720,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[719, 718])).
% 1.14/1.37 tff(721,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[720, 31, 612, 714, 713])).
% 1.14/1.37 tff(722,plain,((~r(s(s(s(z))), z)) | (~r(s(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(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(723,plain,
% 1.14/1.37 (~r(s(s(s(z))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[722, 655, 685, 672, 647, 568])).
% 1.14/1.37 tff(724,plain,
% 1.14/1.37 (b(s(s(s(z))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[527, 723])).
% 1.14/1.37 tff(725,plain,
% 1.14/1.37 (~b(s(s(s(z))), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[628, 112, 724, 591, 609])).
% 1.14/1.37 tff(726,plain,
% 1.14/1.37 (r(s(s(s(z))), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[83, 725])).
% 1.14/1.37 tff(727,plain,
% 1.14/1.37 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[414, 31, 726, 581])).
% 1.14/1.37 tff(728,plain,
% 1.14/1.37 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[160, 727])).
% 1.14/1.37 tff(729,plain,
% 1.14/1.37 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[712, 728, 685, 672, 647])).
% 1.14/1.37 tff(730,assumption,(r(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.37 tff(731,assumption,(r(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.37 tff(732,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(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(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(733,plain,
% 1.14/1.37 (((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(734,plain,
% 1.14/1.37 (((~![X0: $i, 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(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(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(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[733])).
% 1.14/1.37 tff(735,plain,
% 1.14/1.37 (((~![X0: $i, 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(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(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(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[734, 732])).
% 1.14/1.37 tff(736,plain,
% 1.14/1.37 ((~![X0: $i, 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(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(737,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[736, 735])).
% 1.14/1.37 tff(738,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[737, 31, 3, 731, 730])).
% 1.14/1.37 tff(739,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(740,plain,
% 1.14/1.38 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[739, 729, 726])).
% 1.14/1.38 tff(741,plain,
% 1.14/1.38 ((s(z) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 1.14/1.38 inference(commutativity,[status(thm)],[])).
% 1.14/1.38 tff(742,plain,
% 1.14/1.38 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(z) = s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(symmetry,[status(thm)],[741])).
% 1.14/1.38 tff(743,plain,
% 1.14/1.38 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(elem!1)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[742])).
% 1.14/1.38 tff(744,plain,
% 1.14/1.38 (~(s(z) = s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[457, 743])).
% 1.14/1.38 tff(745,plain,
% 1.14/1.38 (((~![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)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(746,plain,
% 1.14/1.38 ((~![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)))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(747,plain,
% 1.14/1.38 ((~![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))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.14/1.38 tff(748,plain,
% 1.14/1.38 ((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))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[747, 78])).
% 1.14/1.38 tff(749,plain,
% 1.14/1.38 (b(s(z), s(s(s(s(s(elem!1)))))) | r(s(z), s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[748, 744])).
% 1.14/1.38 tff(750,plain,
% 1.14/1.38 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[749, 740])).
% 1.14/1.38 tff(751,assumption,(b(s(z), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.38 tff(752,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(753,plain,
% 1.14/1.38 (((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(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))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(754,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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)))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[753])).
% 1.14/1.38 tff(755,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[754, 752])).
% 1.14/1.38 tff(756,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(757,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[756, 755])).
% 1.14/1.38 tff(758,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[757, 112, 18, 443, 334, 751])).
% 1.14/1.38 tff(759,plain,((~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), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(760,plain,
% 1.14/1.38 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[759, 750, 443, 591])).
% 1.14/1.38 tff(761,plain,
% 1.14/1.38 (r(z, s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[322, 760])).
% 1.14/1.38 tff(762,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.38 tff(763,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(764,plain,
% 1.14/1.38 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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(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(z))), 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(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(765,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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(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(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[764])).
% 1.14/1.38 tff(766,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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(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(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[765, 763])).
% 1.14/1.38 tff(767,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~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(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(768,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[767, 766])).
% 1.14/1.38 tff(769,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[768, 112, 4, 196, 442, 762])).
% 1.14/1.38 tff(770,plain,((~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(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(771,plain,
% 1.14/1.38 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[770, 728, 685, 647])).
% 1.14/1.38 tff(772,plain,
% 1.14/1.38 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[384, 78, 381, 771])).
% 1.14/1.38 tff(773,plain,
% 1.14/1.38 (~r(z, s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[310, 772, 761])).
% 1.14/1.38 tff(774,plain,
% 1.14/1.38 (b(z, s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[515, 773])).
% 1.14/1.38 tff(775,plain,
% 1.14/1.38 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.38 inference(commutativity,[status(thm)],[])).
% 1.14/1.38 tff(776,plain,
% 1.14/1.38 (((~![X0: $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(z, s(s(s(s(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(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(777,plain,
% 1.14/1.38 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(778,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), 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(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[777])).
% 1.14/1.38 tff(779,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), 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(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[778, 776])).
% 1.14/1.38 tff(780,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(781,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.14/1.38 tff(782,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[781, 31, 302, 569, 276])).
% 1.14/1.38 tff(783,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(784,plain,
% 1.14/1.38 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[783, 302, 569])).
% 1.14/1.38 tff(785,plain,
% 1.14/1.38 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[404, 784, 274])).
% 1.14/1.38 tff(786,plain,
% 1.14/1.38 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[414, 31, 3, 408])).
% 1.14/1.38 tff(787,plain,
% 1.14/1.38 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[160, 786])).
% 1.14/1.38 tff(788,plain,
% 1.14/1.38 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[636, 31, 3, 408])).
% 1.14/1.38 tff(789,plain,
% 1.14/1.38 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[646, 788])).
% 1.14/1.38 tff(790,plain,
% 1.14/1.38 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[712, 785, 787, 333, 789])).
% 1.14/1.38 tff(791,plain,
% 1.14/1.38 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[739, 790, 3])).
% 1.14/1.38 tff(792,plain,
% 1.14/1.38 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[749, 791])).
% 1.14/1.38 tff(793,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(794,plain,
% 1.14/1.38 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(s(elem!1)))))) | (~b(s(z), 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(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(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(795,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(s(elem!1)))))) | (~b(s(z), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[794])).
% 1.14/1.38 tff(796,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(s(elem!1)))))) | (~b(s(z), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[795, 793])).
% 1.14/1.38 tff(797,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(s(elem!1)))))) | (~b(s(z), 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))))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(798,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[797, 796])).
% 1.14/1.38 tff(799,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[798, 112, 443, 751, 333, 442, 539])).
% 1.14/1.38 tff(800,plain,((~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(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(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(801,plain,
% 1.14/1.38 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[800, 792, 333, 785, 443])).
% 1.14/1.38 tff(802,plain,
% 1.14/1.38 (r(s(z), s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[477, 801])).
% 1.14/1.38 tff(803,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.14/1.38 tff(804,plain,
% 1.14/1.38 (((~![X0: $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))), 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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(805,plain,
% 1.14/1.38 (((~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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(806,plain,
% 1.14/1.38 (((~![X0: $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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[805])).
% 1.14/1.39 tff(807,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[806, 804])).
% 1.14/1.39 tff(808,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(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)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(809,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.14/1.39 tff(810,plain,
% 1.14/1.39 (~r(s(s(s(z))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[809, 31, 302, 790])).
% 1.14/1.39 tff(811,plain,
% 1.14/1.39 (b(s(s(s(z))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[527, 810])).
% 1.14/1.39 tff(812,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.39 tff(813,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(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)))))))) <=> ((~![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(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(814,plain,
% 1.14/1.39 (((~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(s(elem!1))))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(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)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(815,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(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(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[814])).
% 1.14/1.39 tff(816,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(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(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[815, 813])).
% 1.14/1.39 tff(817,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(818,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(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))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[817, 816])).
% 1.14/1.39 tff(819,plain,
% 1.14/1.39 (~r(s(s(elem!1)), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[818, 31, 812, 302, 569])).
% 1.14/1.39 tff(820,plain,
% 1.14/1.39 (((~![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))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(821,plain,
% 1.14/1.39 ((~![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))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(822,plain,
% 1.14/1.39 ((~![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)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.14/1.39 tff(823,plain,
% 1.14/1.39 (b(s(s(elem!1)), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[822, 78, 379, 819])).
% 1.14/1.39 tff(824,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), 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(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(825,plain,
% 1.14/1.39 (((~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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(826,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[825])).
% 1.14/1.39 tff(827,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[826, 824])).
% 1.14/1.39 tff(828,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(829,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[828, 827])).
% 1.14/1.39 tff(830,plain,
% 1.14/1.39 (~r(z, s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[829, 31, 812, 569])).
% 1.14/1.39 tff(831,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.14/1.39 tff(832,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 1.14/1.39 tff(833,plain,
% 1.14/1.39 (s(s(elem!1)) = z),
% 1.14/1.39 inference(symmetry,[status(thm)],[832])).
% 1.14/1.39 tff(834,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[379, 833])).
% 1.14/1.39 tff(835,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(836,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 1.14/1.39 tff(837,plain,
% 1.14/1.39 (((~![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))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(838,plain,
% 1.14/1.39 ((~![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))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(839,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.14/1.39 tff(840,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[839, 78, 836, 835, 831])).
% 1.14/1.39 tff(841,plain,(b(z, s(s(elem!1))) | r(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(842,plain,
% 1.14/1.39 (b(z, s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[841, 830])).
% 1.14/1.39 tff(843,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.39 tff(844,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(845,plain,
% 1.14/1.39 (((~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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(846,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[845])).
% 1.14/1.39 tff(847,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[846, 844])).
% 1.14/1.39 tff(848,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(849,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.14/1.39 tff(850,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[849, 31, 812, 843, 21])).
% 1.14/1.39 tff(851,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,[]))).
% 1.14/1.39 tff(852,plain,
% 1.14/1.39 (~r(s(z), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[851, 812, 21])).
% 1.14/1.39 tff(853,plain,
% 1.14/1.39 (((~![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))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(854,plain,
% 1.14/1.39 ((~![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))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(855,plain,
% 1.14/1.39 ((~![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)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[854, 853])).
% 1.14/1.39 tff(856,plain,
% 1.14/1.39 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[855, 78])).
% 1.14/1.39 tff(857,plain,
% 1.14/1.39 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[856, 150])).
% 1.14/1.39 tff(858,plain,
% 1.14/1.39 (b(s(z), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[857, 852])).
% 1.14/1.39 tff(859,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.14/1.39 tff(860,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(861,plain,
% 1.14/1.39 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(862,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[861])).
% 1.14/1.39 tff(863,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[862, 860])).
% 1.14/1.39 tff(864,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(865,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.14/1.39 tff(866,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[865, 112, 859, 803, 858, 673, 842, 823])).
% 1.14/1.39 tff(867,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(868,plain,
% 1.14/1.39 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[867, 811, 803, 673, 302, 569, 802])).
% 1.14/1.39 tff(869,plain,
% 1.14/1.39 (((~![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))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(870,plain,
% 1.14/1.39 ((~![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))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(871,plain,
% 1.14/1.39 ((~![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)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[870, 869])).
% 1.14/1.39 tff(872,plain,
% 1.14/1.39 ((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)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[871, 78])).
% 1.14/1.39 tff(873,plain,
% 1.14/1.39 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[872, 868, 248])).
% 1.14/1.39 tff(874,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~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(elem!1)), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(875,plain,
% 1.14/1.39 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(z))))) | (~b(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(s(elem!1)))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(876,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[875])).
% 1.14/1.39 tff(877,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[876, 874])).
% 1.24/1.40 tff(878,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(879,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[878, 877])).
% 1.24/1.40 tff(880,plain,
% 1.24/1.40 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[879, 112, 873, 789, 787, 333, 785])).
% 1.24/1.40 tff(881,plain,
% 1.24/1.40 (~r(z, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[589, 408, 569])).
% 1.24/1.40 tff(882,plain,
% 1.24/1.40 (b(z, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[182, 881])).
% 1.24/1.40 tff(883,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.24/1.40 tff(884,plain,
% 1.24/1.40 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[883])).
% 1.24/1.40 tff(885,plain,
% 1.24/1.40 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[884])).
% 1.24/1.40 tff(886,plain,
% 1.24/1.40 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[253, 885, 262])).
% 1.24/1.40 tff(887,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[248, 886])).
% 1.24/1.40 tff(888,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,[]))).
% 1.24/1.40 tff(889,plain,
% 1.24/1.40 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[888, 248])).
% 1.24/1.40 tff(890,plain,
% 1.24/1.40 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(891,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.24/1.40 tff(892,plain,
% 1.24/1.40 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[891])).
% 1.24/1.40 tff(893,plain,
% 1.24/1.40 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.24/1.40 inference(symmetry,[status(thm)],[892])).
% 1.24/1.40 tff(894,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[893])).
% 1.24/1.40 tff(895,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[894, 890])).
% 1.24/1.40 tff(896,plain,
% 1.24/1.40 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[895])).
% 1.24/1.40 tff(897,plain,
% 1.24/1.40 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[896])).
% 1.24/1.40 tff(898,plain,
% 1.24/1.40 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[265, 897])).
% 1.24/1.40 tff(899,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.40 tff(900,plain,
% 1.24/1.40 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(901,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[893])).
% 1.24/1.40 tff(902,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[901, 900])).
% 1.24/1.40 tff(903,plain,
% 1.24/1.40 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[902])).
% 1.24/1.40 tff(904,plain,
% 1.24/1.40 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[903])).
% 1.24/1.40 tff(905,plain,
% 1.24/1.40 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[899, 904])).
% 1.24/1.40 tff(906,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.24/1.40 tff(907,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(908,plain,
% 1.24/1.40 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(909,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[908])).
% 1.24/1.40 tff(910,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[909, 907])).
% 1.24/1.40 tff(911,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(912,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.24/1.40 tff(913,plain,
% 1.24/1.40 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[912, 112, 18, 673])).
% 1.24/1.40 tff(914,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[913, 906])).
% 1.24/1.40 tff(915,plain,
% 1.24/1.40 (((~![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))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(916,plain,
% 1.24/1.40 ((~![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))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(917,plain,
% 1.24/1.40 ((~![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)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[916, 915])).
% 1.24/1.40 tff(918,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[917, 78, 224, 914])).
% 1.24/1.40 tff(919,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(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(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(920,plain,
% 1.24/1.40 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(921,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), 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))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[920])).
% 1.24/1.40 tff(922,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), 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))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[921, 919])).
% 1.24/1.40 tff(923,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(924,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[923, 922])).
% 1.24/1.40 tff(925,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[924, 31, 675, 918])).
% 1.24/1.40 tff(926,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(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(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(927,plain,
% 1.24/1.40 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(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(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(928,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(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(s(s(s(z)))), s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[927])).
% 1.24/1.40 tff(929,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(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(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[928, 926])).
% 1.24/1.40 tff(930,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(931,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(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(s(s(s(z)))), s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.24/1.40 tff(932,plain,
% 1.24/1.40 ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[931, 112, 18, 443, 751, 673])).
% 1.24/1.40 tff(933,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[932, 906])).
% 1.24/1.40 tff(934,plain,
% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(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(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(935,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(936,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[935, 934])).
% 1.24/1.40 tff(937,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[936, 78, 933])).
% 1.24/1.40 tff(938,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[937, 925, 905])).
% 1.24/1.41 tff(939,plain,((~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(940,plain,
% 1.24/1.41 (~b(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[939, 891, 899, 18, 443, 751, 673])).
% 1.24/1.41 tff(941,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.24/1.41 tff(942,plain,
% 1.24/1.41 (s(z) = s(s(s(s(z))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[941])).
% 1.24/1.41 tff(943,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.41 tff(944,plain,
% 1.24/1.41 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[943])).
% 1.24/1.41 tff(945,plain,
% 1.24/1.41 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[944])).
% 1.24/1.41 tff(946,plain,
% 1.24/1.41 (s(s(s(z))) = z),
% 1.24/1.41 inference(transitivity,[status(thm)],[216, 945, 50])).
% 1.24/1.41 tff(947,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[509, 946])).
% 1.24/1.41 tff(948,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(949,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[948, 942])).
% 1.24/1.41 tff(950,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(951,plain,
% 1.24/1.41 (((~![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)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(952,plain,
% 1.24/1.41 ((~![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)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(953,plain,
% 1.24/1.41 ((~![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))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[952, 951])).
% 1.24/1.41 tff(954,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[953, 78, 950, 940])).
% 1.24/1.41 tff(955,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(956,plain,
% 1.24/1.41 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(957,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[956])).
% 1.24/1.41 tff(958,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[957, 955])).
% 1.24/1.41 tff(959,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(960,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[959, 958])).
% 1.24/1.41 tff(961,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[960, 31, 3, 954])).
% 1.24/1.41 tff(962,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.24/1.41 tff(963,plain,
% 1.24/1.41 (s(s(s(z))) = s(s(s(s(z))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[962])).
% 1.24/1.41 tff(964,plain,
% 1.24/1.41 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[963])).
% 1.24/1.41 tff(965,plain,
% 1.24/1.41 (s(s(z)) = s(s(s(z)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[56, 964, 215])).
% 1.24/1.41 tff(966,plain,
% 1.24/1.41 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[965])).
% 1.24/1.41 tff(967,plain,
% 1.24/1.41 (s(z) = s(s(s(z)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[138, 966, 964, 215])).
% 1.24/1.41 tff(968,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[61, 967])).
% 1.24/1.41 tff(969,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(970,plain,
% 1.24/1.41 (((~![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)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(971,plain,
% 1.24/1.41 ((~![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)))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(972,plain,
% 1.24/1.41 ((~![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))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[971, 970])).
% 1.24/1.41 tff(973,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[972, 78, 969, 961])).
% 1.24/1.41 tff(974,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(975,plain,
% 1.24/1.41 (((~b(s(s(s(s(elem!1)))), s(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(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(z))), z)) | (~b(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(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(976,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(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(z)))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[975])).
% 1.24/1.41 tff(977,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(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(z)))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[976, 974])).
% 1.24/1.41 tff(978,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(979,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.24/1.41 tff(980,plain,
% 1.24/1.41 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[979, 112, 859, 803, 789, 787, 973])).
% 1.24/1.41 tff(981,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.24/1.41 tff(982,assumption,(r(s(s(s(s(z)))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.41 tff(983,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(984,plain,
% 1.24/1.41 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(985,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[984])).
% 1.24/1.41 tff(986,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[985, 983])).
% 1.24/1.41 tff(987,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), 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)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(988,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.24/1.41 tff(989,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[988, 31, 408, 982, 981])).
% 1.24/1.41 tff(990,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(991,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[990, 954, 408])).
% 1.24/1.41 tff(992,plain,
% 1.24/1.41 (((~![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))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(993,plain,
% 1.24/1.41 ((~![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))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(994,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.24/1.41 tff(995,plain,
% 1.24/1.41 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[994, 78, 991])).
% 1.24/1.41 tff(996,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[995, 980, 898])).
% 1.24/1.41 tff(997,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (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))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(998,plain,
% 1.24/1.41 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[997, 811, 803, 257, 3, 408, 889, 882, 443, 792, 673])).
% 1.24/1.41 tff(999,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1000,plain,
% 1.24/1.41 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1001,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1000])).
% 1.24/1.41 tff(1002,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1001, 999])).
% 1.24/1.41 tff(1003,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1004,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 1.24/1.41 tff(1005,plain,
% 1.24/1.41 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1004, 112, 873, 789, 787])).
% 1.24/1.41 tff(1006,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1007,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1008,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.24/1.41 tff(1009,plain,
% 1.24/1.41 ((s(s(elem!1)) = s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1008, 78, 1005])).
% 1.24/1.41 tff(1010,plain,
% 1.24/1.41 (r(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1009, 998])).
% 1.24/1.41 tff(1011,plain,
% 1.24/1.41 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[770, 785, 787, 789])).
% 1.24/1.41 tff(1012,plain,
% 1.24/1.41 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[384, 78, 381, 1011])).
% 1.24/1.41 tff(1013,plain,
% 1.24/1.41 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[653, 112, 882, 443, 673])).
% 1.24/1.41 tff(1014,plain,
% 1.24/1.41 (r(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[494, 1013])).
% 1.24/1.41 tff(1015,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1016,plain,
% 1.24/1.42 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1017,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1016])).
% 1.24/1.42 tff(1018,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1017, 1015])).
% 1.24/1.42 tff(1019,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1020,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 1.24/1.42 tff(1021,plain,
% 1.24/1.42 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1020, 31, 1014, 1012, 1010])).
% 1.24/1.42 tff(1022,plain,
% 1.24/1.42 (((~![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)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1023,plain,
% 1.24/1.42 ((~![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)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1024,plain,
% 1.24/1.42 ((~![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))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.24/1.42 tff(1025,plain,
% 1.24/1.42 ((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))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1024, 78])).
% 1.24/1.42 tff(1026,plain,
% 1.24/1.42 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1025, 1021, 880])).
% 1.24/1.42 tff(1027,plain,
% 1.24/1.42 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1026])).
% 1.24/1.42 tff(1028,plain,
% 1.24/1.42 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1027])).
% 1.24/1.42 tff(1029,plain,
% 1.24/1.42 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1028, 775])).
% 1.24/1.42 tff(1030,plain,
% 1.24/1.42 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1029])).
% 1.24/1.42 tff(1031,plain,
% 1.24/1.42 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1030])).
% 1.24/1.42 tff(1032,plain,
% 1.24/1.42 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1033,plain,
% 1.24/1.42 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1032, 48])).
% 1.24/1.42 tff(1034,assumption,(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.24/1.42 tff(1035,plain,
% 1.24/1.42 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1034])).
% 1.24/1.42 tff(1036,plain,
% 1.24/1.42 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[56, 1035, 1033])).
% 1.24/1.42 tff(1037,plain,
% 1.24/1.42 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1036])).
% 1.24/1.42 tff(1038,plain,
% 1.24/1.42 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(z)))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1037])).
% 1.24/1.42 tff(1039,plain,
% 1.24/1.42 (s(s(s(s(elem!1)))) = s(z)),
% 1.24/1.42 inference(transitivity,[status(thm)],[263, 1038, 137])).
% 1.24/1.42 tff(1040,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[424, 1039])).
% 1.24/1.42 tff(1041,plain,(~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(1042,plain,
% 1.24/1.42 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1041, 1031])).
% 1.24/1.42 tff(1043,plain,
% 1.24/1.42 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1027])).
% 1.24/1.42 tff(1044,plain,
% 1.24/1.42 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1043])).
% 1.24/1.42 tff(1045,plain,
% 1.24/1.42 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1044])).
% 1.24/1.42 tff(1046,plain,
% 1.24/1.42 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1043])).
% 1.24/1.42 tff(1047,plain,
% 1.24/1.42 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1046])).
% 1.24/1.42 tff(1048,plain,
% 1.24/1.42 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1026])).
% 1.24/1.42 tff(1049,plain,
% 1.24/1.42 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[145, 1048, 262])).
% 1.24/1.42 tff(1050,plain,
% 1.24/1.42 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1049])).
% 1.24/1.42 tff(1051,plain,
% 1.24/1.42 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1050, 1047])).
% 1.24/1.42 tff(1052,plain,
% 1.24/1.42 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1049])).
% 1.24/1.42 tff(1053,plain,
% 1.24/1.42 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1052, 890])).
% 1.24/1.42 tff(1054,plain,
% 1.24/1.42 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1053])).
% 1.24/1.42 tff(1055,plain,
% 1.24/1.42 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1054])).
% 1.24/1.42 tff(1056,plain,
% 1.24/1.42 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[257, 1055])).
% 1.24/1.42 tff(1057,plain,
% 1.24/1.42 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1027, 1049])).
% 1.24/1.42 tff(1058,plain,
% 1.24/1.42 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1057])).
% 1.24/1.42 tff(1059,plain,
% 1.24/1.42 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1058])).
% 1.24/1.42 tff(1060,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1061,plain,
% 1.24/1.42 (((~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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1062,plain,
% 1.24/1.42 (((~![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(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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1061])).
% 1.24/1.42 tff(1063,plain,
% 1.24/1.42 (((~![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(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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1062, 1060])).
% 1.24/1.42 tff(1064,plain,
% 1.24/1.42 ((~![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(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1065,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 1.24/1.42 tff(1066,plain,
% 1.24/1.42 (~r(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1065, 31, 569, 21])).
% 1.24/1.42 tff(1067,plain,
% 1.24/1.42 (b(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[606, 78, 176, 1066])).
% 1.24/1.42 tff(1068,assumption,(s(s(elem!1)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.42 tff(1069,plain,
% 1.24/1.42 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1068])).
% 1.24/1.42 tff(1070,plain,
% 1.24/1.42 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1068])).
% 1.24/1.42 tff(1071,plain,
% 1.24/1.42 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[145, 1070, 262])).
% 1.24/1.42 tff(1072,plain,
% 1.24/1.42 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1071])).
% 1.24/1.42 tff(1073,plain,
% 1.24/1.42 (elem!1 = inj_0(s(elem!1))),
% 1.24/1.42 inference(symmetry,[status(thm)],[247])).
% 1.24/1.42 tff(1074,plain,
% 1.24/1.42 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1073, 1072, 131, 1069])).
% 1.24/1.42 tff(1075,plain,
% 1.24/1.42 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1074])).
% 1.24/1.42 tff(1076,assumption,(z = elem!1), introduced(assumption)).
% 1.24/1.42 tff(1077,plain,
% 1.24/1.42 (s(z) = s(elem!1)),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1076])).
% 1.24/1.42 tff(1078,plain,
% 1.24/1.42 (s(elem!1) = s(z)),
% 1.24/1.42 inference(symmetry,[status(thm)],[1077])).
% 1.24/1.42 tff(1079,plain,
% 1.24/1.42 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1068])).
% 1.24/1.42 tff(1080,plain,
% 1.24/1.42 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1079])).
% 1.24/1.42 tff(1081,plain,
% 1.24/1.42 (s(s(s(s(elem!1)))) = s(z)),
% 1.24/1.42 inference(transitivity,[status(thm)],[263, 1080, 144, 1078])).
% 1.24/1.42 tff(1082,plain,
% 1.24/1.42 (elem!1 = z),
% 1.24/1.42 inference(symmetry,[status(thm)],[1076])).
% 1.24/1.42 tff(1083,plain,
% 1.24/1.42 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.24/1.42 inference(transitivity,[status(thm)],[418, 1077])).
% 1.24/1.42 tff(1084,plain,
% 1.24/1.42 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1083])).
% 1.24/1.42 tff(1085,plain,
% 1.24/1.42 (s(s(s(elem!1))) = z),
% 1.24/1.42 inference(transitivity,[status(thm)],[132, 1084, 247, 1082])).
% 1.24/1.42 tff(1086,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[422, 1085])).
% 1.24/1.42 tff(1087,plain,((~(s(s(s(s(elem!1)))) = s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(1088,plain,
% 1.24/1.42 (~(s(s(s(s(elem!1)))) = s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1087, 1076])).
% 1.24/1.42 tff(1089,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1088, 1081])).
% 1.24/1.42 tff(1090,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(1091,plain,
% 1.24/1.42 (~(z = elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1090, 1068])).
% 1.24/1.42 tff(1092,plain,
% 1.24/1.42 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1072])).
% 1.24/1.42 tff(1093,plain,
% 1.24/1.42 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1069])).
% 1.24/1.42 tff(1094,plain,
% 1.24/1.42 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.24/1.42 inference(transitivity,[status(thm)],[1093, 132, 1092, 247])).
% 1.24/1.42 tff(1095,plain,
% 1.24/1.42 (r(z, s(s(s(s(s(s(elem!1))))))) <=> r(z, elem!1)),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1094])).
% 1.24/1.42 tff(1096,plain,
% 1.24/1.42 ((~r(z, s(s(s(s(s(s(elem!1)))))))) <=> (~r(z, elem!1))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1095])).
% 1.24/1.42 tff(1097,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.42 tff(1098,plain,
% 1.24/1.42 (((~![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(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1099,plain,
% 1.24/1.42 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1100,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1099])).
% 1.24/1.42 tff(1101,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1100, 1098])).
% 1.24/1.42 tff(1102,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1103,plain,
% 1.24/1.42 ((~![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(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 1.24/1.42 tff(1104,plain,
% 1.24/1.42 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1103, 31, 569, 1097])).
% 1.24/1.42 tff(1105,plain,
% 1.24/1.42 (~r(z, elem!1)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1104, 1096])).
% 1.24/1.42 tff(1106,plain,
% 1.24/1.42 (((~![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))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1107,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1108,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 1.24/1.42 tff(1109,plain,
% 1.24/1.42 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1108, 78])).
% 1.24/1.42 tff(1110,plain,
% 1.24/1.42 (b(z, elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1109, 1105, 1091])).
% 1.24/1.42 tff(1111,plain,
% 1.24/1.42 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1110, 1075])).
% 1.24/1.42 tff(1112,plain,
% 1.24/1.42 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1074])).
% 1.24/1.42 tff(1113,plain,
% 1.24/1.42 ((s(s(s(s(s(s(elem!1)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(commutativity,[status(thm)],[])).
% 1.24/1.42 tff(1114,plain,
% 1.24/1.42 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1074])).
% 1.24/1.42 tff(1115,plain,
% 1.24/1.42 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1114, 1113])).
% 1.24/1.42 tff(1116,plain,
% 1.24/1.42 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1115])).
% 1.24/1.42 tff(1117,plain,
% 1.24/1.42 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1116])).
% 1.24/1.42 tff(1118,assumption,(s(z) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.24/1.42 tff(1119,plain,
% 1.24/1.42 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1118])).
% 1.24/1.42 tff(1120,plain,
% 1.24/1.42 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1119])).
% 1.24/1.42 tff(1121,plain,
% 1.24/1.42 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1033])).
% 1.24/1.42 tff(1122,plain,
% 1.24/1.42 (s(s(s(s(s(elem!1))))) = z),
% 1.24/1.42 inference(transitivity,[status(thm)],[1121, 1120, 50])).
% 1.24/1.42 tff(1123,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[316, 1122])).
% 1.24/1.42 tff(1124,plain,(~(s(z) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(1125,plain,
% 1.24/1.42 (~(elem!1 = s(z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1124, 1117])).
% 1.24/1.42 tff(1126,plain,
% 1.24/1.42 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(elem!1, s(z))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1094])).
% 1.24/1.42 tff(1127,plain,
% 1.24/1.42 ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) <=> (~r(elem!1, s(z)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1126])).
% 1.24/1.42 tff(1128,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1129,plain,
% 1.24/1.42 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1)))))), s(z)))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1130,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(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(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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1129])).
% 1.24/1.42 tff(1131,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(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(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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1130, 1128])).
% 1.24/1.42 tff(1132,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(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(s(elem!1)))))), s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1133,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 1.24/1.42 tff(1134,plain,
% 1.24/1.42 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1133, 31, 1097, 21])).
% 1.24/1.42 tff(1135,plain,
% 1.24/1.42 (~r(elem!1, s(z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1134, 1127])).
% 1.24/1.42 tff(1136,plain,
% 1.24/1.42 (((~![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)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1137,plain,
% 1.24/1.42 ((~![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)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1138,plain,
% 1.24/1.42 ((~![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))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.24/1.42 tff(1139,plain,
% 1.24/1.42 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1138, 78])).
% 1.24/1.42 tff(1140,plain,
% 1.24/1.42 (b(elem!1, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1139, 1135, 1125])).
% 1.24/1.42 tff(1141,plain,
% 1.24/1.42 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1140, 1112])).
% 1.24/1.42 tff(1142,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1143,plain,
% 1.24/1.42 (((~r(s(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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1144,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1143])).
% 1.24/1.43 tff(1145,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1144, 1142])).
% 1.24/1.43 tff(1146,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1147,plain,
% 1.24/1.43 ((~![X0: $i, 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(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.24/1.43 tff(1148,plain,
% 1.24/1.43 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1147, 31, 1097, 21])).
% 1.24/1.43 tff(1149,plain,
% 1.24/1.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1150,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1151,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.24/1.43 tff(1152,plain,
% 1.24/1.43 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1151, 78, 1124, 1148])).
% 1.24/1.43 tff(1153,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1154,plain,
% 1.24/1.43 (((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1155,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1))))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1154])).
% 1.24/1.43 tff(1156,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1155, 1153])).
% 1.24/1.43 tff(1157,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1158,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 1.24/1.43 tff(1159,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1158, 112, 18, 1152, 1141, 1111, 1067])).
% 1.24/1.43 tff(1160,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1161,plain,
% 1.24/1.43 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1160, 1026, 569, 802, 882])).
% 1.24/1.43 tff(1162,plain,
% 1.24/1.43 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1161, 1059])).
% 1.24/1.43 tff(1163,plain,
% 1.24/1.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1164,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1165,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.24/1.43 tff(1166,plain,
% 1.24/1.43 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1165, 78])).
% 1.24/1.43 tff(1167,plain,
% 1.24/1.43 (b(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1166, 1162, 1056])).
% 1.24/1.43 tff(1168,plain,
% 1.24/1.43 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1167, 1051])).
% 1.24/1.43 tff(1169,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1170,plain,
% 1.24/1.43 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1171,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1170])).
% 1.24/1.43 tff(1172,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1171, 1169])).
% 1.24/1.43 tff(1173,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1174,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 1.24/1.43 tff(1175,plain,
% 1.24/1.43 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1174, 112, 789, 787, 1168])).
% 1.24/1.43 tff(1176,plain,
% 1.24/1.43 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1175, 1045])).
% 1.24/1.43 tff(1177,plain,
% 1.24/1.43 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1043])).
% 1.24/1.43 tff(1178,plain,
% 1.24/1.43 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1177])).
% 1.24/1.43 tff(1179,plain,
% 1.24/1.43 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1049])).
% 1.24/1.43 tff(1180,plain,
% 1.24/1.43 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1179])).
% 1.24/1.43 tff(1181,plain,
% 1.24/1.43 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.24/1.43 inference(transitivity,[status(thm)],[1043, 132, 1180, 247])).
% 1.24/1.43 tff(1182,plain,
% 1.24/1.43 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1181])).
% 1.24/1.43 tff(1183,plain,
% 1.24/1.43 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1182])).
% 1.24/1.43 tff(1184,plain,
% 1.24/1.43 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1026])).
% 1.24/1.43 tff(1185,plain,
% 1.24/1.43 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1184])).
% 1.24/1.43 tff(1186,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.24/1.43 tff(1187,plain,
% 1.24/1.43 (s(elem!1) = s(s(s(elem!1)))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1186])).
% 1.24/1.43 tff(1188,plain,
% 1.24/1.43 (s(s(s(elem!1))) = s(elem!1)),
% 1.24/1.43 inference(symmetry,[status(thm)],[1187])).
% 1.24/1.43 tff(1189,plain,
% 1.24/1.43 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1188])).
% 1.24/1.43 tff(1190,plain,
% 1.24/1.43 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1189])).
% 1.24/1.43 tff(1191,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[248, 1190])).
% 1.24/1.43 tff(1192,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1193,plain,
% 1.24/1.43 (~(elem!1 = s(s(elem!1)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1192, 248])).
% 1.24/1.43 tff(1194,plain,
% 1.24/1.43 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1193, 1185])).
% 1.24/1.43 tff(1195,plain,
% 1.24/1.43 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1073, 1179, 131])).
% 1.24/1.43 tff(1196,plain,
% 1.24/1.43 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1195])).
% 1.24/1.43 tff(1197,plain,
% 1.24/1.43 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1196, 890])).
% 1.24/1.43 tff(1198,plain,
% 1.24/1.43 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1197])).
% 1.24/1.43 tff(1199,plain,
% 1.24/1.43 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1198])).
% 1.24/1.43 tff(1200,plain,
% 1.24/1.43 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[257, 1199])).
% 1.24/1.43 tff(1201,plain,
% 1.24/1.43 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1073, 1179, 131, 1027])).
% 1.24/1.43 tff(1202,plain,
% 1.24/1.43 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1201])).
% 1.24/1.43 tff(1203,plain,
% 1.24/1.43 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1202])).
% 1.24/1.43 tff(1204,plain,
% 1.24/1.43 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1203])).
% 1.24/1.43 tff(1205,plain,
% 1.24/1.43 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1161, 1204])).
% 1.24/1.43 tff(1206,plain,
% 1.24/1.43 (((~![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))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1207,plain,
% 1.24/1.43 ((~![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))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1208,plain,
% 1.24/1.43 ((~![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)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.24/1.43 tff(1209,plain,
% 1.24/1.43 ((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)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1208, 78])).
% 1.24/1.43 tff(1210,plain,
% 1.24/1.43 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1209, 1205, 1200])).
% 1.24/1.43 tff(1211,assumption,(b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.24/1.43 tff(1212,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.43 tff(1213,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1214,plain,
% 1.24/1.43 (((~b(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))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1215,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1214])).
% 1.24/1.43 tff(1216,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1215, 1213])).
% 1.24/1.43 tff(1217,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1218,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 1.24/1.44 tff(1219,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1218, 112, 1212, 1211, 332, 333])).
% 1.24/1.44 tff(1220,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | r(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,[]))).
% 1.24/1.44 tff(1221,plain,
% 1.24/1.44 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1220, 1210, 268, 333, 784])).
% 1.24/1.44 tff(1222,plain,
% 1.24/1.44 (((~![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)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1223,plain,
% 1.24/1.44 ((~![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)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1224,plain,
% 1.24/1.44 ((~![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))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.24/1.44 tff(1225,plain,
% 1.24/1.44 ((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))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1224, 78])).
% 1.24/1.44 tff(1226,plain,
% 1.24/1.44 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1225, 1221, 1194])).
% 1.24/1.44 tff(1227,plain,
% 1.24/1.44 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1226, 1183])).
% 1.24/1.44 tff(1228,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(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(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(z))) | (~r(s(s(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(s(s(elem!1)))))), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1229,plain,
% 1.24/1.44 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(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(s(s(elem!1)))))), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1230,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(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(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1229])).
% 1.24/1.44 tff(1231,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(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(s(s(elem!1)))))), s(s(s(z))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1230, 1228])).
% 1.24/1.44 tff(1232,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1233,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(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(s(s(elem!1)))))), s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.24/1.44 tff(1234,plain,
% 1.24/1.44 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1233, 31, 3, 1227, 790])).
% 1.24/1.44 tff(1235,plain,
% 1.24/1.44 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1234, 1178])).
% 1.24/1.44 tff(1236,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(1237,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(1238,assumption,(~r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(1239,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1240,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1241,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 1.24/1.44 tff(1242,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1241, 78, 1238, 1237, 1236])).
% 1.24/1.44 tff(1243,plain,(b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1244,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1243, 1235, 1176, 1042])).
% 1.24/1.44 tff(1245,plain,((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1246,plain,
% 1.24/1.44 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1245, 774, 672, 569, 726, 581, 443, 609, 761])).
% 1.24/1.44 tff(1247,plain,
% 1.24/1.44 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1246])).
% 1.24/1.44 tff(1248,plain,
% 1.24/1.44 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1247])).
% 1.24/1.44 tff(1249,plain,
% 1.24/1.44 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1248])).
% 1.24/1.44 tff(1250,plain,
% 1.24/1.44 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(elem!1))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1249])).
% 1.24/1.44 tff(1251,plain,
% 1.24/1.44 (r(z, s(s(s(s(s(elem!1)))))) <=> r(z, s(s(s(elem!1))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1250])).
% 1.24/1.44 tff(1252,plain,
% 1.24/1.44 (r(z, s(s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[761, 1251])).
% 1.24/1.44 tff(1253,plain,
% 1.24/1.44 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1246])).
% 1.24/1.44 tff(1254,plain,
% 1.24/1.44 (s(elem!1) = s(s(s(elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[145, 1253, 131])).
% 1.24/1.44 tff(1255,plain,
% 1.24/1.44 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1254])).
% 1.24/1.44 tff(1256,plain,
% 1.24/1.44 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.24/1.44 inference(symmetry,[status(thm)],[1255])).
% 1.24/1.44 tff(1257,plain,
% 1.24/1.44 (s(s(s(s(elem!1)))) = elem!1),
% 1.24/1.44 inference(transitivity,[status(thm)],[1247, 253, 1256, 247])).
% 1.24/1.44 tff(1258,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1257])).
% 1.24/1.44 tff(1259,plain,
% 1.24/1.44 ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1258])).
% 1.24/1.44 tff(1260,plain,
% 1.24/1.44 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1248])).
% 1.24/1.44 tff(1261,plain,
% 1.24/1.44 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[685, 1260])).
% 1.24/1.44 tff(1262,plain,
% 1.24/1.44 (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))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1248])).
% 1.24/1.44 tff(1263,plain,
% 1.24/1.44 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[672, 1262])).
% 1.24/1.44 tff(1264,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.44 tff(1265,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.24/1.44 tff(1266,plain,
% 1.24/1.44 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1265])).
% 1.24/1.44 tff(1267,plain,
% 1.24/1.44 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[216, 1266, 127, 1264])).
% 1.24/1.44 tff(1268,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[153, 1267])).
% 1.24/1.44 tff(1269,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1270,plain,
% 1.24/1.44 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1269, 1246])).
% 1.24/1.44 tff(1271,plain,
% 1.24/1.44 (r(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1248])).
% 1.24/1.44 tff(1272,plain,
% 1.24/1.44 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[772, 1271])).
% 1.24/1.44 tff(1273,assumption,(b(s(s(s(s(z)))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.44 tff(1274,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.44 tff(1275,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.44 tff(1276,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1277,plain,
% 1.24/1.44 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1278,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1277])).
% 1.24/1.44 tff(1279,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1278, 1276])).
% 1.24/1.44 tff(1280,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1281,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.24/1.44 tff(1282,plain,
% 1.24/1.44 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1281, 112, 4, 196, 1275, 1274])).
% 1.24/1.44 tff(1283,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1282, 1273])).
% 1.24/1.44 tff(1284,assumption,(~(s(s(s(s(z)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.44 tff(1285,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1286,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1287,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 1.24/1.44 tff(1288,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1287, 78, 1284, 1283])).
% 1.24/1.44 tff(1289,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1290,plain,
% 1.24/1.44 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1291,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1290])).
% 1.24/1.44 tff(1292,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.24/1.44 tff(1293,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1294,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.24/1.44 tff(1295,plain,
% 1.24/1.44 ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1294, 112, 4, 196])).
% 1.24/1.44 tff(1296,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1295, 1273])).
% 1.24/1.44 tff(1297,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[972, 78, 969, 1296])).
% 1.24/1.44 tff(1298,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.45 tff(1299,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), 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(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1300,plain,
% 1.24/1.45 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1301,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(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(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1300])).
% 1.24/1.45 tff(1302,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(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(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1301, 1299])).
% 1.24/1.45 tff(1303,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1304,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 1.24/1.45 tff(1305,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1304, 31, 1298, 1297, 1288])).
% 1.24/1.45 tff(1306,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(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))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1307,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1306, 1272, 1270, 647, 728, 1263, 1261])).
% 1.24/1.45 tff(1308,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1307, 1259])).
% 1.24/1.45 tff(1309,plain,
% 1.24/1.45 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1264])).
% 1.24/1.45 tff(1310,plain,
% 1.24/1.45 (s(elem!1) = s(s(s(elem!1)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[145, 1309, 131])).
% 1.24/1.45 tff(1311,plain,
% 1.24/1.45 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1310])).
% 1.24/1.45 tff(1312,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.24/1.45 tff(1313,plain,
% 1.24/1.45 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1312, 1073, 1311, 127, 1264])).
% 1.24/1.45 tff(1314,plain,
% 1.24/1.45 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1313])).
% 1.24/1.45 tff(1315,plain,
% 1.24/1.45 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[1314])).
% 1.24/1.45 tff(1316,plain,
% 1.24/1.45 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[132, 1315, 215])).
% 1.24/1.45 tff(1317,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.24/1.45 tff(1318,plain,
% 1.24/1.45 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.24/1.45 inference(symmetry,[status(thm)],[1317])).
% 1.24/1.45 tff(1319,plain,
% 1.24/1.45 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1318])).
% 1.24/1.45 tff(1320,plain,
% 1.24/1.45 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[56, 1319, 127, 1264])).
% 1.24/1.45 tff(1321,plain,
% 1.24/1.45 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1320])).
% 1.24/1.45 tff(1322,plain,
% 1.24/1.45 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.24/1.45 inference(symmetry,[status(thm)],[1321])).
% 1.24/1.45 tff(1323,plain,
% 1.24/1.45 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[1264])).
% 1.24/1.45 tff(1324,plain,
% 1.24/1.45 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1323])).
% 1.24/1.45 tff(1325,plain,
% 1.24/1.45 (s(s(s(s(s(elem!1))))) = s(z)),
% 1.24/1.45 inference(transitivity,[status(thm)],[1324, 132, 1322, 137])).
% 1.24/1.45 tff(1326,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[457, 1325])).
% 1.24/1.45 tff(1327,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1328,plain,
% 1.24/1.45 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1327, 1264])).
% 1.24/1.45 tff(1329,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1328, 1316])).
% 1.24/1.45 tff(1330,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1331,plain,
% 1.24/1.45 (~(s(s(s(s(z)))) = elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1330, 1246])).
% 1.24/1.45 tff(1332,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1333,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1334,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.24/1.45 tff(1335,plain,
% 1.24/1.45 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1334, 78])).
% 1.24/1.45 tff(1336,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1335, 1331, 1308])).
% 1.24/1.45 tff(1337,plain,
% 1.24/1.45 (elem!1 = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1073, 1311, 127, 1264])).
% 1.24/1.45 tff(1338,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1337])).
% 1.24/1.45 tff(1339,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.45 tff(1340,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 1.24/1.45 tff(1341,assumption,(~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.45 tff(1342,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1341, 1340])).
% 1.24/1.45 tff(1343,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), s(s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1344,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1343, 1336, 1246])).
% 1.24/1.45 tff(1345,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, 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(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1346,plain,
% 1.24/1.45 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1347,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, 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(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1346])).
% 1.24/1.45 tff(1348,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, 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(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1347, 1345])).
% 1.24/1.45 tff(1349,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1350,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 1.24/1.45 tff(1351,plain,
% 1.24/1.45 (~r(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1350, 31, 569, 1344, 1252])).
% 1.24/1.45 tff(1352,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[917, 78, 224, 1351])).
% 1.24/1.45 tff(1353,plain,
% 1.24/1.45 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[990, 1344, 581])).
% 1.24/1.45 tff(1354,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[953, 78, 1353, 950])).
% 1.24/1.45 tff(1355,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1356,plain,
% 1.24/1.45 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1357,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1356])).
% 1.24/1.45 tff(1358,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1357, 1355])).
% 1.24/1.45 tff(1359,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1360,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.24/1.45 tff(1361,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1360, 112, 724, 774, 591, 609, 1354, 1352])).
% 1.24/1.45 tff(1362,plain,(b(s(s(s(s(elem!1)))), s(z)) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1363,plain,
% 1.24/1.45 (b(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1362, 443, 569, 568])).
% 1.24/1.45 tff(1364,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[451, 1363, 443, 442, 431])).
% 1.24/1.45 tff(1365,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), 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(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1366,plain,
% 1.24/1.45 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1365, 569, 407, 405, 568])).
% 1.24/1.45 tff(1367,plain,
% 1.24/1.45 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[462, 1366])).
% 1.24/1.45 tff(1368,plain,
% 1.24/1.45 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[472, 1367, 3])).
% 1.24/1.45 tff(1369,plain,
% 1.24/1.45 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[384, 78, 381, 1368])).
% 1.24/1.45 tff(1370,plain,
% 1.24/1.45 (~r(s(s(s(z))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[693, 568, 1])).
% 1.24/1.45 tff(1371,plain,
% 1.24/1.45 (b(s(s(s(z))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[527, 1370])).
% 1.24/1.45 tff(1372,plain,
% 1.24/1.45 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[534, 112, 1371, 803, 1369])).
% 1.24/1.45 tff(1373,plain,
% 1.24/1.45 (r(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[494, 1372])).
% 1.24/1.45 tff(1374,plain,
% 1.24/1.45 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[661, 31, 568, 1373])).
% 1.24/1.45 tff(1375,plain,
% 1.24/1.45 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[299, 1374, 268])).
% 1.24/1.45 tff(1376,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(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))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1377,plain,
% 1.24/1.45 (((~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(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))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1378,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(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)))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1377])).
% 1.24/1.45 tff(1379,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(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))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1378, 1376])).
% 1.24/1.45 tff(1380,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1381,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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)))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.24/1.45 tff(1382,plain,
% 1.24/1.45 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1381, 31, 3, 1367])).
% 1.24/1.45 tff(1383,plain,
% 1.24/1.45 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[710, 78, 1382, 699])).
% 1.24/1.45 tff(1384,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1385,plain,
% 1.24/1.45 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(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(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(z, 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(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1386,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(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(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1385])).
% 1.24/1.45 tff(1387,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(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(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1386, 1384])).
% 1.24/1.46 tff(1388,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(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(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1389,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.24/1.46 tff(1390,plain,
% 1.24/1.46 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1389, 112, 1371, 803, 1383, 1369])).
% 1.24/1.46 tff(1391,plain,
% 1.24/1.46 (r(z, s(s(s(s(s(elem!1))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[322, 1390])).
% 1.24/1.46 tff(1392,assumption,(~(s(s(elem!1)) = s(s(s(z))))), introduced(assumption)).
% 1.24/1.46 tff(1393,plain,
% 1.24/1.46 (((~![X0: $i, 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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1394,plain,
% 1.24/1.46 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1395,plain,
% 1.24/1.46 (((~![X0: $i, X3: $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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1394])).
% 1.24/1.46 tff(1396,plain,
% 1.24/1.46 (((~![X0: $i, X3: $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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1395, 1393])).
% 1.24/1.46 tff(1397,plain,
% 1.24/1.46 ((~![X0: $i, X3: $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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1398,plain,
% 1.24/1.46 ((~![X0: $i, 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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 1.24/1.46 tff(1399,plain,
% 1.24/1.46 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1398, 31, 3, 812, 1])).
% 1.24/1.46 tff(1400,plain,
% 1.24/1.46 (b(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1008, 78, 1392, 1399])).
% 1.24/1.46 tff(1401,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1402,plain,
% 1.24/1.46 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1403,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1402])).
% 1.24/1.46 tff(1404,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1403, 1401])).
% 1.24/1.46 tff(1405,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1406,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.24/1.46 tff(1407,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1406, 112, 859, 803, 1400, 823])).
% 1.24/1.46 tff(1408,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1409,plain,
% 1.24/1.46 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1408, 1392, 1371, 803, 3, 1, 1391, 569])).
% 1.24/1.46 tff(1410,plain,
% 1.24/1.46 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[872, 1409, 248])).
% 1.24/1.46 tff(1411,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1412,plain,
% 1.24/1.46 (((~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(elem!1)))))) | (~b(s(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(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(elem!1)), s(s(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(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))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1413,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~b(s(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(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1412])).
% 1.24/1.46 tff(1414,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~b(s(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(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1413, 1411])).
% 1.24/1.46 tff(1415,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~b(s(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(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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1416,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 1.24/1.46 tff(1417,plain,
% 1.24/1.46 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1416, 112, 1410, 1375, 405])).
% 1.24/1.46 tff(1418,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.24/1.46 tff(1419,plain,
% 1.24/1.46 (s(z) = s(s(elem!1))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1418])).
% 1.24/1.46 tff(1420,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[150, 1419])).
% 1.24/1.46 tff(1421,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1422,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[768, 112, 789, 787, 442, 480])).
% 1.24/1.46 tff(1423,plain,((~r(s(s(s(z))), s(z))) | (~b(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)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1424,plain,
% 1.24/1.46 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1423, 1367, 405, 3])).
% 1.24/1.46 tff(1425,plain,
% 1.24/1.46 (b(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[429, 1424])).
% 1.24/1.46 tff(1426,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1427,plain,
% 1.24/1.46 (((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1428,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1427])).
% 1.24/1.46 tff(1429,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1428, 1426])).
% 1.24/1.46 tff(1430,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1431,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.24/1.46 tff(1432,plain,
% 1.24/1.46 (~b(s(s(elem!1)), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1431, 112, 1410, 1425, 1375, 405, 478])).
% 1.24/1.46 tff(1433,plain,
% 1.24/1.46 (((~![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)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1434,plain,
% 1.24/1.46 ((~![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)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1435,plain,
% 1.24/1.46 ((~![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))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.24/1.46 tff(1436,plain,
% 1.24/1.46 (r(s(s(elem!1)), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1435, 78, 1432, 1421])).
% 1.24/1.46 tff(1437,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.24/1.46 tff(1438,assumption,(r(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.24/1.46 tff(1439,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1440,plain,
% 1.24/1.46 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1441,plain,
% 1.24/1.46 (((~![X0: $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(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1440])).
% 1.24/1.46 tff(1442,plain,
% 1.24/1.46 (((~![X0: $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(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.24/1.47 tff(1443,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1444,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.24/1.47 tff(1445,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1444, 31, 464, 1438, 1437])).
% 1.24/1.47 tff(1446,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1447,plain,
% 1.24/1.47 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1446, 1436, 1367])).
% 1.24/1.47 tff(1448,plain,
% 1.24/1.47 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1025, 1447, 1417])).
% 1.24/1.47 tff(1449,plain,
% 1.24/1.47 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1448])).
% 1.24/1.47 tff(1450,plain,
% 1.24/1.47 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1448])).
% 1.24/1.47 tff(1451,plain,
% 1.24/1.47 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[145, 1450, 262])).
% 1.24/1.47 tff(1452,plain,
% 1.24/1.47 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1451])).
% 1.24/1.47 tff(1453,plain,
% 1.24/1.47 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1073, 1452, 131, 1449])).
% 1.24/1.47 tff(1454,plain,
% 1.24/1.47 (r(z, elem!1) <=> r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1453])).
% 1.24/1.47 tff(1455,plain,
% 1.24/1.47 (~(z = elem!1)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1090, 1448])).
% 1.24/1.47 tff(1456,plain,
% 1.24/1.47 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1073, 1452, 131])).
% 1.24/1.47 tff(1457,plain,
% 1.24/1.47 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1456])).
% 1.24/1.47 tff(1458,plain,
% 1.24/1.47 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1457])).
% 1.24/1.47 tff(1459,plain,
% 1.24/1.47 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[472, 464, 3])).
% 1.24/1.47 tff(1460,plain,
% 1.24/1.47 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[384, 78, 381, 1459])).
% 1.24/1.47 tff(1461,plain,
% 1.24/1.47 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[534, 112, 1371, 803, 1460])).
% 1.24/1.47 tff(1462,plain,
% 1.24/1.47 (r(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[494, 1461])).
% 1.24/1.47 tff(1463,plain,
% 1.24/1.47 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[661, 31, 568, 1462])).
% 1.24/1.47 tff(1464,plain,
% 1.24/1.47 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[299, 1463, 268])).
% 1.24/1.47 tff(1465,plain,
% 1.24/1.47 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1381, 31, 3, 464])).
% 1.24/1.47 tff(1466,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[710, 78, 1465, 699])).
% 1.24/1.47 tff(1467,plain,
% 1.24/1.47 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1389, 112, 1371, 803, 1466, 1460])).
% 1.24/1.47 tff(1468,plain,
% 1.24/1.47 (r(z, s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[322, 1467])).
% 1.24/1.47 tff(1469,plain,
% 1.24/1.47 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1408, 803, 1371, 1392, 3, 1, 1468, 569])).
% 1.24/1.47 tff(1470,plain,
% 1.24/1.47 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[872, 1469, 248])).
% 1.24/1.47 tff(1471,plain,
% 1.24/1.47 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1416, 112, 1470, 1464, 442])).
% 1.24/1.47 tff(1472,plain,
% 1.24/1.47 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1423, 464, 442, 3])).
% 1.24/1.47 tff(1473,plain,
% 1.24/1.47 (b(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[429, 1472])).
% 1.24/1.47 tff(1474,plain,
% 1.24/1.47 (~b(s(s(elem!1)), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1431, 112, 1470, 1473, 1464, 442, 478])).
% 1.24/1.47 tff(1475,plain,
% 1.24/1.47 (r(s(s(elem!1)), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1435, 78, 1474, 1421])).
% 1.24/1.47 tff(1476,plain,
% 1.24/1.47 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1446, 1475, 464])).
% 1.24/1.47 tff(1477,plain,
% 1.24/1.47 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1025, 1476, 1471])).
% 1.24/1.47 tff(1478,plain,
% 1.24/1.47 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1477])).
% 1.24/1.47 tff(1479,plain,
% 1.24/1.47 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1477])).
% 1.24/1.47 tff(1480,plain,
% 1.24/1.47 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[145, 1479, 262])).
% 1.24/1.47 tff(1481,plain,
% 1.24/1.47 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1480])).
% 1.24/1.47 tff(1482,plain,
% 1.24/1.47 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1073, 1481, 131, 1478])).
% 1.24/1.47 tff(1483,plain,
% 1.24/1.47 (b(elem!1, z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1482])).
% 1.24/1.47 tff(1484,plain,
% 1.24/1.47 ((~b(elem!1, z)) <=> (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1483])).
% 1.24/1.47 tff(1485,plain,
% 1.24/1.47 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1482])).
% 1.24/1.47 tff(1486,plain,
% 1.24/1.47 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1485, 775])).
% 1.24/1.47 tff(1487,plain,
% 1.24/1.47 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(z))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1486])).
% 1.24/1.47 tff(1488,plain,
% 1.24/1.47 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1487])).
% 1.24/1.47 tff(1489,plain,
% 1.24/1.47 (~(elem!1 = s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1041, 1488])).
% 1.24/1.47 tff(1490,plain,
% 1.24/1.47 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1073, 1481, 131])).
% 1.24/1.47 tff(1491,plain,
% 1.24/1.47 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1490])).
% 1.24/1.47 tff(1492,plain,
% 1.24/1.47 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1491])).
% 1.24/1.47 tff(1493,plain,
% 1.24/1.47 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1492])).
% 1.24/1.47 tff(1494,plain,
% 1.24/1.47 (~r(elem!1, s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1238, 1493])).
% 1.24/1.47 tff(1495,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1496,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1497,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.24/1.47 tff(1498,plain,
% 1.24/1.47 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1497, 78])).
% 1.24/1.47 tff(1499,plain,
% 1.24/1.47 (b(elem!1, s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1498, 1494, 1489])).
% 1.24/1.47 tff(1500,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1501,plain,
% 1.24/1.47 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1502,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1501])).
% 1.24/1.47 tff(1503,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1502, 1500])).
% 1.24/1.47 tff(1504,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1505,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 1.24/1.47 tff(1506,plain,
% 1.24/1.47 ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1505, 112])).
% 1.24/1.47 tff(1507,plain,
% 1.24/1.47 (~b(elem!1, z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1506, 1499, 803, 1371])).
% 1.24/1.47 tff(1508,plain,
% 1.24/1.47 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1507, 1484])).
% 1.24/1.47 tff(1509,plain,
% 1.24/1.47 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1510,plain,
% 1.24/1.47 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1509, 13])).
% 1.24/1.47 tff(1511,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1512,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1513,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.24/1.47 tff(1514,plain,
% 1.24/1.47 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 1508])).
% 1.24/1.47 tff(1515,plain,
% 1.24/1.47 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1481])).
% 1.24/1.47 tff(1516,plain,
% 1.24/1.47 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1478])).
% 1.24/1.47 tff(1517,plain,
% 1.24/1.47 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.24/1.47 inference(transitivity,[status(thm)],[1516, 132, 1515, 247])).
% 1.24/1.47 tff(1518,plain,
% 1.24/1.47 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1517])).
% 1.24/1.47 tff(1519,plain,
% 1.24/1.47 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1518])).
% 1.24/1.47 tff(1520,plain,
% 1.24/1.47 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1477])).
% 1.24/1.47 tff(1521,plain,
% 1.24/1.47 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1520, 1519])).
% 1.24/1.47 tff(1522,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1477])).
% 1.24/1.47 tff(1523,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1522])).
% 1.24/1.47 tff(1524,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1466, 1523])).
% 1.24/1.47 tff(1525,plain,
% 1.24/1.47 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1477])).
% 1.24/1.47 tff(1526,plain,
% 1.24/1.47 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1525])).
% 1.24/1.47 tff(1527,plain,
% 1.24/1.47 (b(s(s(elem!1)), s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1460, 1526])).
% 1.24/1.47 tff(1528,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1529,plain,
% 1.24/1.47 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1530,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1529])).
% 1.24/1.47 tff(1531,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1530, 1528])).
% 1.24/1.47 tff(1532,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1533,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 1.24/1.47 tff(1534,plain,
% 1.24/1.47 ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1533, 112])).
% 1.24/1.47 tff(1535,plain,
% 1.24/1.47 (~b(elem!1, s(s(elem!1)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1534, 1499, 1527, 1524])).
% 1.24/1.47 tff(1536,plain,
% 1.24/1.47 (((~![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))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1537,plain,
% 1.24/1.47 ((~![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))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1538,plain,
% 1.24/1.47 ((~![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)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.24/1.47 tff(1539,plain,
% 1.24/1.47 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1538, 78])).
% 1.24/1.47 tff(1540,plain,
% 1.24/1.47 (r(elem!1, s(s(elem!1)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1539, 1535, 1193])).
% 1.24/1.47 tff(1541,plain,
% 1.24/1.47 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1540, 1521])).
% 1.24/1.47 tff(1542,plain,
% 1.24/1.47 (((~![X0: $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(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(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(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1543,plain,
% 1.24/1.47 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1544,plain,
% 1.24/1.47 (((~![X0: $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(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(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(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1543])).
% 1.24/1.47 tff(1545,plain,
% 1.24/1.47 (((~![X0: $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(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(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(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1544, 1542])).
% 1.24/1.47 tff(1546,plain,
% 1.24/1.47 ((~![X0: $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(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1547,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 1.24/1.47 tff(1548,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1547, 31, 1468, 1541, 1514])).
% 1.24/1.47 tff(1549,plain,((~b(z, s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1550,plain,
% 1.24/1.47 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1549, 1392, 803, 405, 248, 1367, 3, 1, 569, 568])).
% 1.24/1.47 tff(1551,plain,
% 1.24/1.47 (r(elem!1, s(s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1550, 1458])).
% 1.24/1.47 tff(1552,plain,
% 1.24/1.47 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1453])).
% 1.24/1.47 tff(1553,plain,
% 1.24/1.47 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1552, 1113])).
% 1.24/1.47 tff(1554,plain,
% 1.24/1.47 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1553])).
% 1.24/1.47 tff(1555,plain,
% 1.24/1.47 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1554])).
% 1.24/1.47 tff(1556,plain,
% 1.24/1.47 (~(elem!1 = s(z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1124, 1555])).
% 1.24/1.47 tff(1557,plain,
% 1.24/1.47 (~r(z, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[536, 1367, 3])).
% 1.24/1.47 tff(1558,plain,
% 1.24/1.47 (b(z, s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[182, 1557])).
% 1.24/1.47 tff(1559,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.24/1.47 tff(1560,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.24/1.47 tff(1561,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1562,plain,
% 1.24/1.47 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1563,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1562])).
% 1.24/1.47 tff(1564,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1563, 1561])).
% 1.24/1.48 tff(1565,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1566,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.24/1.48 tff(1567,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1566, 31, 1560, 1559, 3])).
% 1.24/1.48 tff(1568,plain,((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1569,plain,
% 1.24/1.48 (~r(elem!1, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1568, 1551, 3])).
% 1.24/1.48 tff(1570,plain,
% 1.24/1.48 (b(elem!1, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1139, 1569, 1556])).
% 1.24/1.48 tff(1571,plain,
% 1.24/1.48 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(1572,plain,
% 1.24/1.48 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.24/1.48 inference(symmetry,[status(thm)],[1571])).
% 1.24/1.48 tff(1573,plain,
% 1.24/1.48 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1572])).
% 1.24/1.48 tff(1574,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.24/1.48 tff(1575,plain,
% 1.24/1.48 (~(s(z) = elem!1)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 1.24/1.48 tff(1576,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.24/1.48 tff(1577,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.24/1.48 tff(1578,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1579,plain,
% 1.24/1.48 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1580,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1579])).
% 1.24/1.48 tff(1581,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1580, 1578])).
% 1.24/1.48 tff(1582,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1583,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 1.24/1.48 tff(1584,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1583, 112, 1576, 102, 803, 1577, 18])).
% 1.24/1.48 tff(1585,plain,((~b(s(z), s(s(s(z))))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1586,plain,
% 1.24/1.48 (~b(s(z), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1585, 1577, 803, 1576, 18])).
% 1.24/1.48 tff(1587,plain,
% 1.24/1.48 (r(s(z), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[98, 1586, 65])).
% 1.24/1.48 tff(1588,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1589,plain,
% 1.24/1.48 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1590,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1589])).
% 1.24/1.48 tff(1591,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1590, 1588])).
% 1.24/1.48 tff(1592,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1593,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.24/1.48 tff(1594,plain,
% 1.24/1.48 (~r(s(z), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1593, 31, 1587, 1560])).
% 1.24/1.48 tff(1595,plain,
% 1.24/1.48 (((~![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))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1596,plain,
% 1.24/1.48 ((~![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))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1597,plain,
% 1.24/1.48 ((~![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)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 1.24/1.48 tff(1598,plain,
% 1.24/1.48 ((s(z) = elem!1) | b(s(z), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1597, 78, 1594])).
% 1.24/1.48 tff(1599,plain,
% 1.24/1.48 (b(s(z), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1598, 1575])).
% 1.24/1.48 tff(1600,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1601,plain,
% 1.24/1.48 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1602,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1601])).
% 1.24/1.48 tff(1603,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1602, 1600])).
% 1.24/1.48 tff(1604,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1605,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.24/1.48 tff(1606,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1605, 112, 1576, 1577, 18, 1599])).
% 1.24/1.48 tff(1607,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | (~r(elem!1, s(s(s(z))))) | (s(z) = s(s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1608,plain,
% 1.24/1.48 ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | (~r(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1607, 61])).
% 1.24/1.48 tff(1609,plain,
% 1.24/1.48 (~b(z, elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1608, 1570, 1558, 803, 1556, 1551])).
% 1.24/1.48 tff(1610,plain,
% 1.24/1.48 (r(z, elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1109, 1609, 1455])).
% 1.24/1.48 tff(1611,plain,
% 1.24/1.48 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1610, 1454])).
% 1.24/1.48 tff(1612,plain,
% 1.24/1.48 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1453])).
% 1.24/1.48 tff(1613,plain,
% 1.24/1.48 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1456])).
% 1.24/1.48 tff(1614,plain,
% 1.24/1.48 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1613, 890])).
% 1.24/1.48 tff(1615,plain,
% 1.24/1.48 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(symmetry,[status(thm)],[1614])).
% 1.24/1.48 tff(1616,plain,
% 1.24/1.48 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1615])).
% 1.24/1.48 tff(1617,plain,
% 1.24/1.48 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[257, 1616])).
% 1.24/1.48 tff(1618,plain,
% 1.24/1.48 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1448])).
% 1.24/1.48 tff(1619,plain,
% 1.24/1.48 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1618])).
% 1.24/1.48 tff(1620,plain,
% 1.24/1.48 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1193, 1619])).
% 1.24/1.48 tff(1621,assumption,(r(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.24/1.48 tff(1622,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.24/1.48 tff(1623,plain,
% 1.24/1.48 (((~![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(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(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1624,plain,
% 1.24/1.48 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1625,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(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(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1624])).
% 1.24/1.48 tff(1626,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(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(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1625, 1623])).
% 1.24/1.48 tff(1627,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, elem!1)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1628,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 1.24/1.48 tff(1629,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1628, 31, 1622, 1621, 302])).
% 1.24/1.48 tff(1630,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1631,plain,
% 1.24/1.48 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1630, 1610, 1391])).
% 1.24/1.48 tff(1632,plain,
% 1.24/1.48 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1225, 1631, 1620])).
% 1.24/1.48 tff(1633,plain,
% 1.24/1.48 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1220, 1632, 268, 1375, 301])).
% 1.24/1.48 tff(1634,plain,
% 1.24/1.48 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1209, 1633, 1617])).
% 1.24/1.48 tff(1635,plain,
% 1.24/1.48 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1634, 1612])).
% 1.24/1.48 tff(1636,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1103, 31, 569, 1635, 1611])).
% 1.24/1.48 tff(1637,plain,((s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (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(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1638,plain,
% 1.24/1.48 (s(s(elem!1)) = s(s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1637, 569, 301, 579, 3, 248, 1, 568])).
% 1.24/1.48 tff(1639,plain,
% 1.24/1.48 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[534, 112, 1371, 579, 1369])).
% 1.24/1.48 tff(1640,plain,
% 1.24/1.48 (r(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[494, 1639])).
% 1.24/1.48 tff(1641,plain,
% 1.24/1.48 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[661, 31, 568, 1640])).
% 1.24/1.48 tff(1642,plain,
% 1.24/1.48 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[299, 1641, 268])).
% 1.24/1.48 tff(1643,plain,
% 1.24/1.48 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1638])).
% 1.24/1.48 tff(1644,plain,
% 1.24/1.48 (s(elem!1) = s(s(z))),
% 1.24/1.48 inference(transitivity,[status(thm)],[145, 1643, 55])).
% 1.24/1.48 tff(1645,plain,
% 1.24/1.48 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1644])).
% 1.24/1.48 tff(1646,plain,
% 1.24/1.48 (elem!1 = s(z)),
% 1.24/1.48 inference(transitivity,[status(thm)],[1073, 1645, 137])).
% 1.24/1.48 tff(1647,plain,
% 1.24/1.48 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1638])).
% 1.24/1.48 tff(1648,plain,
% 1.24/1.48 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.48 tff(1649,plain,
% 1.24/1.48 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.24/1.48 inference(symmetry,[status(thm)],[1648])).
% 1.24/1.48 tff(1650,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1649, 1646])).
% 1.24/1.48 tff(1651,plain,
% 1.24/1.48 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.48 inference(symmetry,[status(thm)],[1650])).
% 1.24/1.48 tff(1652,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), elem!1)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1425, 1651])).
% 1.24/1.48 tff(1653,plain,
% 1.24/1.48 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1389, 112, 1371, 579, 1383, 1369])).
% 1.24/1.48 tff(1654,plain,
% 1.24/1.48 (r(z, s(s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[322, 1653])).
% 1.24/1.48 tff(1655,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1656,plain,
% 1.24/1.48 (((~b(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))))))) | (~b(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1657,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1656])).
% 1.24/1.49 tff(1658,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1657, 1655])).
% 1.24/1.49 tff(1659,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(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(z), s(s(s(s(s(elem!1))))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1660,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 1.24/1.49 tff(1661,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1660, 112, 751, 333, 442, 539])).
% 1.24/1.49 tff(1662,plain,((~b(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1663,plain,
% 1.24/1.49 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1662, 1642, 405, 478])).
% 1.24/1.49 tff(1664,plain,
% 1.24/1.49 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[749, 1663])).
% 1.24/1.49 tff(1665,plain,
% 1.24/1.49 (((~![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(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), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1666,plain,
% 1.24/1.49 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1667,plain,
% 1.24/1.49 (((~![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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1666])).
% 1.24/1.49 tff(1668,plain,
% 1.24/1.49 (((~![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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1667, 1665])).
% 1.24/1.49 tff(1669,plain,
% 1.24/1.49 ((~![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(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1670,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.24/1.49 tff(1671,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1670, 31, 592, 302, 731])).
% 1.24/1.49 tff(1672,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1673,plain,
% 1.24/1.49 (~r(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1672, 1664, 1654])).
% 1.24/1.49 tff(1674,plain,
% 1.24/1.49 (b(s(z), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[608, 1673])).
% 1.24/1.49 tff(1675,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1676,plain,
% 1.24/1.49 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1677,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1676])).
% 1.24/1.49 tff(1678,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1677, 1675])).
% 1.24/1.49 tff(1679,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1680,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.24/1.49 tff(1681,plain,
% 1.24/1.49 (~b(s(z), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1680, 112, 1371, 579, 1674])).
% 1.24/1.49 tff(1682,plain,
% 1.24/1.49 (r(s(z), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[99, 1681])).
% 1.24/1.49 tff(1683,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.49 tff(1684,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.49 tff(1685,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1686,plain,
% 1.24/1.49 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1687,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1686])).
% 1.24/1.49 tff(1688,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1687, 1685])).
% 1.24/1.49 tff(1689,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1690,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 1.24/1.49 tff(1691,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1690, 112, 859, 803, 1683, 1684])).
% 1.24/1.49 tff(1692,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1693,plain,
% 1.24/1.49 (~b(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1692, 1683, 803, 859])).
% 1.24/1.49 tff(1694,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[917, 78, 224, 1693])).
% 1.24/1.49 tff(1695,plain,
% 1.24/1.49 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[534, 112, 859, 803, 762])).
% 1.24/1.49 tff(1696,plain,
% 1.24/1.49 (r(s(s(s(s(s(elem!1))))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[494, 1695])).
% 1.24/1.49 tff(1697,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(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(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1698,plain,
% 1.24/1.49 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1699,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), 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))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1698])).
% 1.24/1.49 tff(1700,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), 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))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1699, 1697])).
% 1.24/1.49 tff(1701,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1702,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1701, 1700])).
% 1.24/1.49 tff(1703,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1702, 31, 464, 1696, 1694])).
% 1.24/1.49 tff(1704,plain,
% 1.24/1.49 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[936, 78, 1703])).
% 1.24/1.49 tff(1705,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1704, 905])).
% 1.24/1.49 tff(1706,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1707,plain,
% 1.24/1.49 (((~b(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(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(s(z)))), 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(s(s(elem!1)))))))) <=> ((~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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1708,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(s(z)))), 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(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1707])).
% 1.34/1.50 tff(1709,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(s(z)))), 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(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1708, 1706])).
% 1.34/1.50 tff(1710,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(s(z)))), 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(s(s(elem!1))))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1711,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 1.34/1.50 tff(1712,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1711, 112, 406, 762, 1683, 1705])).
% 1.34/1.50 tff(1713,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1714,plain,
% 1.34/1.50 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1713, 1383, 1369, 889, 1638, 1367, 579, 1371])).
% 1.34/1.50 tff(1715,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.50 tff(1716,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.50 tff(1717,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[972, 78, 969, 1716, 1715])).
% 1.34/1.50 tff(1718,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1719,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1718, 1714])).
% 1.34/1.50 tff(1720,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.50 tff(1721,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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1722,plain,
% 1.34/1.50 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1723,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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1722])).
% 1.34/1.50 tff(1724,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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1723, 1721])).
% 1.34/1.50 tff(1725,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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1726,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 1.34/1.50 tff(1727,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1726, 31, 85, 981, 1720])).
% 1.34/1.50 tff(1728,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1729,plain,
% 1.34/1.50 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1728, 1719, 1682])).
% 1.34/1.50 tff(1730,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.34/1.50 tff(1731,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.34/1.50 tff(1732,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[953, 78, 1731, 950, 1730])).
% 1.34/1.50 tff(1733,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1734,plain,
% 1.34/1.50 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1733, 1729])).
% 1.34/1.50 tff(1735,plain,
% 1.34/1.50 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[892])).
% 1.34/1.50 tff(1736,plain,
% 1.34/1.50 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1735])).
% 1.34/1.50 tff(1737,plain,
% 1.34/1.50 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1736])).
% 1.34/1.50 tff(1738,plain,
% 1.34/1.50 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1737])).
% 1.34/1.50 tff(1739,plain,
% 1.34/1.50 (b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[539, 1738])).
% 1.34/1.50 tff(1740,plain,
% 1.34/1.50 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[891])).
% 1.34/1.50 tff(1741,plain,
% 1.34/1.50 (s(elem!1) = s(s(z))),
% 1.34/1.50 inference(transitivity,[status(thm)],[145, 1740, 55])).
% 1.34/1.50 tff(1742,plain,
% 1.34/1.50 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1741])).
% 1.34/1.50 tff(1743,plain,
% 1.34/1.50 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1742])).
% 1.34/1.50 tff(1744,plain,
% 1.34/1.50 (s(z) = elem!1),
% 1.34/1.50 inference(transitivity,[status(thm)],[138, 1743, 247])).
% 1.34/1.50 tff(1745,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1744])).
% 1.34/1.50 tff(1746,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1745])).
% 1.34/1.50 tff(1747,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.34/1.50 tff(1748,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(z))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 1.34/1.50 tff(1749,plain,
% 1.34/1.50 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1736])).
% 1.34/1.50 tff(1750,plain,
% 1.34/1.50 (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(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1749])).
% 1.34/1.50 tff(1751,plain,
% 1.34/1.50 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[442, 1750])).
% 1.34/1.50 tff(1752,plain,
% 1.34/1.50 (b(s(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))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1736])).
% 1.34/1.50 tff(1753,plain,
% 1.34/1.50 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1752])).
% 1.34/1.50 tff(1754,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[333, 1753])).
% 1.34/1.50 tff(1755,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.50 tff(1756,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1757,plain,
% 1.34/1.50 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1758,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1757])).
% 1.34/1.50 tff(1759,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.34/1.50 tff(1760,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1761,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.34/1.50 tff(1762,plain,
% 1.34/1.50 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1761, 112, 906, 1755])).
% 1.34/1.50 tff(1763,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1762, 1754, 1751, 1748, 1739])).
% 1.34/1.50 tff(1764,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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,[]))).
% 1.34/1.50 tff(1765,plain,
% 1.34/1.50 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1764, 1734, 478, 1638, 1652, 1642, 405])).
% 1.34/1.50 tff(1766,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1736])).
% 1.34/1.50 tff(1767,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1766])).
% 1.34/1.50 tff(1768,plain,
% 1.34/1.50 ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1767])).
% 1.34/1.50 tff(1769,plain,
% 1.34/1.50 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1341, 1768])).
% 1.34/1.50 tff(1770,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[893, 1736])).
% 1.34/1.50 tff(1771,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1770, 890])).
% 1.34/1.50 tff(1772,plain,
% 1.34/1.50 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1771])).
% 1.34/1.50 tff(1773,plain,
% 1.34/1.50 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1772])).
% 1.34/1.50 tff(1774,plain,
% 1.34/1.50 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[265, 1773])).
% 1.34/1.50 tff(1775,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.50 tff(1776,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1777,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1778,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.34/1.50 tff(1779,plain,
% 1.34/1.50 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1778, 78, 1775])).
% 1.34/1.50 tff(1780,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1779, 1774, 1769])).
% 1.34/1.50 tff(1781,plain,(b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1782,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1781, 1765, 1638, 257])).
% 1.34/1.50 tff(1783,plain,
% 1.34/1.50 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1736])).
% 1.34/1.50 tff(1784,plain,
% 1.34/1.50 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.34/1.50 inference(symmetry,[status(thm)],[1783])).
% 1.34/1.50 tff(1785,plain,
% 1.34/1.50 (r(s(s(s(s(s(z))))), z)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[568, 1784])).
% 1.34/1.50 tff(1786,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.34/1.50 tff(1787,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1786, 1785])).
% 1.34/1.50 tff(1788,plain,(r(s(s(s(s(s(z))))), z) | (~r(s(s(s(s(elem!1)))), z)) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1789,plain,
% 1.34/1.50 (r(s(s(s(s(s(z))))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1788, 1638, 568])).
% 1.34/1.50 tff(1790,plain,
% 1.34/1.50 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[982, 1767])).
% 1.34/1.50 tff(1791,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.34/1.50 tff(1792,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.34/1.50 tff(1793,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(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1794,plain,
% 1.34/1.50 (((~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1795,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(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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1794])).
% 1.34/1.50 tff(1796,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(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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1795, 1793])).
% 1.34/1.50 tff(1797,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(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))))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1798,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 1.34/1.51 tff(1799,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1798, 31, 1792, 1791, 1790])).
% 1.34/1.51 tff(1800,plain,((~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(elem!1)))))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1801,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1800, 1789, 1782, 1638])).
% 1.34/1.51 tff(1802,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[917, 78, 224, 1801])).
% 1.34/1.51 tff(1803,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1360, 112, 1371, 579, 1558, 1674, 1734, 1802])).
% 1.34/1.51 tff(1804,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1805,plain,
% 1.34/1.51 (~r(z, s(s(s(s(elem!1)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1804, 568, 301, 3, 248, 1, 249])).
% 1.34/1.51 tff(1806,plain,
% 1.34/1.51 (b(z, s(s(s(s(elem!1)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[356, 1805])).
% 1.34/1.51 tff(1807,plain,
% 1.34/1.51 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[638, 18, 249, 568])).
% 1.34/1.51 tff(1808,plain,
% 1.34/1.51 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[547, 18, 539, 2])).
% 1.34/1.51 tff(1809,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[429, 1808, 1807])).
% 1.34/1.51 tff(1810,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(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)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1811,plain,
% 1.34/1.51 (~b(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1810, 1806, 478, 249, 568])).
% 1.34/1.51 tff(1812,plain,
% 1.34/1.51 (r(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[182, 1811])).
% 1.34/1.51 tff(1813,plain,
% 1.34/1.51 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[536, 1812, 3])).
% 1.34/1.51 tff(1814,plain,
% 1.34/1.51 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[462, 1813])).
% 1.34/1.51 tff(1815,plain,
% 1.34/1.51 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[451, 1814, 405, 407])).
% 1.34/1.51 tff(1816,plain,
% 1.34/1.51 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[429, 1815])).
% 1.34/1.51 tff(1817,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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1818,plain,
% 1.34/1.51 (((~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)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1819,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(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)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1818])).
% 1.34/1.51 tff(1820,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(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)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1819, 1817])).
% 1.34/1.51 tff(1821,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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1822,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 1.34/1.51 tff(1823,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1822, 31, 1812, 1816, 568])).
% 1.34/1.51 tff(1824,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1825,plain,
% 1.34/1.51 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1824, 3, 249, 301, 248, 1])).
% 1.34/1.51 tff(1826,plain,
% 1.34/1.51 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[398, 1825])).
% 1.34/1.51 tff(1827,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.34/1.51 tff(1828,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1829,plain,
% 1.34/1.51 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1830,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1829])).
% 1.34/1.51 tff(1831,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1830, 1828])).
% 1.34/1.51 tff(1832,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1833,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 1.34/1.51 tff(1834,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1833, 112, 18, 19, 1827, 673])).
% 1.34/1.51 tff(1835,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1836,plain,
% 1.34/1.51 (~b(s(z), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1835, 538, 430, 1826])).
% 1.34/1.51 tff(1837,plain,
% 1.34/1.51 (r(s(z), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[608, 1836])).
% 1.34/1.51 tff(1838,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(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))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1839,plain,
% 1.34/1.51 (((~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))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1840,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(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)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1839])).
% 1.34/1.51 tff(1841,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(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))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1840, 1838])).
% 1.34/1.51 tff(1842,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(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1843,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 1.34/1.51 tff(1844,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1843, 31, 1837, 463, 567])).
% 1.34/1.51 tff(1845,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1846,plain,
% 1.34/1.51 (~r(s(s(s(z))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1845, 301, 249, 1, 248])).
% 1.34/1.51 tff(1847,plain,
% 1.34/1.51 (b(s(s(s(z))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[83, 1846])).
% 1.34/1.51 tff(1848,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), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), 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(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))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1849,plain,
% 1.34/1.51 (((~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(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(1850,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), 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(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1849])).
% 1.34/1.51 tff(1851,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), 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(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1850, 1848])).
% 1.34/1.51 tff(1852,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), 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))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1853,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 1.34/1.51 tff(1854,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1853, 31, 85, 408, 249])).
% 1.34/1.51 tff(1855,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,[]))).
% 1.34/1.51 tff(1856,plain,
% 1.34/1.51 (~r(s(z), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1855, 408, 249])).
% 1.34/1.51 tff(1857,plain,
% 1.34/1.51 (b(s(z), s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[99, 1856])).
% 1.34/1.51 tff(1858,plain,
% 1.34/1.51 (~r(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[589, 569, 408])).
% 1.34/1.51 tff(1859,plain,
% 1.34/1.51 (b(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[182, 1858])).
% 1.34/1.51 tff(1860,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1861,plain,
% 1.34/1.51 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1862,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1861])).
% 1.34/1.51 tff(1863,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1862, 1860])).
% 1.34/1.51 tff(1864,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1865,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 1.34/1.51 tff(1866,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1865, 112, 102, 803, 101, 18])).
% 1.34/1.51 tff(1867,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1868,plain,
% 1.34/1.51 (~b(z, s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1867, 1859, 101, 1857])).
% 1.34/1.51 tff(1869,plain,
% 1.34/1.51 (r(z, s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[515, 1868])).
% 1.34/1.51 tff(1870,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(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1871,plain,
% 1.34/1.51 (((~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(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1872,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(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1871])).
% 1.34/1.51 tff(1873,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(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1872, 1870])).
% 1.34/1.51 tff(1874,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(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1875,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 1.34/1.51 tff(1876,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1875, 31, 1869, 408, 569, 249])).
% 1.34/1.51 tff(1877,plain,((~r(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(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1878,plain,
% 1.34/1.52 (~r(z, s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1877, 408, 249, 101])).
% 1.34/1.52 tff(1879,plain,
% 1.34/1.52 (b(z, s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[356, 1878])).
% 1.34/1.52 tff(1880,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(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(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)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1881,plain,
% 1.34/1.52 (((~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(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)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1882,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(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(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))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1881])).
% 1.34/1.52 tff(1883,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(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(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)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1882, 1880])).
% 1.34/1.52 tff(1884,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(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)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1885,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(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))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.34/1.52 tff(1886,plain,
% 1.34/1.52 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1885, 31, 464, 408])).
% 1.34/1.52 tff(1887,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.52 tff(1888,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(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))))))))) <=> ((~![X0: $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(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1889,plain,
% 1.34/1.52 (((~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(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))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1890,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(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(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)))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1889])).
% 1.34/1.52 tff(1891,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(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(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))))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1890, 1888])).
% 1.34/1.52 tff(1892,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(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))))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1893,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1892, 1891])).
% 1.34/1.52 tff(1894,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1893, 31, 464, 408, 1887])).
% 1.34/1.52 tff(1895,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,[]))).
% 1.34/1.52 tff(1896,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1895, 408, 464])).
% 1.34/1.52 tff(1897,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[299, 1896, 271])).
% 1.34/1.52 tff(1898,plain,
% 1.34/1.52 (~r(z, s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[589, 162, 408])).
% 1.34/1.52 tff(1899,plain,
% 1.34/1.52 (b(z, s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[356, 1898])).
% 1.34/1.52 tff(1900,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(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))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1901,plain,
% 1.34/1.52 (((~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))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1902,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(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)))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1901])).
% 1.34/1.52 tff(1903,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(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))))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1902, 1900])).
% 1.34/1.52 tff(1904,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(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))))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1905,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1904, 1903])).
% 1.34/1.52 tff(1906,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1905, 31, 162, 464, 302])).
% 1.34/1.52 tff(1907,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1908,plain,
% 1.34/1.52 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1907, 162, 464])).
% 1.34/1.52 tff(1909,plain,
% 1.34/1.52 (b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[322, 1908])).
% 1.34/1.52 tff(1910,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[342, 1909, 1899, 1897, 271, 1886])).
% 1.34/1.52 tff(1911,plain,((~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1912,plain,
% 1.34/1.52 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1911, 162, 408, 271])).
% 1.34/1.52 tff(1913,plain,
% 1.34/1.52 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[462, 1912])).
% 1.34/1.52 tff(1914,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1915,plain,
% 1.34/1.52 (((~b(s(s(s(z))), s(z))) | (~b(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(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(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1916,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(elem!1))))), s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1915])).
% 1.34/1.52 tff(1917,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.34/1.52 tff(1918,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1919,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.34/1.52 tff(1920,plain,
% 1.34/1.52 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1919, 112, 1857, 101, 1913])).
% 1.34/1.52 tff(1921,plain,
% 1.34/1.52 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[384, 78, 381, 1920])).
% 1.34/1.52 tff(1922,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[291, 31, 249, 1921])).
% 1.34/1.52 tff(1923,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[299, 1922, 271])).
% 1.34/1.52 tff(1924,plain,
% 1.34/1.52 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[342, 1923, 301, 271, 2])).
% 1.34/1.52 tff(1925,plain,
% 1.34/1.52 (r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[322, 1924])).
% 1.34/1.52 tff(1926,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(z))) | (~r(z, 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(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1927,plain,
% 1.34/1.52 (((~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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1928,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(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1927])).
% 1.34/1.52 tff(1929,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(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1928, 1926])).
% 1.34/1.52 tff(1930,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(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))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1931,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 1.34/1.52 tff(1932,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1931, 31, 162, 302, 731])).
% 1.34/1.52 tff(1933,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,[]))).
% 1.34/1.52 tff(1934,plain,
% 1.34/1.52 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1933, 1925, 162])).
% 1.34/1.52 tff(1935,plain,
% 1.34/1.52 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[749, 1934])).
% 1.34/1.52 tff(1936,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1937,plain,
% 1.34/1.52 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(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(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1938,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1937])).
% 1.34/1.52 tff(1939,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.34/1.52 tff(1940,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1941,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.34/1.52 tff(1942,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1941, 112, 1857, 101, 1913, 1935, 406])).
% 1.34/1.52 tff(1943,plain,((~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | r(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)))))) | (~b(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)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1944,plain,
% 1.34/1.52 (~r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1943, 1879, 406, 301, 268, 101, 249, 408])).
% 1.34/1.53 tff(1945,plain,
% 1.34/1.53 (b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[182, 1944])).
% 1.34/1.53 tff(1946,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[638, 1945, 249, 408])).
% 1.34/1.53 tff(1947,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[398, 1946])).
% 1.34/1.53 tff(1948,plain,
% 1.34/1.53 ((elem!1 = z) <=> (z = elem!1)),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(1949,plain,
% 1.34/1.53 (~r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1943, 2, 406, 301, 268, 101, 249, 408])).
% 1.34/1.53 tff(1950,plain,
% 1.34/1.53 (b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[182, 1949])).
% 1.34/1.53 tff(1951,plain,
% 1.34/1.53 (~b(z, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1867, 1950, 101, 1857])).
% 1.34/1.53 tff(1952,plain,
% 1.34/1.53 (r(z, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[515, 1951])).
% 1.34/1.53 tff(1953,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.34/1.53 tff(1954,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(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1955,plain,
% 1.34/1.53 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1956,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(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1955])).
% 1.34/1.53 tff(1957,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(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1956, 1954])).
% 1.34/1.53 tff(1958,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(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1959,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(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 1.34/1.53 tff(1960,plain,
% 1.34/1.53 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1959, 31, 408, 249, 1953])).
% 1.34/1.53 tff(1961,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[872, 1960, 248])).
% 1.34/1.53 tff(1962,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(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1963,plain,
% 1.34/1.53 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1964,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(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(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(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1963])).
% 1.34/1.53 tff(1965,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(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(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(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1964, 1962])).
% 1.34/1.53 tff(1966,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(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1967,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 1.34/1.53 tff(1968,plain,
% 1.34/1.53 (~r(z, s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1967, 31, 20, 1953])).
% 1.34/1.53 tff(1969,plain,
% 1.34/1.53 (b(z, s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[841, 1968])).
% 1.34/1.53 tff(1970,plain,
% 1.34/1.53 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(1971,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.53 tff(1972,plain,
% 1.34/1.53 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1971, 1970])).
% 1.34/1.53 tff(1973,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[248, 1972])).
% 1.34/1.53 tff(1974,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,[]))).
% 1.34/1.53 tff(1975,plain,
% 1.34/1.53 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1974, 248])).
% 1.34/1.53 tff(1976,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(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1977,plain,
% 1.34/1.53 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1978,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(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1977])).
% 1.34/1.53 tff(1979,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(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1978, 1976])).
% 1.34/1.53 tff(1980,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(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1981,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(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 1.34/1.53 tff(1982,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1981, 31, 249, 1953])).
% 1.34/1.53 tff(1983,plain,
% 1.34/1.53 (((~![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))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1984,plain,
% 1.34/1.53 ((~![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))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1985,plain,
% 1.34/1.53 ((~![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)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 1.34/1.53 tff(1986,plain,
% 1.34/1.53 ((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)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1985, 78])).
% 1.34/1.53 tff(1987,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1986, 1982, 1975])).
% 1.34/1.53 tff(1988,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.53 tff(1989,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.53 tff(1990,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.34/1.53 tff(1991,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), 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)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1992,plain,
% 1.34/1.53 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1993,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1992])).
% 1.34/1.53 tff(1994,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), 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)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1993, 1991])).
% 1.34/1.53 tff(1995,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1996,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 1.34/1.53 tff(1997,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1996, 112, 1990, 1989, 2, 1988])).
% 1.34/1.53 tff(1998,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1999,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1998, 1987, 1969, 2, 1961])).
% 1.34/1.53 tff(2000,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = 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(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2001,plain,
% 1.34/1.53 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2000, 2, 248, 408, 249, 1952])).
% 1.34/1.53 tff(2002,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1008, 78, 1392, 2001])).
% 1.34/1.53 tff(2003,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2004,plain,
% 1.34/1.53 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2005,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2004])).
% 1.34/1.53 tff(2006,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2005, 2003])).
% 1.34/1.53 tff(2007,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2008,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 1.34/1.53 tff(2009,plain,
% 1.34/1.53 (~b(s(s(elem!1)), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2008, 112, 1857, 101, 2002])).
% 1.34/1.53 tff(2010,plain,
% 1.34/1.53 (r(s(s(elem!1)), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1435, 78, 2009, 1421])).
% 1.34/1.53 tff(2011,plain,
% 1.34/1.53 (~b(z, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1867, 18, 101, 102])).
% 1.34/1.53 tff(2012,plain,
% 1.34/1.53 (r(z, s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[515, 2011])).
% 1.34/1.53 tff(2013,plain,
% 1.34/1.53 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1919, 112, 102, 101, 443])).
% 1.34/1.53 tff(2014,plain,
% 1.34/1.53 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[384, 78, 381, 2013])).
% 1.34/1.53 tff(2015,plain,
% 1.34/1.53 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[310, 2014, 2012])).
% 1.34/1.53 tff(2016,plain,
% 1.34/1.53 (b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[322, 2015])).
% 1.34/1.53 tff(2017,plain,
% 1.34/1.53 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[342, 2016, 301, 271, 2])).
% 1.34/1.53 tff(2018,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[299, 2017, 271])).
% 1.34/1.53 tff(2019,plain,
% 1.34/1.53 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[759, 2016, 18, 443])).
% 1.34/1.53 tff(2020,plain,
% 1.34/1.53 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[749, 2019])).
% 1.34/1.53 tff(2021,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(z))) | (~r(s(z), s(s(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(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2022,plain,
% 1.34/1.54 (((~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(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2023,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(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(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2022])).
% 1.34/1.54 tff(2024,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(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(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2023, 2021])).
% 1.34/1.54 tff(2025,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(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))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2026,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 1.34/1.54 tff(2027,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2026, 31, 408, 731, 1887])).
% 1.34/1.54 tff(2028,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,[]))).
% 1.34/1.54 tff(2029,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2028, 2020, 2018, 408])).
% 1.34/1.54 tff(2030,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(z))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2031,plain,
% 1.34/1.54 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2030, 1950, 268, 408, 301, 2, 1857, 101])).
% 1.34/1.54 tff(2032,plain,
% 1.34/1.54 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[462, 2031])).
% 1.34/1.54 tff(2033,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(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2034,plain,
% 1.34/1.54 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(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(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2035,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(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~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)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2034])).
% 1.34/1.54 tff(2036,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(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~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)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2035, 2033])).
% 1.34/1.54 tff(2037,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(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2038,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(elem!1)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 1.34/1.54 tff(2039,plain,
% 1.34/1.54 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2038, 31, 2032, 2010])).
% 1.34/1.54 tff(2040,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(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2041,plain,
% 1.34/1.54 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2042,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(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2041])).
% 1.34/1.54 tff(2043,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(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.34/1.54 tff(2044,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(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2045,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(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.34/1.54 tff(2046,plain,
% 1.34/1.54 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2045, 31, 408, 2010])).
% 1.34/1.54 tff(2047,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1986, 2046, 1975])).
% 1.34/1.54 tff(2048,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(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2049,plain,
% 1.34/1.54 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2050,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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2049])).
% 1.34/1.54 tff(2051,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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2050, 2048])).
% 1.34/1.54 tff(2052,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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2053,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(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 1.34/1.54 tff(2054,plain,
% 1.34/1.54 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2053, 31, 408, 2010])).
% 1.34/1.54 tff(2055,plain,
% 1.34/1.54 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[872, 2054, 248])).
% 1.34/1.54 tff(2056,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2057,plain,
% 1.34/1.54 (((~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(s(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(s(elem!1))))), s(s(elem!1)))) | (~b(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(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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2058,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2057])).
% 1.34/1.54 tff(2059,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2058, 2056])).
% 1.34/1.54 tff(2060,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(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(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2061,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 1.34/1.54 tff(2062,plain,
% 1.34/1.54 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2061, 112, 2055, 2047, 405])).
% 1.34/1.54 tff(2063,plain,
% 1.34/1.54 (((~![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))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2064,plain,
% 1.34/1.54 ((~![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))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2065,plain,
% 1.34/1.54 ((~![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)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 1.34/1.54 tff(2066,plain,
% 1.34/1.54 ((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)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2065, 78])).
% 1.34/1.54 tff(2067,plain,
% 1.34/1.54 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2066, 2062, 2039])).
% 1.34/1.54 tff(2068,plain,
% 1.34/1.54 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2067])).
% 1.34/1.54 tff(2069,plain,
% 1.34/1.54 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[2068])).
% 1.34/1.54 tff(2070,plain,
% 1.34/1.54 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[145, 2069, 262])).
% 1.34/1.54 tff(2071,plain,
% 1.34/1.54 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2070])).
% 1.34/1.54 tff(2072,plain,
% 1.34/1.54 (elem!1 = s(s(s(elem!1)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1073, 2071, 131])).
% 1.34/1.54 tff(2073,plain,
% 1.34/1.54 ((elem!1 = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2072])).
% 1.34/1.54 tff(2074,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[2073])).
% 1.34/1.54 tff(2075,plain,
% 1.34/1.54 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2074])).
% 1.34/1.54 tff(2076,plain,
% 1.34/1.54 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.34/1.54 inference(commutativity,[status(thm)],[])).
% 1.34/1.54 tff(2077,plain,
% 1.34/1.54 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2067])).
% 1.34/1.54 tff(2078,plain,
% 1.34/1.54 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2077])).
% 1.34/1.54 tff(2079,plain,
% 1.34/1.54 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2078, 2076])).
% 1.34/1.54 tff(2080,plain,
% 1.34/1.54 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2079])).
% 1.34/1.54 tff(2081,plain,
% 1.34/1.54 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1041, 2080])).
% 1.34/1.54 tff(2082,plain,
% 1.34/1.54 (~(elem!1 = s(s(s(z))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2081, 2075])).
% 1.34/1.54 tff(2083,plain,
% 1.34/1.54 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2067])).
% 1.34/1.54 tff(2084,plain,
% 1.34/1.54 (b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[406, 2083])).
% 1.34/1.54 tff(2085,plain,
% 1.34/1.54 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1446, 2010, 2032])).
% 1.34/1.54 tff(2086,plain,
% 1.34/1.54 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1895, 2032, 408])).
% 1.34/1.54 tff(2087,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[299, 2086, 268])).
% 1.34/1.54 tff(2088,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2089,plain,
% 1.34/1.54 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2090,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2089])).
% 1.34/1.55 tff(2091,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2090, 2088])).
% 1.34/1.55 tff(2092,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2093,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.34/1.55 tff(2094,plain,
% 1.34/1.55 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2093, 112, 2055, 2047, 2087, 405])).
% 1.34/1.55 tff(2095,plain,
% 1.34/1.55 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1025, 2094, 2085])).
% 1.34/1.55 tff(2096,assumption,(s(s(s(s(s(elem!1))))) = s(s(elem!1))), introduced(assumption)).
% 1.34/1.55 tff(2097,plain,
% 1.34/1.55 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2096])).
% 1.34/1.55 tff(2098,plain,
% 1.34/1.55 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2097])).
% 1.34/1.55 tff(2099,plain,
% 1.34/1.55 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[145, 2098, 262])).
% 1.34/1.55 tff(2100,plain,
% 1.34/1.55 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2099])).
% 1.34/1.55 tff(2101,plain,
% 1.34/1.55 (elem!1 = s(s(s(elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1073, 2100, 131])).
% 1.34/1.55 tff(2102,plain,
% 1.34/1.55 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2101])).
% 1.34/1.55 tff(2103,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2102])).
% 1.34/1.55 tff(2104,plain,
% 1.34/1.55 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2103])).
% 1.34/1.55 tff(2105,plain,
% 1.34/1.55 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2101])).
% 1.34/1.55 tff(2106,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.34/1.55 tff(2107,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.34/1.55 tff(2108,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2109,plain,
% 1.34/1.55 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2110,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2109])).
% 1.34/1.55 tff(2111,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2110, 2108])).
% 1.34/1.55 tff(2112,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2113,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.34/1.55 tff(2114,plain,
% 1.34/1.55 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2113, 112, 102, 101, 2107])).
% 1.34/1.55 tff(2115,plain,
% 1.34/1.55 (~b(elem!1, s(z))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2114, 2104])).
% 1.34/1.55 tff(2116,plain,
% 1.34/1.55 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2096])).
% 1.34/1.55 tff(2117,plain,
% 1.34/1.55 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2116])).
% 1.34/1.55 tff(2118,plain,
% 1.34/1.55 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1073, 2100, 131, 2117])).
% 1.34/1.55 tff(2119,plain,
% 1.34/1.55 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2118])).
% 1.34/1.55 tff(2120,plain,
% 1.34/1.55 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2119, 1113])).
% 1.34/1.55 tff(2121,plain,
% 1.34/1.55 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2120])).
% 1.34/1.55 tff(2122,plain,
% 1.34/1.55 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2121])).
% 1.34/1.55 tff(2123,plain,
% 1.34/1.55 (~(elem!1 = s(z))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1124, 2122])).
% 1.34/1.55 tff(2124,plain,
% 1.34/1.55 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2100])).
% 1.34/1.55 tff(2125,plain,
% 1.34/1.55 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.34/1.55 inference(transitivity,[status(thm)],[2116, 132, 2124, 247])).
% 1.34/1.55 tff(2126,plain,
% 1.34/1.55 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2125, 2096])).
% 1.34/1.55 tff(2127,plain,
% 1.34/1.55 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2126])).
% 1.34/1.55 tff(2128,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.34/1.55 tff(2129,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.55 tff(2130,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.34/1.55 tff(2131,plain,
% 1.34/1.55 (~b(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1534, 2106, 2130, 2129])).
% 1.34/1.55 tff(2132,plain,
% 1.34/1.55 (r(elem!1, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1539, 2131, 2128])).
% 1.34/1.55 tff(2133,plain,
% 1.34/1.55 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2132, 2127])).
% 1.34/1.55 tff(2134,plain,
% 1.34/1.55 (r(elem!1, s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.34/1.55 inference(symmetry,[status(thm)],[1126])).
% 1.34/1.55 tff(2135,plain,
% 1.34/1.55 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1559, 2134])).
% 1.34/1.55 tff(2136,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.55 tff(2137,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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(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(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2138,plain,
% 1.34/1.55 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2139,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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2138])).
% 1.34/1.55 tff(2140,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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2139, 2137])).
% 1.34/1.55 tff(2141,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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2142,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 1.34/1.55 tff(2143,plain,
% 1.34/1.55 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2142, 31, 464, 2136])).
% 1.34/1.55 tff(2144,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2143, 2135])).
% 1.34/1.55 tff(2145,plain,((~r(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2146,plain,
% 1.34/1.55 (~r(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2145, 2133, 464, 1068])).
% 1.34/1.55 tff(2147,plain,
% 1.34/1.55 (b(elem!1, s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1139, 2146, 2123])).
% 1.34/1.55 tff(2148,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2147, 2115])).
% 1.34/1.55 tff(2149,plain,((~b(elem!1, s(s(s(z))))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2150,plain,
% 1.34/1.55 (~b(elem!1, s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2149, 2067, 2032, 2095, 1857, 101, 1193, 2002, 2084])).
% 1.34/1.55 tff(2151,plain,
% 1.34/1.55 (r(elem!1, s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1498, 2150, 2082])).
% 1.34/1.55 tff(2152,plain,
% 1.34/1.55 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2077])).
% 1.34/1.55 tff(2153,plain,
% 1.34/1.55 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1073, 2071, 131, 2152])).
% 1.34/1.55 tff(2154,plain,
% 1.34/1.55 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2153])).
% 1.34/1.55 tff(2155,plain,
% 1.34/1.55 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2154, 1113])).
% 1.34/1.55 tff(2156,plain,
% 1.34/1.55 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2155])).
% 1.34/1.55 tff(2157,plain,
% 1.34/1.55 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2156])).
% 1.34/1.55 tff(2158,plain,
% 1.34/1.55 (~(elem!1 = s(z))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1124, 2157])).
% 1.34/1.55 tff(2159,plain,
% 1.34/1.55 (~b(z, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1998, 2047, 2, 2055])).
% 1.34/1.55 tff(2160,plain,
% 1.34/1.55 (r(z, s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[841, 2159])).
% 1.34/1.55 tff(2161,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2162,plain,
% 1.34/1.55 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2163,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2162])).
% 1.34/1.55 tff(2164,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2163, 2161])).
% 1.34/1.55 tff(2165,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2166,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 1.34/1.55 tff(2167,plain,
% 1.34/1.55 (~b(s(z), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2166, 112, 1857, 101, 2084, 2002])).
% 1.34/1.55 tff(2168,plain,
% 1.34/1.55 (r(s(z), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[857, 2167])).
% 1.34/1.55 tff(2169,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(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), 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(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2170,plain,
% 1.34/1.55 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2171,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(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2170])).
% 1.34/1.55 tff(2172,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(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.34/1.56 tff(2173,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(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2174,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(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.34/1.56 tff(2175,plain,
% 1.34/1.56 (~r(s(z), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2174, 31, 1952, 2168, 2160])).
% 1.34/1.56 tff(2176,plain,
% 1.34/1.56 (b(s(z), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[608, 2175])).
% 1.34/1.56 tff(2177,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2178,plain,
% 1.34/1.56 (((~b(z, 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(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2179,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2178])).
% 1.34/1.56 tff(2180,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2179, 2177])).
% 1.34/1.56 tff(2181,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2182,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.34/1.56 tff(2183,plain,
% 1.34/1.56 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2182, 112, 1827, 2, 405])).
% 1.34/1.56 tff(2184,plain,
% 1.34/1.56 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.34/1.56 inference(transitivity,[status(thm)],[263, 2068, 144])).
% 1.34/1.56 tff(2185,plain,
% 1.34/1.56 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2072, 2184])).
% 1.34/1.56 tff(2186,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2185])).
% 1.34/1.56 tff(2187,plain,
% 1.34/1.56 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(2188,plain,
% 1.34/1.56 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2184])).
% 1.34/1.56 tff(2189,plain,
% 1.34/1.56 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2188, 2187])).
% 1.34/1.56 tff(2190,plain,
% 1.34/1.56 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2189])).
% 1.34/1.56 tff(2191,plain,
% 1.34/1.56 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[257, 2190])).
% 1.34/1.56 tff(2192,plain,
% 1.34/1.56 (r(s(elem!1), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2070])).
% 1.34/1.56 tff(2193,plain,
% 1.34/1.56 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2192])).
% 1.34/1.56 tff(2194,plain,
% 1.34/1.56 (r(s(elem!1), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[408, 2193])).
% 1.34/1.56 tff(2195,plain,
% 1.34/1.56 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2070])).
% 1.34/1.56 tff(2196,plain,
% 1.34/1.56 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2195])).
% 1.34/1.56 tff(2197,plain,
% 1.34/1.56 (r(s(elem!1), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[249, 2196])).
% 1.34/1.56 tff(2198,plain,
% 1.34/1.56 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2067])).
% 1.34/1.56 tff(2199,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2198])).
% 1.34/1.56 tff(2200,plain,
% 1.34/1.56 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2002, 2199])).
% 1.34/1.56 tff(2201,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1069])).
% 1.34/1.56 tff(2202,plain,
% 1.34/1.56 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2201])).
% 1.34/1.56 tff(2203,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1069])).
% 1.34/1.56 tff(2204,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2203, 775])).
% 1.34/1.56 tff(2205,plain,
% 1.34/1.56 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2204])).
% 1.34/1.56 tff(2206,plain,
% 1.34/1.56 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2205])).
% 1.34/1.56 tff(2207,plain,
% 1.34/1.56 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1041, 2206])).
% 1.34/1.56 tff(2208,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1243, 2207, 1238])).
% 1.34/1.56 tff(2209,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.56 tff(2210,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.34/1.56 tff(2211,plain,
% 1.34/1.56 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2212,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2211])).
% 1.34/1.56 tff(2213,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2212, 2108])).
% 1.34/1.56 tff(2214,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2215,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 1.34/1.56 tff(2216,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2215, 112, 102, 101, 2210, 2209])).
% 1.34/1.56 tff(2217,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2218,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2217, 2208, 102, 101])).
% 1.34/1.56 tff(2219,plain,
% 1.34/1.56 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2218, 2202])).
% 1.34/1.56 tff(2220,plain,
% 1.34/1.56 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1094])).
% 1.34/1.56 tff(2221,plain,
% 1.34/1.56 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2220])).
% 1.34/1.56 tff(2222,plain,
% 1.34/1.56 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1068])).
% 1.34/1.56 tff(2223,plain,
% 1.34/1.56 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2222, 2221])).
% 1.34/1.56 tff(2224,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1068])).
% 1.34/1.56 tff(2225,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2224])).
% 1.34/1.56 tff(2226,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[406, 2225])).
% 1.34/1.56 tff(2227,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1068])).
% 1.34/1.56 tff(2228,plain,
% 1.34/1.56 (b(s(s(s(s(s(elem!1))))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2227])).
% 1.34/1.56 tff(2229,plain,
% 1.34/1.56 (b(s(s(elem!1)), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[762, 2228])).
% 1.34/1.56 tff(2230,plain,
% 1.34/1.56 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1074])).
% 1.34/1.56 tff(2231,plain,
% 1.34/1.56 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2230, 775])).
% 1.34/1.56 tff(2232,plain,
% 1.34/1.56 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2231])).
% 1.34/1.56 tff(2233,plain,
% 1.34/1.56 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2232])).
% 1.34/1.56 tff(2234,plain,
% 1.34/1.56 (~(elem!1 = s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1041, 2233])).
% 1.34/1.56 tff(2235,plain,
% 1.34/1.56 (elem!1 = s(s(s(elem!1)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1073, 1072, 131])).
% 1.34/1.56 tff(2236,plain,
% 1.34/1.56 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2235])).
% 1.34/1.56 tff(2237,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2236])).
% 1.34/1.56 tff(2238,plain,
% 1.34/1.56 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2237])).
% 1.34/1.56 tff(2239,plain,
% 1.34/1.56 (~r(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1238, 2238])).
% 1.34/1.56 tff(2240,plain,
% 1.34/1.56 (b(elem!1, s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1498, 2239, 2234])).
% 1.34/1.56 tff(2241,plain,
% 1.34/1.56 (~b(elem!1, s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1534, 2240, 2229, 2226])).
% 1.34/1.56 tff(2242,plain,
% 1.34/1.56 (r(elem!1, s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1539, 2241, 2128])).
% 1.34/1.56 tff(2243,plain,
% 1.34/1.56 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2242, 2223])).
% 1.34/1.56 tff(2244,plain,
% 1.34/1.56 (~r(elem!1, s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2145, 2243, 464, 1068])).
% 1.34/1.56 tff(2245,plain,
% 1.34/1.56 (b(elem!1, s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1139, 2244, 1125])).
% 1.34/1.56 tff(2246,plain,
% 1.34/1.56 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1577, 1112])).
% 1.34/1.56 tff(2247,assumption,(~b(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 1.34/1.56 tff(2248,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2247, 2246])).
% 1.34/1.56 tff(2249,plain,((~b(elem!1, s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2250,plain,
% 1.34/1.56 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2249, 2245, 1068])).
% 1.34/1.56 tff(2251,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2250, 2219])).
% 1.34/1.56 tff(2252,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | r(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(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2253,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2252, 2200, 1193, 1857, 101, 2032, 2095, 406])).
% 1.34/1.56 tff(2254,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(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2255,plain,
% 1.34/1.56 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2256,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(elem!1), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(elem!1), s(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(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2255])).
% 1.34/1.56 tff(2257,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(elem!1), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(elem!1), s(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(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2256, 2254])).
% 1.34/1.56 tff(2258,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(elem!1), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2259,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(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 1.34/1.56 tff(2260,plain,
% 1.34/1.56 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2259, 31, 2253])).
% 1.34/1.56 tff(2261,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2260, 2197, 2194])).
% 1.34/1.56 tff(2262,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1166, 2261, 2191])).
% 1.34/1.56 tff(2263,plain,
% 1.34/1.56 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2262, 2186])).
% 1.34/1.56 tff(2264,plain,
% 1.34/1.56 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1220, 2263, 268, 2087, 301])).
% 1.34/1.56 tff(2265,assumption,(~b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.56 tff(2266,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.34/1.56 tff(2267,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(elem!1, z)) | (~r(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(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2268,plain,
% 1.34/1.56 (((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2269,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(elem!1, s(s(s(z))))) | (~r(z, s(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(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2268])).
% 1.34/1.56 tff(2270,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(elem!1, s(s(s(z))))) | (~r(z, s(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(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2269, 2267])).
% 1.34/1.56 tff(2271,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(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, z)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2272,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(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.34/1.57 tff(2273,plain,
% 1.34/1.57 (~r(elem!1, z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2272, 31, 20, 1560])).
% 1.34/1.57 tff(2274,plain,
% 1.34/1.57 (((~![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))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2275,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2276,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2275, 2274])).
% 1.34/1.57 tff(2277,plain,
% 1.34/1.57 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2276, 78])).
% 1.34/1.57 tff(2278,plain,
% 1.34/1.57 (b(elem!1, z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2277, 2273, 2266])).
% 1.34/1.57 tff(2279,plain,
% 1.34/1.57 ((~(elem!1 = z)) <=> (~(z = elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1948])).
% 1.34/1.57 tff(2280,plain,
% 1.34/1.57 (~(z = elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2266, 2279])).
% 1.34/1.57 tff(2281,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, elem!1)) | (~r(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, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2282,plain,
% 1.34/1.57 (((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2283,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(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2282])).
% 1.34/1.57 tff(2284,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(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2283, 2281])).
% 1.34/1.57 tff(2285,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(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2286,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, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2285, 2284])).
% 1.34/1.57 tff(2287,plain,
% 1.34/1.57 (~r(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2286, 31, 20, 1560])).
% 1.34/1.57 tff(2288,plain,
% 1.34/1.57 (b(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1109, 2287, 2280])).
% 1.34/1.57 tff(2289,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2290,plain,
% 1.34/1.57 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2291,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2290])).
% 1.34/1.57 tff(2292,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2291, 2289])).
% 1.34/1.57 tff(2293,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2294,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 1.34/1.57 tff(2295,plain,
% 1.34/1.57 (~b(elem!1, s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2294, 112, 2288, 2278, 18, 673])).
% 1.34/1.57 tff(2296,plain,
% 1.34/1.57 (r(elem!1, s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1139, 2295, 1574])).
% 1.34/1.57 tff(2297,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(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2298,plain,
% 1.34/1.57 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2299,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(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2298])).
% 1.34/1.57 tff(2300,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(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2299, 2297])).
% 1.34/1.57 tff(2301,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(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2302,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 1.34/1.57 tff(2303,plain,
% 1.34/1.57 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2302, 31, 2296, 464])).
% 1.34/1.57 tff(2304,plain,
% 1.34/1.57 (elem!1 = s(s(s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1225, 2303, 2265])).
% 1.34/1.57 tff(2305,plain,
% 1.34/1.57 (b(elem!1, z) <=> b(s(s(s(s(s(elem!1))))), z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2304])).
% 1.34/1.57 tff(2306,plain,
% 1.34/1.57 (b(s(s(s(s(s(elem!1))))), z) <=> b(elem!1, z)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2305])).
% 1.34/1.57 tff(2307,plain,
% 1.34/1.57 ((~b(s(s(s(s(s(elem!1))))), z)) <=> (~b(elem!1, z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2306])).
% 1.34/1.57 tff(2308,plain,
% 1.34/1.57 (~b(elem!1, z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[489, 2307])).
% 1.34/1.57 tff(2309,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2278, 2308])).
% 1.34/1.57 tff(2310,plain,((~r(elem!1, s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), z) | b(elem!1, s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (elem!1 = s(z)) | (~b(z, s(z))) | (~b(s(z), z)) | (elem!1 = z) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2311,plain,
% 1.34/1.57 (elem!1 = z),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2310, 2264, 2032, 2183, 2176, 1950, 2158, 2151, 1952])).
% 1.34/1.57 tff(2312,plain,
% 1.34/1.57 (z = elem!1),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2311, 1948])).
% 1.34/1.57 tff(2313,plain,
% 1.34/1.57 (~(z = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1090, 2095])).
% 1.34/1.57 tff(2314,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2313, 2312])).
% 1.34/1.57 tff(2315,plain,((~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))) | (~r(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))))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2316,plain,
% 1.34/1.57 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2315, 1947, 408, 249, 101, 406, 248, 301, 1879])).
% 1.34/1.57 tff(2317,plain,
% 1.34/1.57 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2316])).
% 1.34/1.57 tff(2318,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2317])).
% 1.34/1.57 tff(2319,plain,
% 1.34/1.57 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2318])).
% 1.34/1.57 tff(2320,plain,
% 1.34/1.57 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2030, 1945, 268, 408, 301, 1879, 1857, 101])).
% 1.34/1.57 tff(2321,plain,
% 1.34/1.57 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[462, 2320])).
% 1.34/1.57 tff(2322,plain,
% 1.34/1.57 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2316])).
% 1.34/1.57 tff(2323,plain,
% 1.34/1.57 (s(elem!1) = s(s(z))),
% 1.34/1.57 inference(transitivity,[status(thm)],[145, 2322, 55])).
% 1.34/1.57 tff(2324,plain,
% 1.34/1.57 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2323])).
% 1.34/1.57 tff(2325,plain,
% 1.34/1.57 (elem!1 = s(z)),
% 1.34/1.57 inference(transitivity,[status(thm)],[1073, 2324, 137])).
% 1.34/1.57 tff(2326,plain,
% 1.34/1.57 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2317])).
% 1.34/1.57 tff(2327,plain,
% 1.34/1.57 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2326])).
% 1.34/1.57 tff(2328,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2327, 2325])).
% 1.34/1.57 tff(2329,plain,
% 1.34/1.57 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2328])).
% 1.34/1.57 tff(2330,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[408, 2329])).
% 1.34/1.57 tff(2331,plain,
% 1.34/1.57 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1895, 2321, 408])).
% 1.34/1.57 tff(2332,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[299, 2331, 268])).
% 1.34/1.57 tff(2333,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.57 tff(2334,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2333, 1754])).
% 1.34/1.57 tff(2335,plain,(b(s(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))))))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2336,plain,
% 1.34/1.57 (b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2335, 2332, 2316])).
% 1.34/1.57 tff(2337,plain,
% 1.34/1.57 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1736, 893])).
% 1.34/1.57 tff(2338,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2337])).
% 1.34/1.57 tff(2339,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1736, 893])).
% 1.34/1.57 tff(2340,plain,
% 1.34/1.57 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2339])).
% 1.34/1.57 tff(2341,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1744])).
% 1.34/1.57 tff(2342,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2341])).
% 1.34/1.57 tff(2343,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.34/1.57 tff(2344,plain,
% 1.34/1.57 (r(s(s(s(s(s(z))))), s(z))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 1.34/1.57 tff(2345,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(z)))), s(z))) | (~r(s(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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2346,plain,
% 1.34/1.57 (((~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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2347,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(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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2346])).
% 1.34/1.57 tff(2348,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(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(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2347, 2345])).
% 1.34/1.57 tff(2349,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(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)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2350,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(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2349, 2348])).
% 1.34/1.57 tff(2351,plain,
% 1.34/1.57 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2350, 31, 981])).
% 1.34/1.57 tff(2352,plain,
% 1.34/1.57 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2351, 2344])).
% 1.34/1.57 tff(2353,plain,
% 1.34/1.57 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2352, 2340])).
% 1.34/1.57 tff(2354,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.57 tff(2355,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.57 tff(2356,plain,
% 1.34/1.57 (((~![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)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2357,plain,
% 1.34/1.57 ((~![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)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2358,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 1.34/1.57 tff(2359,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2358, 78, 265, 2355, 2354])).
% 1.34/1.57 tff(2360,plain,(b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2361,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2360, 2353, 265])).
% 1.34/1.57 tff(2362,plain,
% 1.34/1.57 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2361, 2338])).
% 1.34/1.57 tff(2363,plain,
% 1.34/1.57 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[893])).
% 1.34/1.57 tff(2364,plain,
% 1.34/1.57 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2363])).
% 1.34/1.57 tff(2365,plain,
% 1.34/1.57 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(s(z))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2364])).
% 1.34/1.57 tff(2366,plain,
% 1.34/1.57 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[899, 2365])).
% 1.34/1.57 tff(2367,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(z))) | (~r(s(s(s(s(s(elem!1))))), 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(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2368,plain,
% 1.34/1.57 (((~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(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2369,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(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(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2368])).
% 1.34/1.57 tff(2370,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(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(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2369, 2367])).
% 1.34/1.57 tff(2371,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(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)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2372,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(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 1.34/1.57 tff(2373,plain,
% 1.34/1.57 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2372, 31, 464, 981])).
% 1.34/1.57 tff(2374,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(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2375,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(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2376,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(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 1.34/1.58 tff(2377,plain,
% 1.34/1.58 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2376, 78, 2373])).
% 1.34/1.58 tff(2378,plain,
% 1.34/1.58 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2377, 2366])).
% 1.34/1.58 tff(2379,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(s(s(z)))), s(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(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2380,plain,
% 1.34/1.58 (((~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(z))) | (~r(s(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(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2381,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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), 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(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2380])).
% 1.34/1.58 tff(2382,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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), 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(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2381, 2379])).
% 1.34/1.58 tff(2383,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(s(s(z)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(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(2384,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(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 1.34/1.58 tff(2385,plain,
% 1.34/1.58 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2384, 31, 464, 981])).
% 1.34/1.58 tff(2386,plain,
% 1.34/1.58 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[936, 78, 2385])).
% 1.34/1.58 tff(2387,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2386, 905])).
% 1.34/1.58 tff(2388,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.34/1.58 tff(2389,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2390,plain,
% 1.34/1.58 (((~b(s(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(s(z))))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(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(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2391,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z))))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2390])).
% 1.34/1.58 tff(2392,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z))))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2391, 2389])).
% 1.34/1.58 tff(2393,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z))))), s(s(s(s(s(elem!1))))))) | (~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)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(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(2394,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2393, 2392])).
% 1.34/1.58 tff(2395,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2394, 112, 2388, 2387, 2378, 2362])).
% 1.34/1.58 tff(2396,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2397,plain,
% 1.34/1.58 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2396, 2336, 2316, 257, 889, 2330, 2321])).
% 1.34/1.58 tff(2398,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1733, 2397])).
% 1.34/1.58 tff(2399,plain,
% 1.34/1.58 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[342, 2332, 301, 268, 1879])).
% 1.34/1.58 tff(2400,plain,
% 1.34/1.58 (r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[322, 2399])).
% 1.34/1.58 tff(2401,plain,
% 1.34/1.58 (~b(z, s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1867, 1945, 101, 1857])).
% 1.34/1.58 tff(2402,plain,
% 1.34/1.58 (r(z, s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[515, 2401])).
% 1.34/1.58 tff(2403,plain,
% 1.34/1.58 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[310, 2400, 2402])).
% 1.34/1.58 tff(2404,plain,
% 1.34/1.58 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[386, 2403])).
% 1.34/1.58 tff(2405,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2406,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~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(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), 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(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2407,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~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(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2406])).
% 1.34/1.58 tff(2408,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~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(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2407, 2405])).
% 1.34/1.58 tff(2409,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~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(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2410,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 1.34/1.58 tff(2411,plain,
% 1.34/1.58 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2410, 112, 1857, 406, 2404])).
% 1.34/1.58 tff(2412,plain,
% 1.34/1.58 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[749, 2411])).
% 1.34/1.58 tff(2413,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(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, 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(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2414,plain,
% 1.34/1.58 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2415,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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2414])).
% 1.34/1.58 tff(2416,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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2415, 2413])).
% 1.34/1.58 tff(2417,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(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2418,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 1.34/1.58 tff(2419,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2418, 31, 20, 592, 302, 731])).
% 1.34/1.58 tff(2420,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2421,plain,
% 1.34/1.58 (~r(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2420, 2412, 2402, 2400])).
% 1.34/1.58 tff(2422,plain,
% 1.34/1.58 (b(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[608, 2421])).
% 1.34/1.58 tff(2423,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2424,plain,
% 1.34/1.58 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2425,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2424])).
% 1.34/1.58 tff(2426,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2425, 2423])).
% 1.34/1.58 tff(2427,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2428,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2427, 2426])).
% 1.34/1.59 tff(2429,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2428, 112, 1857, 101, 1945, 2422, 2398])).
% 1.34/1.59 tff(2430,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[917, 78, 224, 2429])).
% 1.34/1.59 tff(2431,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2430, 2319])).
% 1.34/1.59 tff(2432,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2433,plain,
% 1.34/1.59 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(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(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2434,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2433])).
% 1.34/1.59 tff(2435,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(z))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2434, 2432])).
% 1.34/1.59 tff(2436,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2437,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 1.34/1.59 tff(2438,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2437, 112, 102, 101, 906])).
% 1.34/1.59 tff(2439,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1718, 2438, 1715])).
% 1.34/1.59 tff(2440,plain,(r(s(s(s(s(z)))), 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)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2441,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2440, 1715, 101, 102])).
% 1.34/1.59 tff(2442,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1733, 2441])).
% 1.34/1.59 tff(2443,plain,
% 1.34/1.59 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2384, 31, 464, 2442])).
% 1.34/1.59 tff(2444,plain,
% 1.34/1.59 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[936, 78, 2443])).
% 1.34/1.59 tff(2445,plain,
% 1.34/1.59 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2444, 905])).
% 1.34/1.59 tff(2446,plain,
% 1.34/1.59 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1718, 1715])).
% 1.34/1.59 tff(2447,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1711, 112, 406, 762, 2446, 2445])).
% 1.34/1.59 tff(2448,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2449,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2448, 2404, 406, 889, 2316, 2321, 101, 1857])).
% 1.34/1.59 tff(2450,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[892])).
% 1.34/1.59 tff(2451,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2450])).
% 1.34/1.59 tff(2452,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[1720, 2451])).
% 1.34/1.59 tff(2453,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1238, 2452])).
% 1.34/1.59 tff(2454,plain,((~(s(s(elem!1)) = s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2455,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2454, 2449, 2316])).
% 1.34/1.59 tff(2456,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.34/1.59 tff(2457,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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2458,plain,
% 1.34/1.59 (((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2459,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(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~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(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2458])).
% 1.34/1.59 tff(2460,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(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~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(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2459, 2457])).
% 1.34/1.59 tff(2461,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(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2462,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 1.34/1.59 tff(2463,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2462, 31, 20, 2456, 1298])).
% 1.34/1.59 tff(2464,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2465,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2464, 2455, 2402])).
% 1.34/1.59 tff(2466,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2465, 2431])).
% 1.34/1.59 tff(2467,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2468,plain,
% 1.34/1.59 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2467, 406, 1847, 301, 249, 248])).
% 1.34/1.59 tff(2469,plain,
% 1.34/1.59 (b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[429, 2468])).
% 1.34/1.59 tff(2470,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[291, 31, 1887, 249, 275])).
% 1.34/1.59 tff(2471,plain,((~r(s(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(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2472,plain,
% 1.34/1.59 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2471, 1887, 249])).
% 1.34/1.59 tff(2473,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[386, 2472])).
% 1.34/1.59 tff(2474,plain,
% 1.34/1.59 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[273, 271])).
% 1.34/1.59 tff(2475,plain,
% 1.34/1.59 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[404, 301, 2474])).
% 1.34/1.59 tff(2476,plain,
% 1.34/1.59 (r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[451, 443, 2475, 19])).
% 1.34/1.59 tff(2477,plain,
% 1.34/1.59 (~r(s(z), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[93, 2476, 1])).
% 1.34/1.59 tff(2478,plain,
% 1.34/1.59 (b(s(z), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[99, 2477])).
% 1.34/1.59 tff(2479,plain,
% 1.34/1.59 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1919, 112, 2478, 101, 443])).
% 1.34/1.59 tff(2480,plain,
% 1.34/1.59 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[386, 2479])).
% 1.34/1.59 tff(2481,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)],[291, 31, 249, 2480])).
% 1.34/1.59 tff(2482,plain,
% 1.34/1.59 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[299, 2481, 271])).
% 1.34/1.59 tff(2483,plain,
% 1.34/1.59 (~r(z, s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[365, 2480, 301, 271, 249])).
% 1.34/1.59 tff(2484,plain,
% 1.34/1.59 (b(z, s(s(s(z))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[515, 2483])).
% 1.34/1.59 tff(2485,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1941, 112, 102, 101, 443, 751, 406])).
% 1.34/1.59 tff(2486,plain,((~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(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2487,plain,
% 1.34/1.59 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2486, 2478, 101, 443, 406])).
% 1.34/1.59 tff(2488,plain,
% 1.34/1.59 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[749, 2487])).
% 1.34/1.59 tff(2489,plain,
% 1.34/1.59 (~b(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1867, 2484, 101, 2478])).
% 1.34/1.59 tff(2490,plain,
% 1.34/1.59 (r(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[182, 2489])).
% 1.34/1.59 tff(2491,plain,
% 1.34/1.59 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1933, 2490, 2488])).
% 1.34/1.59 tff(2492,plain,
% 1.34/1.59 (b(z, s(s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[322, 2491])).
% 1.34/1.59 tff(2493,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2494,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(s(elem!1)))), s(z))) | (~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(z))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2495,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(z))) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2494])).
% 1.34/1.59 tff(2496,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(z))) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2495, 2493])).
% 1.34/1.59 tff(2497,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))), s(z))) | (~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(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2498,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 1.34/1.59 tff(2499,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2498, 112, 803, 101, 19, 1827, 443, 334, 333])).
% 1.34/1.59 tff(2500,plain,((~b(z, s(s(s(s(s(elem!1))))))) | (~b(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)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2501,plain,
% 1.34/1.59 (~b(s(s(s(s(elem!1)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2500, 2492, 101, 19, 2484, 443, 2482])).
% 1.34/1.59 tff(2502,plain,
% 1.34/1.59 (r(s(s(s(s(elem!1)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[398, 2501])).
% 1.34/1.59 tff(2503,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), 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(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2504,plain,
% 1.34/1.59 (((~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(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2505,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)))), 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(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2504])).
% 1.34/1.59 tff(2506,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)))), 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(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2505, 2503])).
% 1.34/1.59 tff(2507,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)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2508,plain,
% 1.34/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 1.34/1.59 tff(2509,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2508, 31, 592, 568, 21])).
% 1.34/1.59 tff(2510,plain,((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2511,plain,
% 1.34/1.59 (~r(s(z), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2510, 2502, 2476])).
% 1.34/1.59 tff(2512,plain,
% 1.34/1.59 (b(s(z), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[608, 2511])).
% 1.34/1.59 tff(2513,plain,
% 1.34/1.59 (~r(s(s(s(z))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[693, 2502, 1])).
% 1.34/1.59 tff(2514,plain,
% 1.34/1.59 (b(s(s(s(z))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[527, 2513])).
% 1.34/1.59 tff(2515,plain,
% 1.34/1.59 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2516,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2515])).
% 1.44/1.60 tff(2517,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2516, 1675])).
% 1.44/1.60 tff(2518,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2519,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2518, 2517])).
% 1.44/1.60 tff(2520,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2519, 112, 2478, 2514, 2484, 2512])).
% 1.44/1.60 tff(2521,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | r(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(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2522,plain,
% 1.44/1.60 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2521, 19, 101, 1, 301, 271, 249, 406])).
% 1.44/1.60 tff(2523,plain,
% 1.44/1.60 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[462, 2522])).
% 1.44/1.60 tff(2524,plain,
% 1.44/1.60 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[93, 85, 1])).
% 1.44/1.60 tff(2525,plain,
% 1.44/1.60 (b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[477, 2524])).
% 1.44/1.60 tff(2526,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2527,plain,
% 1.44/1.60 (((~b(s(s(s(s(s(elem!1))))), s(s(s(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))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(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(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2528,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(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))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2527])).
% 1.44/1.60 tff(2529,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(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))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2528, 2526])).
% 1.44/1.60 tff(2530,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(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))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2531,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 1.44/1.60 tff(2532,plain,
% 1.44/1.60 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2531, 112, 803, 406, 762])).
% 1.44/1.60 tff(2533,plain,
% 1.44/1.60 (r(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[322, 2532])).
% 1.44/1.60 tff(2534,plain,
% 1.44/1.60 (~r(z, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1907, 2533, 464])).
% 1.44/1.60 tff(2535,plain,
% 1.44/1.60 (b(z, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[182, 2534])).
% 1.44/1.60 tff(2536,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2537,plain,
% 1.44/1.60 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2538,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2537])).
% 1.44/1.60 tff(2539,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2538, 2536])).
% 1.44/1.60 tff(2540,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2541,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 1.44/1.60 tff(2542,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2541, 112, 803, 101, 18, 2, 539])).
% 1.44/1.60 tff(2543,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2544,plain,
% 1.44/1.60 (~b(z, s(s(s(s(elem!1)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2543, 2535, 101, 539, 803])).
% 1.44/1.60 tff(2545,plain,
% 1.44/1.60 (r(z, s(s(s(s(elem!1)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[356, 2544])).
% 1.44/1.60 tff(2546,plain,
% 1.44/1.60 (((~![X0: $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(z, s(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(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2547,plain,
% 1.44/1.60 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2548,plain,
% 1.44/1.60 (((~![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)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(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(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2547])).
% 1.44/1.60 tff(2549,plain,
% 1.44/1.60 (((~![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)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(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(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2548, 2546])).
% 1.44/1.60 tff(2550,plain,
% 1.44/1.60 ((~![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)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2551,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 1.44/1.60 tff(2552,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2551, 31, 2533, 2545, 1887])).
% 1.44/1.60 tff(2553,plain,((~b(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2554,plain,
% 1.44/1.60 (~b(z, s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2553, 2525, 101, 1887, 464, 406, 2473])).
% 1.44/1.60 tff(2555,plain,
% 1.44/1.60 (r(z, s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[515, 2554])).
% 1.44/1.60 tff(2556,plain,
% 1.44/1.60 (~r(z, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[170, 2555, 85])).
% 1.44/1.60 tff(2557,plain,
% 1.44/1.60 (b(z, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[182, 2556])).
% 1.44/1.60 tff(2558,plain,
% 1.44/1.60 (~b(z, s(s(s(s(elem!1)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[547, 2557, 19, 2525])).
% 1.44/1.60 tff(2559,plain,
% 1.44/1.60 (r(z, s(s(s(s(elem!1)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[356, 2558])).
% 1.44/1.60 tff(2560,plain,
% 1.44/1.60 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[577, 2559, 2555, 249])).
% 1.44/1.60 tff(2561,plain,
% 1.44/1.60 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[398, 2560])).
% 1.44/1.60 tff(2562,plain,
% 1.44/1.60 (~b(s(z), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1835, 2561, 19, 2557])).
% 1.44/1.60 tff(2563,plain,
% 1.44/1.60 (r(s(z), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[608, 2562])).
% 1.44/1.60 tff(2564,plain,
% 1.44/1.60 (((~![X0: $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), 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(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2565,plain,
% 1.44/1.60 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2566,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2565])).
% 1.44/1.60 tff(2567,plain,
% 1.44/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2566, 2564])).
% 1.44/1.60 tff(2568,plain,
% 1.44/1.60 ((~![X0: $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)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2569,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2568, 2567])).
% 1.44/1.60 tff(2570,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2569, 31, 85, 2555, 2563])).
% 1.44/1.60 tff(2571,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(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), 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))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2572,plain,
% 1.44/1.60 (~r(s(z), s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2571, 1887, 249, 101, 19, 2523, 406, 1])).
% 1.44/1.60 tff(2573,plain,
% 1.44/1.60 (b(s(z), s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[99, 2572])).
% 1.44/1.60 tff(2574,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2575,plain,
% 1.44/1.60 (((~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(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(s(s(z))), s(z))) | (~b(s(z), 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))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2576,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2575])).
% 1.44/1.60 tff(2577,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.44/1.60 tff(2578,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2579,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.44/1.61 tff(2580,plain,
% 1.44/1.61 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2579, 112, 2573, 101, 406, 2473])).
% 1.44/1.61 tff(2581,plain,
% 1.44/1.61 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[749, 2580])).
% 1.44/1.61 tff(2582,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(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(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2583,plain,
% 1.44/1.61 (((~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(s(s(s(elem!1))))))) | (~r(s(z), 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(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2584,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(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(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2583])).
% 1.44/1.61 tff(2585,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(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(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2584, 2582])).
% 1.44/1.61 tff(2586,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(elem!1)))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2587,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), 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(elem!1))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2586, 2585])).
% 1.44/1.61 tff(2588,plain,
% 1.44/1.61 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2587, 31, 2581, 1887])).
% 1.44/1.61 tff(2589,plain,
% 1.44/1.61 (b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[477, 2588])).
% 1.44/1.61 tff(2590,plain,
% 1.44/1.61 (~b(z, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2553, 2589, 101, 1887, 2523, 406, 2473])).
% 1.44/1.61 tff(2591,plain,
% 1.44/1.61 (r(z, s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[515, 2590])).
% 1.44/1.61 tff(2592,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(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(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2593,plain,
% 1.44/1.61 (((~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(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2594,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(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(s(s(z))))) | (~r(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(s(z)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2593])).
% 1.44/1.61 tff(2595,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(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(s(s(z))))) | (~r(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(s(z))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2594, 2592])).
% 1.44/1.61 tff(2596,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2597,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(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(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 1.44/1.61 tff(2598,plain,
% 1.44/1.61 (~r(z, s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2597, 31, 2591, 1887, 249])).
% 1.44/1.61 tff(2599,plain,
% 1.44/1.61 (b(z, s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[356, 2598])).
% 1.44/1.61 tff(2600,plain,
% 1.44/1.61 (~b(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[547, 2599, 19, 2589])).
% 1.44/1.61 tff(2601,plain,
% 1.44/1.61 (r(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[182, 2600])).
% 1.44/1.61 tff(2602,plain,
% 1.44/1.61 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1933, 2601, 2581])).
% 1.44/1.61 tff(2603,plain,
% 1.44/1.61 (b(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[322, 2602])).
% 1.44/1.61 tff(2604,assumption,(b(s(s(s(s(s(elem!1))))), z)), introduced(assumption)).
% 1.44/1.61 tff(2605,plain,
% 1.44/1.61 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 1.44/1.61 inference(commutativity,[status(thm)],[])).
% 1.44/1.61 tff(2606,plain,
% 1.44/1.61 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[2605])).
% 1.44/1.61 tff(2607,plain,
% 1.44/1.61 ((~(s(s(s(s(s(elem!1))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2606])).
% 1.44/1.61 tff(2608,plain,
% 1.44/1.61 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[381, 2607])).
% 1.44/1.61 tff(2609,plain,
% 1.44/1.61 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[342, 2, 334, 271, 301])).
% 1.44/1.61 tff(2610,plain,
% 1.44/1.61 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[299, 2609, 271])).
% 1.44/1.61 tff(2611,plain,
% 1.44/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(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(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))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2612,plain,
% 1.44/1.61 (((~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(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))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2613,plain,
% 1.44/1.61 (((~![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(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(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)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2612])).
% 1.44/1.61 tff(2614,plain,
% 1.44/1.61 (((~![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(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(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))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2613, 2611])).
% 1.44/1.61 tff(2615,plain,
% 1.44/1.61 ((~![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(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))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2616,plain,
% 1.44/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 1.44/1.61 tff(2617,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2616, 31, 1887, 249, 730])).
% 1.44/1.61 tff(2618,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,[]))).
% 1.44/1.61 tff(2619,plain,
% 1.44/1.61 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2618, 2610, 249])).
% 1.44/1.61 tff(2620,plain,
% 1.44/1.61 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[710, 78, 2619])).
% 1.44/1.61 tff(2621,plain,
% 1.44/1.61 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2620, 2608])).
% 1.44/1.61 tff(2622,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2623,plain,
% 1.44/1.61 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2624,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2623])).
% 1.44/1.61 tff(2625,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2624, 2622])).
% 1.44/1.61 tff(2626,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2627,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 1.44/1.61 tff(2628,plain,
% 1.44/1.61 (~b(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2627, 112, 334, 2604, 2621])).
% 1.44/1.61 tff(2629,plain,
% 1.44/1.61 (r(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[527, 2628])).
% 1.44/1.61 tff(2630,plain,
% 1.44/1.61 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[693, 2629, 1])).
% 1.44/1.61 tff(2631,plain,
% 1.44/1.61 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[398, 2630])).
% 1.44/1.61 tff(2632,plain,
% 1.44/1.61 (((~b(s(s(s(s(elem!1)))), z)) | (~b(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(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(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2633,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2632])).
% 1.44/1.61 tff(2634,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2633, 2177])).
% 1.44/1.61 tff(2635,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2636,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 1.44/1.61 tff(2637,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2636, 112, 2631, 2, 2475, 2604])).
% 1.44/1.61 tff(2638,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2639,plain,
% 1.44/1.61 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2638, 2603, 1, 301, 249, 271, 2599])).
% 1.44/1.61 tff(2640,plain,
% 1.44/1.61 (r(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[494, 2639])).
% 1.44/1.61 tff(2641,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[486, 31, 2601, 2523, 2640])).
% 1.44/1.61 tff(2642,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2643,plain,
% 1.44/1.61 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2642, 2469, 301, 249, 268, 1, 1847, 406])).
% 1.44/1.61 tff(2644,plain,
% 1.44/1.61 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[299, 2643, 268])).
% 1.44/1.61 tff(2645,plain,
% 1.44/1.61 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2521, 2469, 1847, 1, 301, 268, 249, 406])).
% 1.44/1.61 tff(2646,plain,
% 1.44/1.61 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[462, 2645])).
% 1.44/1.61 tff(2647,plain,
% 1.44/1.61 (~b(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2627, 112, 1909, 495, 406])).
% 1.44/1.61 tff(2648,plain,
% 1.44/1.61 (~b(z, s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[342, 1909, 301, 271, 333])).
% 1.44/1.61 tff(2649,plain,
% 1.44/1.61 (r(z, s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[356, 2648])).
% 1.44/1.61 tff(2650,plain,
% 1.44/1.61 (~r(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[563, 31, 2649, 1])).
% 1.44/1.61 tff(2651,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[527, 2650, 2647])).
% 1.44/1.61 tff(2652,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(s(s(elem!1))))), s(s(s(s(elem!1))))) | (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)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2653,plain,
% 1.44/1.61 (~r(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2652, 406, 1, 2646, 301, 268, 2644])).
% 1.44/1.62 tff(2654,plain,
% 1.44/1.62 (b(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[182, 2653])).
% 1.44/1.62 tff(2655,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, 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(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2656,plain,
% 1.44/1.62 (((~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(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2657,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2656])).
% 1.44/1.62 tff(2658,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2657, 2655])).
% 1.44/1.62 tff(2659,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2660,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 1.44/1.62 tff(2661,plain,
% 1.44/1.62 (~r(z, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2660, 31, 569, 1])).
% 1.44/1.62 tff(2662,plain,
% 1.44/1.62 (b(z, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[515, 2661])).
% 1.44/1.62 tff(2663,plain,
% 1.44/1.62 (~b(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1867, 2662, 101, 18])).
% 1.44/1.62 tff(2664,plain,
% 1.44/1.62 (r(s(z), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[99, 2663])).
% 1.44/1.62 tff(2665,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[93, 2664, 1])).
% 1.44/1.62 tff(2666,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[477, 2665])).
% 1.44/1.62 tff(2667,plain,
% 1.44/1.62 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1662, 2666, 442, 333])).
% 1.44/1.62 tff(2668,plain,
% 1.44/1.62 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[749, 2667])).
% 1.44/1.62 tff(2669,plain,
% 1.44/1.62 (((~![X0: $i, 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(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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2670,plain,
% 1.44/1.62 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2671,plain,
% 1.44/1.62 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), 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(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2670])).
% 1.44/1.62 tff(2672,plain,
% 1.44/1.62 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), 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(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2671, 2669])).
% 1.44/1.62 tff(2673,plain,
% 1.44/1.62 ((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2674,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 1.44/1.62 tff(2675,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2674, 31, 85, 731, 275])).
% 1.44/1.62 tff(2676,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2677,plain,
% 1.44/1.62 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2676, 2664, 2668])).
% 1.44/1.62 tff(2678,plain,
% 1.44/1.62 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[386, 2677])).
% 1.44/1.62 tff(2679,plain,
% 1.44/1.62 (~r(s(z), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1670, 31, 302, 731])).
% 1.44/1.62 tff(2680,plain,
% 1.44/1.62 (b(s(z), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[606, 78, 176, 2679])).
% 1.44/1.62 tff(2681,plain,
% 1.44/1.62 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2682,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2681])).
% 1.44/1.62 tff(2683,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2682, 623])).
% 1.44/1.62 tff(2684,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2685,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.44/1.62 tff(2686,plain,
% 1.44/1.62 (~b(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2685, 112, 101, 18, 2680])).
% 1.44/1.62 tff(2687,plain,
% 1.44/1.62 (r(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[527, 2686])).
% 1.44/1.62 tff(2688,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)))))))) <=> ((~![X0: $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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2689,plain,
% 1.44/1.62 (((~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(s(elem!1))))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(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)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2690,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), 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(z, s(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))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2689])).
% 1.44/1.62 tff(2691,plain,
% 1.44/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), 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(z, s(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)))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2690, 2688])).
% 1.44/1.62 tff(2692,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2693,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 1.44/1.62 tff(2694,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2693, 31, 612, 302, 569, 1])).
% 1.44/1.62 tff(2695,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2696,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2695, 2687, 302, 569])).
% 1.44/1.62 tff(2697,plain,
% 1.44/1.62 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[160, 2696])).
% 1.44/1.62 tff(2698,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z))), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2699,plain,
% 1.44/1.62 (((~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(elem!1)))))) | (~b(s(s(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(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(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2700,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~b(s(s(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(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(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2699])).
% 1.44/1.62 tff(2701,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~b(s(s(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(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(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2700, 2698])).
% 1.44/1.62 tff(2702,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~b(s(s(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(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(z))), s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2703,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.44/1.62 tff(2704,plain,
% 1.44/1.62 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2703, 112, 2697, 333, 442])).
% 1.44/1.62 tff(2705,plain,
% 1.44/1.62 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[710, 78, 2704])).
% 1.44/1.62 tff(2706,plain,
% 1.44/1.62 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2705, 2608])).
% 1.44/1.62 tff(2707,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[809, 31, 2687, 302, 2706])).
% 1.44/1.62 tff(2708,plain,((~r(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2709,plain,
% 1.44/1.62 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2708, 2668, 442, 101, 333, 18, 569])).
% 1.44/1.62 tff(2710,plain,
% 1.44/1.62 (b(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[322, 2709])).
% 1.44/1.62 tff(2711,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2712,plain,
% 1.44/1.62 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2713,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2712])).
% 1.44/1.62 tff(2714,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2713, 2711])).
% 1.44/1.62 tff(2715,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2716,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 1.44/1.62 tff(2717,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2716, 112, 2662, 101, 18, 2710, 2678])).
% 1.44/1.63 tff(2718,plain,((~r(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(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(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2719,plain,
% 1.44/1.63 (~r(z, s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2718, 2654, 1847, 405, 2644, 1])).
% 1.44/1.63 tff(2720,plain,
% 1.44/1.63 (b(z, s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[356, 2719])).
% 1.44/1.63 tff(2721,plain,
% 1.44/1.63 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[342, 2720, 301, 268, 2644])).
% 1.44/1.63 tff(2722,plain,
% 1.44/1.63 (r(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[322, 2721])).
% 1.44/1.63 tff(2723,plain,
% 1.44/1.63 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[547, 2720, 2469, 2654])).
% 1.44/1.63 tff(2724,plain,
% 1.44/1.63 (r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[477, 2723])).
% 1.44/1.63 tff(2725,plain,
% 1.44/1.63 (~r(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[93, 2724, 1])).
% 1.44/1.63 tff(2726,plain,
% 1.44/1.63 (b(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[99, 2725])).
% 1.44/1.63 tff(2727,plain,
% 1.44/1.63 (~b(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1867, 2726, 1847, 2654])).
% 1.44/1.63 tff(2728,plain,
% 1.44/1.63 (r(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[515, 2727])).
% 1.44/1.63 tff(2729,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(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))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2730,plain,
% 1.44/1.63 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(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))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2731,plain,
% 1.44/1.63 (((~![X0: $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(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(z, s(s(s(z))))) | (~r(z, s(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)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2730])).
% 1.44/1.63 tff(2732,plain,
% 1.44/1.63 (((~![X0: $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(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(z, s(s(s(z))))) | (~r(z, s(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))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2731, 2729])).
% 1.44/1.63 tff(2733,plain,
% 1.44/1.63 ((~![X0: $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(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2734,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 1.44/1.63 tff(2735,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2734, 31, 2728, 2722, 249])).
% 1.44/1.63 tff(2736,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[398, 2735])).
% 1.44/1.63 tff(2737,plain,
% 1.44/1.63 (~b(s(z), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1835, 2736, 2469, 2654])).
% 1.44/1.63 tff(2738,plain,
% 1.44/1.63 (r(s(z), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[608, 2737])).
% 1.44/1.63 tff(2739,plain,
% 1.44/1.63 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1672, 2738, 2722])).
% 1.44/1.63 tff(2740,plain,
% 1.44/1.63 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[749, 2739])).
% 1.44/1.63 tff(2741,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2742,plain,
% 1.44/1.63 (((~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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, 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(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2743,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2742])).
% 1.44/1.63 tff(2744,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2743, 2741])).
% 1.44/1.63 tff(2745,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2746,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 1.44/1.63 tff(2747,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2746, 112, 2654, 2469, 2736, 2740, 2644])).
% 1.44/1.63 tff(2748,plain,((~b(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(z))), s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2749,plain,
% 1.44/1.63 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2748, 301, 1, 249, 248])).
% 1.44/1.63 tff(2750,assumption,(~b(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.63 tff(2751,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[710, 78, 707, 2750, 699])).
% 1.44/1.63 tff(2752,plain,(b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2753,plain,
% 1.44/1.63 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2752, 2749])).
% 1.44/1.63 tff(2754,plain,
% 1.44/1.63 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2618, 2753, 249])).
% 1.44/1.63 tff(2755,plain,
% 1.44/1.63 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[299, 2754, 268])).
% 1.44/1.63 tff(2756,plain,
% 1.44/1.63 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[342, 2, 301, 268, 2755])).
% 1.44/1.63 tff(2757,plain,
% 1.44/1.63 (r(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[322, 2756])).
% 1.44/1.63 tff(2758,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(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)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2759,plain,
% 1.44/1.63 (((~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))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~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))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2760,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(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(z, s(s(s(z))))) | (~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))), s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2759])).
% 1.44/1.63 tff(2761,plain,
% 1.44/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(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(z, s(s(s(z))))) | (~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))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2760, 2758])).
% 1.44/1.63 tff(2762,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2763,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(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))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 1.44/1.63 tff(2764,plain,
% 1.44/1.63 (~r(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2763, 31, 2757, 1, 2753])).
% 1.44/1.63 tff(2765,plain,
% 1.44/1.63 (b(z, s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[515, 2764])).
% 1.44/1.63 tff(2766,plain,
% 1.44/1.63 (~r(s(s(s(z))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[809, 31, 2757, 2753])).
% 1.44/1.63 tff(2767,plain,
% 1.44/1.63 (b(s(s(s(z))), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[527, 2766])).
% 1.44/1.63 tff(2768,plain,
% 1.44/1.63 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1933, 162, 2757])).
% 1.44/1.63 tff(2769,plain,
% 1.44/1.63 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[749, 2768])).
% 1.44/1.63 tff(2770,plain,
% 1.44/1.63 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1662, 2769, 405, 2755])).
% 1.44/1.63 tff(2771,plain,
% 1.44/1.63 (r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[477, 2770])).
% 1.44/1.63 tff(2772,plain,
% 1.44/1.63 (~r(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[93, 2771, 1])).
% 1.44/1.63 tff(2773,plain,
% 1.44/1.63 (b(s(z), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[99, 2772])).
% 1.44/1.63 tff(2774,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2775,plain,
% 1.44/1.63 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2776,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2775])).
% 1.44/1.63 tff(2777,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2776, 2774])).
% 1.44/1.63 tff(2778,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2779,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 1.44/1.63 tff(2780,plain,
% 1.44/1.63 (~b(s(s(elem!1)), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2779, 112, 102, 859, 803, 101, 2130])).
% 1.44/1.63 tff(2781,plain,
% 1.44/1.63 (r(s(s(elem!1)), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[822, 78, 379, 2780])).
% 1.44/1.63 tff(2782,plain,
% 1.44/1.63 (~b(s(s(elem!1)), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2008, 112, 102, 101, 2130])).
% 1.44/1.63 tff(2783,plain,
% 1.44/1.63 (r(s(s(elem!1)), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1435, 78, 2782, 1421])).
% 1.44/1.63 tff(2784,plain,
% 1.44/1.63 (((~![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)), z)) | (~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(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2785,plain,
% 1.44/1.63 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2786,plain,
% 1.44/1.63 (((~![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(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2785])).
% 1.44/1.63 tff(2787,plain,
% 1.44/1.63 (((~![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(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2786, 2784])).
% 1.44/1.63 tff(2788,plain,
% 1.44/1.63 ((~![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)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2789,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 1.44/1.63 tff(2790,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2789, 31, 162, 2783, 2781])).
% 1.44/1.63 tff(2791,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2792,plain,
% 1.44/1.63 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2791, 162, 2773, 2767, 2765, 1847])).
% 1.44/1.63 tff(2793,plain,
% 1.44/1.63 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1907, 162, 2757])).
% 1.44/1.63 tff(2794,plain,
% 1.44/1.63 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[462, 2793])).
% 1.44/1.63 tff(2795,plain,
% 1.44/1.63 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1919, 112, 2773, 1847, 2794])).
% 1.44/1.63 tff(2796,plain,
% 1.44/1.63 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[386, 2795])).
% 1.44/1.63 tff(2797,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2798,plain,
% 1.44/1.64 (((~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(elem!1)))), s(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(s(elem!1))))), 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(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2799,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))), s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2798])).
% 1.44/1.64 tff(2800,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))), s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.44/1.64 tff(2801,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))), s(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(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2802,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.44/1.64 tff(2803,plain,
% 1.44/1.64 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2802, 112, 2794, 2769, 2755])).
% 1.44/1.64 tff(2804,plain,
% 1.44/1.64 (r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[429, 2803])).
% 1.44/1.64 tff(2805,plain,
% 1.44/1.64 (((~![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(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2806,plain,
% 1.44/1.64 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2807,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~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(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2806])).
% 1.44/1.64 tff(2808,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~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(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2807, 2805])).
% 1.44/1.64 tff(2809,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2810,plain,
% 1.44/1.64 ((~![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(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2809, 2808])).
% 1.44/1.64 tff(2811,plain,
% 1.44/1.64 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2810, 31, 275, 1953])).
% 1.44/1.64 tff(2812,plain,
% 1.44/1.64 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2061, 112, 1961, 1987, 405])).
% 1.44/1.64 tff(2813,plain,
% 1.44/1.64 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2066, 2812, 2811])).
% 1.44/1.64 tff(2814,plain,
% 1.44/1.64 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2813])).
% 1.44/1.64 tff(2815,plain,
% 1.44/1.64 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.44/1.64 inference(transitivity,[status(thm)],[263, 2814, 144])).
% 1.44/1.64 tff(2816,plain,
% 1.44/1.64 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2814])).
% 1.44/1.64 tff(2817,plain,
% 1.44/1.64 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[145, 2816, 262])).
% 1.44/1.64 tff(2818,plain,
% 1.44/1.64 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2817])).
% 1.44/1.64 tff(2819,plain,
% 1.44/1.64 (elem!1 = s(s(s(elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[1073, 2818, 131])).
% 1.44/1.64 tff(2820,plain,
% 1.44/1.64 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2819, 2815])).
% 1.44/1.64 tff(2821,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2820])).
% 1.44/1.64 tff(2822,plain,
% 1.44/1.64 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2815])).
% 1.44/1.64 tff(2823,plain,
% 1.44/1.64 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2822, 2187])).
% 1.44/1.64 tff(2824,plain,
% 1.44/1.64 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2823])).
% 1.44/1.64 tff(2825,plain,
% 1.44/1.64 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[257, 2824])).
% 1.44/1.64 tff(2826,plain,
% 1.44/1.64 (r(s(elem!1), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2817])).
% 1.44/1.64 tff(2827,plain,
% 1.44/1.64 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2826])).
% 1.44/1.64 tff(2828,plain,
% 1.44/1.64 (r(s(elem!1), s(z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[408, 2827])).
% 1.44/1.64 tff(2829,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2817])).
% 1.44/1.64 tff(2830,plain,
% 1.44/1.64 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2829])).
% 1.44/1.64 tff(2831,plain,
% 1.44/1.64 (r(s(elem!1), s(s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[249, 2830])).
% 1.44/1.64 tff(2832,plain,
% 1.44/1.64 (s(s(s(elem!1))) = elem!1),
% 1.44/1.64 inference(transitivity,[status(thm)],[132, 2124, 247])).
% 1.44/1.64 tff(2833,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2832])).
% 1.44/1.64 tff(2834,plain,
% 1.44/1.64 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2833])).
% 1.44/1.64 tff(2835,plain,
% 1.44/1.64 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2116])).
% 1.44/1.64 tff(2836,plain,
% 1.44/1.64 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2835, 2076])).
% 1.44/1.64 tff(2837,plain,
% 1.44/1.64 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2836])).
% 1.44/1.64 tff(2838,plain,
% 1.44/1.64 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1041, 2837])).
% 1.44/1.64 tff(2839,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1243, 1238, 2838])).
% 1.44/1.64 tff(2840,plain,
% 1.44/1.64 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2217, 2839, 102, 101])).
% 1.44/1.64 tff(2841,plain,
% 1.44/1.64 (~b(elem!1, s(z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2840, 2104])).
% 1.44/1.64 tff(2842,plain,
% 1.44/1.64 (r(elem!1, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1139, 2841, 2123])).
% 1.44/1.64 tff(2843,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2842, 2834])).
% 1.44/1.64 tff(2844,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2117])).
% 1.44/1.64 tff(2845,plain,
% 1.44/1.64 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(symmetry,[status(thm)],[2844])).
% 1.44/1.64 tff(2846,plain,
% 1.44/1.64 ((~b(s(s(s(s(s(s(elem!1)))))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2845])).
% 1.44/1.64 tff(2847,plain,
% 1.44/1.64 (b(elem!1, z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2118])).
% 1.44/1.64 tff(2848,plain,
% 1.44/1.64 ((~b(elem!1, z)) <=> (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2847])).
% 1.44/1.64 tff(2849,plain,
% 1.44/1.64 ((elem!1 = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2101])).
% 1.44/1.64 tff(2850,plain,
% 1.44/1.64 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2849])).
% 1.44/1.64 tff(2851,plain,
% 1.44/1.64 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2850])).
% 1.44/1.64 tff(2852,plain,
% 1.44/1.64 (~(elem!1 = s(s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2838, 2851])).
% 1.44/1.64 tff(2853,plain,
% 1.44/1.64 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2101])).
% 1.44/1.64 tff(2854,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1560, 2853])).
% 1.44/1.64 tff(2855,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1238, 2854])).
% 1.44/1.64 tff(2856,plain,((~r(elem!1, s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(z)))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2857,plain,
% 1.44/1.64 (~r(elem!1, s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2856, 1238, 2096])).
% 1.44/1.64 tff(2858,plain,
% 1.44/1.64 (b(elem!1, s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1498, 2857, 2852])).
% 1.44/1.64 tff(2859,plain,
% 1.44/1.64 (~b(elem!1, z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1506, 2858, 803, 859])).
% 1.44/1.64 tff(2860,plain,
% 1.44/1.64 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2859, 2848])).
% 1.44/1.64 tff(2861,plain,
% 1.44/1.64 (~b(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2860, 2846])).
% 1.44/1.64 tff(2862,plain,
% 1.44/1.64 (((~![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))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2863,plain,
% 1.44/1.64 ((~![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))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2864,plain,
% 1.44/1.64 ((~![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)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 1.44/1.64 tff(2865,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2864, 78, 422])).
% 1.44/1.64 tff(2866,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2865, 2861])).
% 1.44/1.64 tff(2867,plain,
% 1.44/1.64 (((~![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(elem!1))), s(z))) | (~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(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2868,plain,
% 1.44/1.64 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2869,plain,
% 1.44/1.64 (((~![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(elem!1))), s(z))) | (~r(z, s(z))) | (~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(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2868])).
% 1.44/1.64 tff(2870,plain,
% 1.44/1.64 (((~![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(elem!1))), s(z))) | (~r(z, s(z))) | (~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(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2869, 2867])).
% 1.44/1.64 tff(2871,plain,
% 1.44/1.64 ((~![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(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2872,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 1.44/1.64 tff(2873,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2872, 31, 162, 2866, 2843])).
% 1.44/1.64 tff(2874,plain,(r(s(s(s(elem!1))), s(s(s(z)))) | (~r(z, s(z))) | (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2875,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2874, 2813, 162, 803, 859, 102, 101])).
% 1.44/1.64 tff(2876,plain,
% 1.44/1.64 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2259, 31, 2875])).
% 1.44/1.64 tff(2877,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2876, 2831, 2828])).
% 1.44/1.64 tff(2878,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1166, 2877, 2825])).
% 1.44/1.64 tff(2879,plain,
% 1.44/1.64 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2878, 2821])).
% 1.44/1.64 tff(2880,plain,
% 1.44/1.64 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2813])).
% 1.44/1.64 tff(2881,plain,
% 1.44/1.64 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2880])).
% 1.44/1.64 tff(2882,plain,
% 1.44/1.64 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2881])).
% 1.44/1.64 tff(2883,plain,
% 1.44/1.64 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[1193, 2882])).
% 1.44/1.64 tff(2884,plain,
% 1.44/1.64 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2813])).
% 1.44/1.64 tff(2885,plain,
% 1.44/1.64 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2884])).
% 1.44/1.64 tff(2886,plain,
% 1.44/1.64 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2818])).
% 1.44/1.64 tff(2887,plain,
% 1.44/1.64 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2813])).
% 1.44/1.64 tff(2888,plain,
% 1.44/1.64 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.44/1.64 inference(transitivity,[status(thm)],[2887, 132, 2886, 247])).
% 1.44/1.64 tff(2889,plain,
% 1.44/1.64 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2888, 2813])).
% 1.44/1.64 tff(2890,plain,
% 1.44/1.64 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2813])).
% 1.44/1.64 tff(2891,plain,
% 1.44/1.64 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(symmetry,[status(thm)],[2887])).
% 1.44/1.64 tff(2892,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2891, 2890])).
% 1.44/1.64 tff(2893,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2892, 2889, 2885])).
% 1.44/1.64 tff(2894,plain,
% 1.44/1.64 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2893])).
% 1.44/1.64 tff(2895,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2896,plain,
% 1.44/1.64 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2897,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(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(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2896])).
% 1.44/1.64 tff(2898,plain,
% 1.44/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(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(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2897, 2895])).
% 1.44/1.64 tff(2899,plain,
% 1.44/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2900,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2899, 2898])).
% 1.44/1.65 tff(2901,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2900, 31, 2875, 1953])).
% 1.44/1.65 tff(2902,plain,
% 1.44/1.65 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2901, 2894])).
% 1.44/1.65 tff(2903,plain,
% 1.44/1.65 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1225, 2902, 2883])).
% 1.44/1.65 tff(2904,plain,
% 1.44/1.65 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1220, 2903, 268, 333, 301])).
% 1.44/1.65 tff(2905,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2904, 2879])).
% 1.44/1.65 tff(2906,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2907,plain,
% 1.44/1.65 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2906, 2804, 301, 2755, 249, 162, 2765, 2767, 2773, 1847, 248, 2796])).
% 1.44/1.65 tff(2908,plain,
% 1.44/1.65 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1008, 78, 2907])).
% 1.44/1.65 tff(2909,plain,
% 1.44/1.65 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2908, 2792])).
% 1.44/1.65 tff(2910,plain,
% 1.44/1.65 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2909])).
% 1.44/1.65 tff(2911,plain,
% 1.44/1.65 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2910])).
% 1.44/1.65 tff(2912,plain,
% 1.44/1.65 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2910])).
% 1.44/1.65 tff(2913,plain,
% 1.44/1.65 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2912])).
% 1.44/1.65 tff(2914,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2913, 2911])).
% 1.44/1.65 tff(2915,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2914])).
% 1.44/1.65 tff(2916,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2913, 2911])).
% 1.44/1.65 tff(2917,plain,
% 1.44/1.65 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2916])).
% 1.44/1.65 tff(2918,plain,
% 1.44/1.65 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2909])).
% 1.44/1.65 tff(2919,plain,
% 1.44/1.65 (s(elem!1) = s(s(z))),
% 1.44/1.65 inference(transitivity,[status(thm)],[145, 2918, 55])).
% 1.44/1.65 tff(2920,plain,
% 1.44/1.65 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2919])).
% 1.44/1.65 tff(2921,plain,
% 1.44/1.65 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2920])).
% 1.44/1.65 tff(2922,plain,
% 1.44/1.65 (s(z) = elem!1),
% 1.44/1.65 inference(transitivity,[status(thm)],[138, 2921, 247])).
% 1.44/1.65 tff(2923,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2922])).
% 1.44/1.65 tff(2924,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2923])).
% 1.44/1.65 tff(2925,plain,
% 1.44/1.65 (elem!1 = s(z)),
% 1.44/1.65 inference(transitivity,[status(thm)],[1073, 2920, 137])).
% 1.44/1.65 tff(2926,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2913, 2925])).
% 1.44/1.65 tff(2927,plain,
% 1.44/1.65 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.65 inference(symmetry,[status(thm)],[2926])).
% 1.44/1.65 tff(2928,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2804, 2927])).
% 1.44/1.65 tff(2929,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), s(z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2928, 2924])).
% 1.44/1.65 tff(2930,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2911])).
% 1.44/1.65 tff(2931,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2930, 900])).
% 1.44/1.65 tff(2932,plain,
% 1.44/1.65 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2931])).
% 1.44/1.65 tff(2933,plain,
% 1.44/1.65 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2932])).
% 1.44/1.65 tff(2934,plain,
% 1.44/1.65 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[889, 2933])).
% 1.44/1.65 tff(2935,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2936,plain,
% 1.44/1.65 (((~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)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2937,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2936])).
% 1.44/1.65 tff(2938,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2937, 2935])).
% 1.44/1.65 tff(2939,plain,
% 1.44/1.65 ((~![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)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2940,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2939, 2938])).
% 1.44/1.65 tff(2941,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2940, 31, 162, 2442])).
% 1.44/1.65 tff(2942,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1692, 2446, 803, 859])).
% 1.44/1.65 tff(2943,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[917, 78, 224, 2942, 2941])).
% 1.44/1.65 tff(2944,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | (~r(z, s(z))) | (~b(z, 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,[]))).
% 1.44/1.65 tff(2945,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2944, 162, 2765, 2767, 1847, 2773])).
% 1.44/1.65 tff(2946,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.65 tff(2947,plain,
% 1.44/1.65 (((~![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(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(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(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2948,plain,
% 1.44/1.65 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(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(s(s(z)))), s(s(s(z))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2949,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2948])).
% 1.44/1.65 tff(2950,plain,
% 1.44/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2949, 2947])).
% 1.44/1.65 tff(2951,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(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(s(s(z)))), s(s(s(z))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2952,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2951, 2950])).
% 1.44/1.65 tff(2953,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2952, 31, 730, 1720, 2946])).
% 1.44/1.65 tff(2954,plain,((~r(s(s(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(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2955,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2954, 2945, 2753])).
% 1.44/1.65 tff(2956,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[936, 78, 2955])).
% 1.44/1.65 tff(2957,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2956, 2934])).
% 1.44/1.65 tff(2958,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2959,plain,
% 1.44/1.65 (((~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(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(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(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2960,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z)))), s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2959])).
% 1.44/1.65 tff(2961,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2960, 2958])).
% 1.44/1.65 tff(2962,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2963,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))), s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2962, 2961])).
% 1.44/1.65 tff(2964,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2963, 112, 2794, 2769, 2957])).
% 1.44/1.65 tff(2965,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1733, 2964])).
% 1.44/1.65 tff(2966,plain,
% 1.44/1.65 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2350, 31, 2965])).
% 1.44/1.65 tff(2967,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2966, 2929])).
% 1.44/1.65 tff(2968,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2967, 2917])).
% 1.44/1.65 tff(2969,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2360, 2968, 257])).
% 1.44/1.65 tff(2970,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2969, 2915])).
% 1.44/1.65 tff(2971,plain,
% 1.44/1.65 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2913])).
% 1.44/1.65 tff(2972,plain,
% 1.44/1.65 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[2971])).
% 1.44/1.65 tff(2973,plain,
% 1.44/1.65 (b(z, s(s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2, 2972])).
% 1.44/1.65 tff(2974,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2913])).
% 1.44/1.65 tff(2975,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.44/1.65 inference(symmetry,[status(thm)],[2974])).
% 1.44/1.65 tff(2976,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2977,plain,
% 1.44/1.65 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~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(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2978,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2977])).
% 1.44/1.65 tff(2979,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2978, 2976])).
% 1.44/1.65 tff(2980,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2981,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2980, 2979])).
% 1.44/1.65 tff(2982,plain,
% 1.44/1.65 (~b(s(z), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2981, 112, 2773, 2767, 2765, 1847])).
% 1.44/1.65 tff(2983,plain,
% 1.44/1.65 (r(s(z), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[608, 2982])).
% 1.44/1.65 tff(2984,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2510, 2983, 2771])).
% 1.44/1.65 tff(2985,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[398, 2984])).
% 1.44/1.65 tff(2986,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2985, 2975])).
% 1.44/1.65 tff(2987,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2940, 31, 162, 2965])).
% 1.44/1.65 tff(2988,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[917, 78, 224, 2987])).
% 1.44/1.65 tff(2989,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[990, 2965, 2804])).
% 1.44/1.65 tff(2990,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1781, 2989, 2909, 257])).
% 1.44/1.65 tff(2991,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2992,plain,
% 1.44/1.66 (((~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)))), s(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(s(z))))), 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(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(2993,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2992])).
% 1.44/1.66 tff(2994,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[2993, 2991])).
% 1.44/1.66 tff(2995,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))), s(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(2996,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2995, 2994])).
% 1.44/1.66 tff(2997,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2996, 112, 2990, 2988, 2986, 2973, 2970])).
% 1.44/1.66 tff(2998,plain,((~r(z, s(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(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(2999,plain,
% 1.44/1.66 (~r(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2998, 2, 301, 249, 248, 1])).
% 1.44/1.66 tff(3000,plain,
% 1.44/1.66 (b(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[182, 2999])).
% 1.44/1.66 tff(3001,plain,
% 1.44/1.66 (~b(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1867, 3000, 1847, 2765])).
% 1.44/1.66 tff(3002,plain,
% 1.44/1.66 (r(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[99, 3001])).
% 1.44/1.66 tff(3003,plain,
% 1.44/1.66 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2543, 3000, 1847, 2, 2765])).
% 1.44/1.66 tff(3004,plain,
% 1.44/1.66 (r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[477, 3003])).
% 1.44/1.66 tff(3005,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[93, 3004, 3002, 1])).
% 1.44/1.66 tff(3006,plain,((~b(z, 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(s(elem!1)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3007,plain,
% 1.44/1.66 (~b(z, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3006, 301, 1, 249, 248])).
% 1.44/1.66 tff(3008,plain,
% 1.44/1.66 (r(z, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[356, 3007])).
% 1.44/1.66 tff(3009,plain,
% 1.44/1.66 (~b(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2718, 3008, 1847, 405, 2755, 1])).
% 1.44/1.66 tff(3010,plain,
% 1.44/1.66 (r(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[182, 3009])).
% 1.44/1.66 tff(3011,plain,
% 1.44/1.66 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1877, 3008, 249, 1847])).
% 1.44/1.66 tff(3012,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[429, 3011])).
% 1.44/1.66 tff(3013,plain,
% 1.44/1.66 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1933, 302, 162])).
% 1.44/1.66 tff(3014,plain,
% 1.44/1.66 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[749, 3013])).
% 1.44/1.66 tff(3015,plain,
% 1.44/1.66 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1907, 302, 162])).
% 1.44/1.66 tff(3016,plain,
% 1.44/1.66 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[462, 3015])).
% 1.44/1.66 tff(3017,plain,
% 1.44/1.66 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), 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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3018,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3017])).
% 1.44/1.66 tff(3019,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3018, 2797])).
% 1.44/1.66 tff(3020,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3021,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 1.44/1.66 tff(3022,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3021, 112, 19, 3016, 3014, 333])).
% 1.44/1.66 tff(3023,plain,((~r(z, s(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))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3024,plain,
% 1.44/1.66 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3023, 3012, 2755, 3010])).
% 1.44/1.66 tff(3025,plain,
% 1.44/1.66 (b(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[322, 3024])).
% 1.44/1.66 tff(3026,plain,
% 1.44/1.66 (~r(z, s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2660, 31, 3008, 1])).
% 1.44/1.66 tff(3027,plain,
% 1.44/1.66 (b(z, s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[515, 3026])).
% 1.44/1.66 tff(3028,plain,
% 1.44/1.66 (~r(s(s(s(z))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[563, 31, 3008, 1])).
% 1.44/1.66 tff(3029,plain,
% 1.44/1.66 (b(s(s(s(z))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[527, 3028])).
% 1.44/1.66 tff(3030,plain,
% 1.44/1.66 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1662, 2525, 442, 333])).
% 1.44/1.66 tff(3031,plain,
% 1.44/1.66 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[749, 3030])).
% 1.44/1.66 tff(3032,plain,
% 1.44/1.66 (((~![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(s(z))))) | (~r(s(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))), 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(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)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3033,plain,
% 1.44/1.66 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(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))), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3034,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(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))), s(s(s(s(elem!1))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3033])).
% 1.44/1.66 tff(3035,plain,
% 1.44/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(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))), s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3034, 3032])).
% 1.44/1.66 tff(3036,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3037,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 1.44/1.66 tff(3038,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3037, 31, 85, 3031, 1, 730])).
% 1.44/1.66 tff(3039,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(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(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3040,plain,
% 1.44/1.66 (~r(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3039, 2753, 1, 405, 2755])).
% 1.44/1.66 tff(3041,plain,
% 1.44/1.66 (b(s(z), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[99, 3040])).
% 1.44/1.66 tff(3042,plain,
% 1.44/1.66 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2791, 3041, 3010, 3029, 3027, 1847])).
% 1.44/1.66 tff(3043,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(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))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3044,plain,
% 1.44/1.66 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(z))))) | (~b(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(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))))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3045,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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)))))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3044])).
% 1.44/1.66 tff(3046,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(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))))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3045, 3043])).
% 1.44/1.66 tff(3047,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~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(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3048,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3047, 3046])).
% 1.44/1.66 tff(3049,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3048, 112, 859, 803, 1827, 334, 333, 2604])).
% 1.44/1.66 tff(3050,plain,((~b(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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3051,plain,
% 1.44/1.66 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3050, 334, 333, 803, 859, 1827])).
% 1.44/1.66 tff(3052,plain,
% 1.44/1.66 (r(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[494, 3051])).
% 1.44/1.66 tff(3053,plain,
% 1.44/1.66 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2500, 334, 101, 19, 803, 1827, 333])).
% 1.44/1.66 tff(3054,plain,
% 1.44/1.66 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[462, 3053])).
% 1.44/1.66 tff(3055,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[486, 31, 162, 3054, 3052])).
% 1.44/1.66 tff(3056,plain,((~b(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3057,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3056, 3025, 2755, 3027, 3029, 3010, 1847, 3012])).
% 1.44/1.66 tff(3058,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[398, 3057])).
% 1.44/1.66 tff(3059,plain,
% 1.44/1.66 (~b(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2981, 112, 3041, 3029, 3027, 1847])).
% 1.44/1.66 tff(3060,plain,
% 1.44/1.66 (r(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[608, 3059])).
% 1.44/1.66 tff(3061,plain,
% 1.44/1.66 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2510, 3058, 3060])).
% 1.44/1.66 tff(3062,plain,
% 1.44/1.66 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[451, 3061, 405, 3012])).
% 1.44/1.66 tff(3063,plain,
% 1.44/1.66 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[462, 3062])).
% 1.44/1.66 tff(3064,plain,
% 1.44/1.66 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[267, 265])).
% 1.44/1.66 tff(3065,plain,
% 1.44/1.66 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2235])).
% 1.44/1.66 tff(3066,plain,
% 1.44/1.66 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3065, 890])).
% 1.44/1.66 tff(3067,plain,
% 1.44/1.66 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[3066])).
% 1.44/1.66 tff(3068,plain,
% 1.44/1.66 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3067])).
% 1.44/1.66 tff(3069,plain,
% 1.44/1.66 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[265, 3068])).
% 1.44/1.66 tff(3070,plain,
% 1.44/1.66 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[1074])).
% 1.44/1.66 tff(3071,plain,
% 1.44/1.66 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[3070])).
% 1.44/1.66 tff(3072,plain,
% 1.44/1.66 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3071])).
% 1.44/1.67 tff(3073,plain,
% 1.44/1.67 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1093])).
% 1.44/1.67 tff(3074,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3073])).
% 1.44/1.67 tff(3075,plain,
% 1.44/1.67 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.44/1.67 inference(commutativity,[status(thm)],[])).
% 1.44/1.67 tff(3076,plain,
% 1.44/1.67 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[1068, 3075])).
% 1.44/1.67 tff(3077,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2874, 3076, 162, 803, 859, 102, 101])).
% 1.44/1.67 tff(3078,plain,
% 1.44/1.67 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3077, 3074])).
% 1.44/1.67 tff(3079,plain,
% 1.44/1.67 (((~![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)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3080,plain,
% 1.44/1.67 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3081,plain,
% 1.44/1.67 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(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)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3080])).
% 1.44/1.67 tff(3082,plain,
% 1.44/1.67 (((~![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(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(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)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3081, 3079])).
% 1.44/1.67 tff(3083,plain,
% 1.44/1.67 ((~![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(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3084,plain,
% 1.44/1.67 ((~![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)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 1.44/1.67 tff(3085,plain,
% 1.44/1.67 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3084, 31, 568, 249])).
% 1.44/1.67 tff(3086,plain,
% 1.44/1.67 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3085, 3078])).
% 1.44/1.67 tff(3087,plain,
% 1.44/1.67 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3086, 3072])).
% 1.44/1.67 tff(3088,plain,
% 1.44/1.67 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1209, 3087, 3069])).
% 1.44/1.67 tff(3089,plain,
% 1.44/1.67 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1068])).
% 1.44/1.67 tff(3090,plain,
% 1.44/1.67 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3089])).
% 1.44/1.67 tff(3091,plain,
% 1.44/1.67 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[2128, 3090])).
% 1.44/1.67 tff(3092,plain,
% 1.44/1.67 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[2220])).
% 1.44/1.67 tff(3093,plain,
% 1.44/1.67 (~b(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2981, 112, 102, 859, 803, 101])).
% 1.44/1.67 tff(3094,plain,
% 1.44/1.67 (r(s(z), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[608, 3093])).
% 1.44/1.67 tff(3095,plain,
% 1.44/1.67 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[273, 3064])).
% 1.44/1.67 tff(3096,plain,
% 1.44/1.67 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[404, 301, 3095])).
% 1.44/1.67 tff(3097,plain,
% 1.44/1.67 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2510, 568, 3094])).
% 1.44/1.67 tff(3098,plain,
% 1.44/1.67 (b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[477, 3097])).
% 1.44/1.67 tff(3099,plain,
% 1.44/1.67 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1662, 3098, 3096, 333])).
% 1.44/1.67 tff(3100,plain,
% 1.44/1.67 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[749, 3099])).
% 1.44/1.67 tff(3101,plain,
% 1.44/1.67 (((~![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(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))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3102,plain,
% 1.44/1.67 (((~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))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3103,plain,
% 1.44/1.67 (((~![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(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)))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3102])).
% 1.44/1.67 tff(3104,plain,
% 1.44/1.67 (((~![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(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))))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3103, 3101])).
% 1.44/1.67 tff(3105,plain,
% 1.44/1.67 ((~![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(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))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3106,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 1.44/1.67 tff(3107,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3106, 31, 592, 731, 714])).
% 1.44/1.67 tff(3108,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3109,plain,
% 1.44/1.67 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3108, 3100, 3094])).
% 1.44/1.67 tff(3110,plain,
% 1.44/1.67 (b(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[494, 3109])).
% 1.44/1.67 tff(3111,plain,
% 1.44/1.67 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3112,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3111])).
% 1.44/1.67 tff(3113,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3112, 529])).
% 1.44/1.67 tff(3114,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3115,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 1.44/1.67 tff(3116,plain,
% 1.44/1.67 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3115, 112, 859, 803, 3110])).
% 1.44/1.67 tff(3117,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[386, 3116])).
% 1.44/1.67 tff(3118,plain,
% 1.44/1.67 (((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3119,plain,
% 1.44/1.67 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(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(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3120,plain,
% 1.44/1.67 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(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(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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3119])).
% 1.44/1.67 tff(3121,plain,
% 1.44/1.67 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(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(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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3120, 3118])).
% 1.44/1.67 tff(3122,plain,
% 1.44/1.67 ((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(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(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3123,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3122, 3121])).
% 1.44/1.67 tff(3124,plain,
% 1.44/1.67 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3123, 31, 464, 3117])).
% 1.44/1.67 tff(3125,plain,
% 1.44/1.67 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3124, 3078])).
% 1.44/1.67 tff(3126,plain,
% 1.44/1.67 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3125, 3092])).
% 1.44/1.67 tff(3127,plain,
% 1.44/1.67 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1225, 3126, 3091])).
% 1.44/1.67 tff(3128,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1220, 3127, 3088, 3064, 333, 301])).
% 1.44/1.67 tff(3129,plain,((~(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(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3130,plain,
% 1.44/1.67 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3129, 2755, 301, 3063, 3058, 249, 3010, 3027, 3029, 3041, 1847, 257, 1193])).
% 1.44/1.67 tff(3131,plain,
% 1.44/1.67 (b(s(z), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[477, 3061])).
% 1.44/1.67 tff(3132,plain,
% 1.44/1.67 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1662, 3131, 405, 2755])).
% 1.44/1.67 tff(3133,plain,
% 1.44/1.67 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[749, 3132])).
% 1.44/1.67 tff(3134,plain,
% 1.44/1.67 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3108, 3133, 3060])).
% 1.44/1.67 tff(3135,plain,
% 1.44/1.67 (b(s(s(s(s(s(elem!1))))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[494, 3134])).
% 1.44/1.67 tff(3136,plain,
% 1.44/1.67 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3115, 112, 3029, 3027, 3135])).
% 1.44/1.67 tff(3137,plain,
% 1.44/1.67 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[386, 3136])).
% 1.44/1.67 tff(3138,assumption,(~b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.44/1.67 tff(3139,plain,
% 1.44/1.67 ((s(s(elem!1)) = s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1008, 78, 3138])).
% 1.44/1.67 tff(3140,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3139, 1392])).
% 1.44/1.67 tff(3141,assumption,(~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.67 tff(3142,assumption,(b(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.67 tff(3143,plain,
% 1.44/1.67 (((~b(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))))))) | (~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)))))) | (~b(s(s(elem!1)), s(s(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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3144,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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)))))) | (~b(s(s(elem!1)), s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3143])).
% 1.44/1.67 tff(3145,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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)))))) | (~b(s(s(elem!1)), s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3144, 1411])).
% 1.44/1.67 tff(3146,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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)))))) | (~b(s(s(elem!1)), s(s(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))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3147,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 1.44/1.67 tff(3148,plain,
% 1.44/1.68 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3147, 112, 3142, 333, 442])).
% 1.44/1.68 tff(3149,plain,
% 1.44/1.68 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[872, 3148, 248])).
% 1.44/1.68 tff(3150,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3151,plain,
% 1.44/1.68 (((~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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3152,plain,
% 1.44/1.68 (((~![X0: $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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3151])).
% 1.44/1.68 tff(3153,plain,
% 1.44/1.68 (((~![X0: $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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3152, 3150])).
% 1.44/1.68 tff(3154,plain,
% 1.44/1.68 ((~![X0: $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)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3155,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3154, 3153])).
% 1.44/1.68 tff(3156,plain,
% 1.44/1.68 (~r(s(s(elem!1)), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3155, 31, 3149, 569])).
% 1.44/1.68 tff(3157,plain,
% 1.44/1.68 (b(s(s(elem!1)), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[822, 78, 379, 3156])).
% 1.44/1.68 tff(3158,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3159,plain,
% 1.44/1.68 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3160,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3159])).
% 1.44/1.68 tff(3161,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3160, 3158])).
% 1.44/1.68 tff(3162,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3163,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3162, 3161])).
% 1.44/1.68 tff(3164,plain,
% 1.44/1.68 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3163, 31, 3149, 1])).
% 1.44/1.68 tff(3165,plain,
% 1.44/1.68 (b(s(s(elem!1)), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1008, 78, 1392, 3164])).
% 1.44/1.68 tff(3166,plain,
% 1.44/1.68 (~r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[563, 31, 569, 1])).
% 1.44/1.68 tff(3167,plain,
% 1.44/1.68 (b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[527, 3166])).
% 1.44/1.68 tff(3168,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3169,plain,
% 1.44/1.68 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3170,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3169])).
% 1.44/1.68 tff(3171,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3170, 3168])).
% 1.44/1.68 tff(3172,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3173,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3172, 3171])).
% 1.44/1.68 tff(3174,plain,
% 1.44/1.68 ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3173, 112, 3167, 334, 3142])).
% 1.44/1.68 tff(3175,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3174, 3165, 3157])).
% 1.44/1.68 tff(3176,plain,((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (s(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(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3177,plain,
% 1.44/1.68 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3176, 1392, 334, 1, 569, 248, 333, 442])).
% 1.44/1.68 tff(3178,plain,
% 1.44/1.68 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1025, 3177, 3141])).
% 1.44/1.68 tff(3179,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(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(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3180,plain,
% 1.44/1.68 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(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(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3181,plain,
% 1.44/1.68 (((~![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(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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)), s(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(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3180])).
% 1.44/1.68 tff(3182,plain,
% 1.44/1.68 (((~![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(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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)), s(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(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3181, 3179])).
% 1.44/1.68 tff(3183,plain,
% 1.44/1.68 ((~![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(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3184,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3183, 3182])).
% 1.44/1.68 tff(3185,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3184, 31, 464, 3178, 275, 3140])).
% 1.44/1.68 tff(3186,plain,((s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(z)))) | (~b(z, s(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)))))) | (s(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(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3187,plain,
% 1.44/1.68 (s(s(elem!1)) = s(s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3186, 3063, 3137, 3130, 3042, 3025, 1, 3008, 248, 2755, 405])).
% 1.44/1.68 tff(3188,plain,
% 1.44/1.68 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3187])).
% 1.44/1.68 tff(3189,plain,
% 1.44/1.68 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3188])).
% 1.44/1.68 tff(3190,plain,
% 1.44/1.68 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3188])).
% 1.44/1.68 tff(3191,plain,
% 1.44/1.68 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3190])).
% 1.44/1.68 tff(3192,plain,
% 1.44/1.68 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3191])).
% 1.44/1.68 tff(3193,plain,
% 1.44/1.68 (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(s(z))))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3192])).
% 1.44/1.68 tff(3194,plain,
% 1.44/1.68 (b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[405, 3193])).
% 1.44/1.68 tff(3195,plain,
% 1.44/1.68 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3187])).
% 1.44/1.68 tff(3196,plain,
% 1.44/1.68 (s(elem!1) = s(s(z))),
% 1.44/1.68 inference(transitivity,[status(thm)],[145, 3195, 55])).
% 1.44/1.68 tff(3197,plain,
% 1.44/1.68 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3196])).
% 1.44/1.68 tff(3198,plain,
% 1.44/1.68 (elem!1 = s(z)),
% 1.44/1.68 inference(transitivity,[status(thm)],[1073, 3197, 137])).
% 1.44/1.68 tff(3199,plain,
% 1.44/1.68 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3191, 3198])).
% 1.44/1.68 tff(3200,plain,
% 1.44/1.68 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.68 inference(symmetry,[status(thm)],[3199])).
% 1.44/1.68 tff(3201,plain,
% 1.44/1.68 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3012, 3200])).
% 1.44/1.68 tff(3202,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3191])).
% 1.44/1.68 tff(3203,plain,
% 1.44/1.68 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3202])).
% 1.44/1.68 tff(3204,plain,
% 1.44/1.68 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1736])).
% 1.44/1.68 tff(3205,plain,
% 1.44/1.68 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3204])).
% 1.44/1.68 tff(3206,plain,
% 1.44/1.68 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1, 3205])).
% 1.44/1.68 tff(3207,assumption,(~r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.68 tff(3208,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3207, 3206])).
% 1.44/1.68 tff(3209,plain,(r(s(s(s(z))), s(s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3210,plain,
% 1.44/1.68 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3209, 3187, 1])).
% 1.44/1.68 tff(3211,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2944, 3041, 3010, 3029, 1847, 3027])).
% 1.44/1.68 tff(3212,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.68 tff(3213,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.68 tff(3214,plain,
% 1.44/1.68 (((~![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)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(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(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3215,plain,
% 1.44/1.68 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3216,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3215])).
% 1.44/1.68 tff(3217,plain,
% 1.44/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3216, 3214])).
% 1.44/1.68 tff(3218,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3219,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3218, 3217])).
% 1.44/1.68 tff(3220,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3219, 31, 1720, 3213, 3212])).
% 1.44/1.68 tff(3221,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3222,plain,
% 1.44/1.68 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3221, 3211, 3210])).
% 1.44/1.68 tff(3223,plain,
% 1.44/1.68 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3222, 3203])).
% 1.44/1.68 tff(3224,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1781, 3223, 3187, 257])).
% 1.44/1.68 tff(3225,plain,
% 1.44/1.68 (~b(s(s(s(s(z)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1764, 3224, 2755, 3131, 3187, 3201, 405])).
% 1.44/1.68 tff(3226,plain,
% 1.44/1.68 (r(s(s(s(s(z)))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1733, 3225])).
% 1.44/1.68 tff(3227,plain,
% 1.44/1.68 (~r(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2940, 31, 3010, 3226])).
% 1.44/1.68 tff(3228,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[917, 78, 224, 3227])).
% 1.44/1.68 tff(3229,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3230,plain,
% 1.44/1.69 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3231,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3230])).
% 1.44/1.69 tff(3232,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3231, 3229])).
% 1.44/1.69 tff(3233,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3234,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3233, 3232])).
% 1.44/1.69 tff(3235,plain,
% 1.44/1.69 ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(z)))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3234, 112, 3025, 3224])).
% 1.44/1.69 tff(3236,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3235, 3228, 3194])).
% 1.44/1.69 tff(3237,plain,
% 1.44/1.69 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2954, 3211, 2753])).
% 1.44/1.69 tff(3238,plain,
% 1.44/1.69 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[936, 78, 3237])).
% 1.44/1.69 tff(3239,plain,
% 1.44/1.69 (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3238, 3236])).
% 1.44/1.69 tff(3240,plain,
% 1.44/1.69 (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[3239])).
% 1.44/1.69 tff(3241,plain,
% 1.44/1.69 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3240, 3189])).
% 1.44/1.69 tff(3242,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[889, 3241])).
% 1.44/1.69 tff(3243,plain,(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)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3244,plain,
% 1.44/1.69 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3243, 400, 248, 249])).
% 1.44/1.69 tff(3245,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))) <=> ((~![X0: $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(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3246,plain,
% 1.44/1.69 (((~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(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)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3247,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(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))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3246])).
% 1.44/1.69 tff(3248,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(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)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3247, 3245])).
% 1.44/1.69 tff(3249,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3250,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 1.44/1.69 tff(3251,plain,
% 1.44/1.69 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3250, 31, 3244, 400])).
% 1.44/1.69 tff(3252,plain,
% 1.44/1.69 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2752, 3251])).
% 1.44/1.69 tff(3253,plain,
% 1.44/1.69 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[284, 3244, 249])).
% 1.44/1.69 tff(3254,plain,
% 1.44/1.69 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[386, 3253])).
% 1.44/1.69 tff(3255,plain,
% 1.44/1.69 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3243, 1, 248, 249])).
% 1.44/1.69 tff(3256,plain,
% 1.44/1.69 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[284, 3255, 249])).
% 1.44/1.69 tff(3257,plain,
% 1.44/1.69 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[386, 3256])).
% 1.44/1.69 tff(3258,plain,
% 1.44/1.69 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3250, 31, 3255, 1])).
% 1.44/1.69 tff(3259,plain,
% 1.44/1.69 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2752, 3258])).
% 1.44/1.69 tff(3260,plain,
% 1.44/1.69 (~r(z, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[503, 20, 3])).
% 1.44/1.69 tff(3261,plain,
% 1.44/1.69 (b(z, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[182, 3260])).
% 1.44/1.69 tff(3262,plain,
% 1.44/1.69 (~b(z, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[547, 3261, 19, 539])).
% 1.44/1.69 tff(3263,plain,
% 1.44/1.69 (r(z, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[356, 3262])).
% 1.44/1.69 tff(3264,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[363, 31, 20, 3263, 249])).
% 1.44/1.69 tff(3265,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3266,plain,
% 1.44/1.69 (~r(z, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3265, 430, 249, 478, 3])).
% 1.44/1.69 tff(3267,plain,
% 1.44/1.69 (b(z, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[515, 3266])).
% 1.44/1.69 tff(3268,plain,
% 1.44/1.69 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2531, 112, 3267, 3259, 3257])).
% 1.44/1.69 tff(3269,plain,
% 1.44/1.69 (r(z, s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[322, 3268])).
% 1.44/1.69 tff(3270,plain,
% 1.44/1.69 (~r(z, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[783, 3269, 3255])).
% 1.44/1.69 tff(3271,plain,
% 1.44/1.69 (b(z, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[356, 3270])).
% 1.44/1.69 tff(3272,plain,
% 1.44/1.69 (~b(z, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[547, 3271, 430, 478])).
% 1.44/1.69 tff(3273,plain,
% 1.44/1.69 (r(z, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[182, 3272])).
% 1.44/1.69 tff(3274,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[522, 31, 612, 3, 162])).
% 1.44/1.69 tff(3275,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3276,plain,
% 1.44/1.69 (~r(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3275, 3273, 3])).
% 1.44/1.69 tff(3277,plain,
% 1.44/1.69 (b(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[527, 3276])).
% 1.44/1.69 tff(3278,plain,
% 1.44/1.69 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3023, 3273, 430, 3269])).
% 1.44/1.69 tff(3279,plain,
% 1.44/1.69 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[299, 3278, 268])).
% 1.44/1.69 tff(3280,plain,
% 1.44/1.69 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3023, 162, 19, 2533])).
% 1.44/1.69 tff(3281,plain,
% 1.44/1.69 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[299, 3280, 3064])).
% 1.44/1.69 tff(3282,plain,
% 1.44/1.69 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[1074])).
% 1.44/1.69 tff(3283,plain,
% 1.44/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[3282])).
% 1.44/1.69 tff(3284,plain,
% 1.44/1.69 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3283])).
% 1.44/1.69 tff(3285,plain,
% 1.44/1.69 (~r(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3275, 162, 3])).
% 1.44/1.69 tff(3286,plain,
% 1.44/1.69 (b(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[527, 3285])).
% 1.44/1.69 tff(3287,plain,
% 1.44/1.69 (b(elem!1, z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.44/1.69 inference(monotonicity,[status(thm)],[1074])).
% 1.44/1.69 tff(3288,plain,
% 1.44/1.69 ((~b(elem!1, z)) <=> (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3287])).
% 1.44/1.69 tff(3289,plain,
% 1.44/1.69 (~b(elem!1, z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1506, 2106, 803, 859])).
% 1.44/1.69 tff(3290,plain,
% 1.44/1.69 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3289, 3288])).
% 1.44/1.69 tff(3291,plain,
% 1.44/1.69 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 3290])).
% 1.44/1.69 tff(3292,plain,
% 1.44/1.69 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2132, 2223])).
% 1.44/1.69 tff(3293,plain,
% 1.44/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3294,plain,
% 1.44/1.69 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3295,plain,
% 1.44/1.69 (((~![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(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(s(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3294])).
% 1.44/1.69 tff(3296,plain,
% 1.44/1.69 (((~![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(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(s(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3295, 3293])).
% 1.44/1.69 tff(3297,plain,
% 1.44/1.69 ((~![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(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3298,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3297, 3296])).
% 1.44/1.69 tff(3299,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3298, 31, 162, 302, 3292, 3291])).
% 1.44/1.69 tff(3300,plain,((~b(elem!1, s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3301,plain,
% 1.44/1.69 (~b(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3300, 1068, 2533, 162, 2128, 2229, 2226, 803, 3286])).
% 1.44/1.69 tff(3302,plain,
% 1.44/1.69 (r(elem!1, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1498, 3301, 2234])).
% 1.44/1.69 tff(3303,plain,
% 1.44/1.69 (~r(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1568, 3302, 3])).
% 1.44/1.69 tff(3304,plain,
% 1.44/1.69 (b(elem!1, s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1139, 3303, 1125])).
% 1.44/1.69 tff(3305,plain,
% 1.44/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2249, 3304, 1068])).
% 1.44/1.69 tff(3306,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3307,plain,
% 1.44/1.69 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3308,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3307])).
% 1.44/1.69 tff(3309,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3308, 3306])).
% 1.44/1.69 tff(3310,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3311,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 1.44/1.69 tff(3312,plain,
% 1.44/1.69 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3311, 112, 19, 3305, 539])).
% 1.44/1.69 tff(3313,plain,
% 1.44/1.69 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3312, 3284])).
% 1.44/1.69 tff(3314,plain,
% 1.44/1.69 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1209, 3313, 3069])).
% 1.44/1.69 tff(3315,plain,
% 1.44/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[1094])).
% 1.44/1.69 tff(3316,plain,
% 1.44/1.69 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) <=> (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3315])).
% 1.44/1.69 tff(3317,plain,
% 1.44/1.69 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1933, 162, 2533])).
% 1.44/1.69 tff(3318,plain,
% 1.44/1.69 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[749, 3317])).
% 1.44/1.69 tff(3319,plain,
% 1.44/1.69 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[536, 162, 3])).
% 1.44/1.69 tff(3320,plain,
% 1.44/1.69 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[462, 3319])).
% 1.44/1.69 tff(3321,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3322,plain,
% 1.44/1.69 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(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(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(s(elem!1)))))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3323,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3322])).
% 1.44/1.69 tff(3324,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3323, 3321])).
% 1.54/1.70 tff(3325,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(elem!1)))))), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3326,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3325, 3324])).
% 1.54/1.70 tff(3327,plain,
% 1.54/1.70 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3326, 112, 19, 3320, 3318, 3305, 539])).
% 1.54/1.70 tff(3328,plain,
% 1.54/1.70 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3327, 3316])).
% 1.54/1.70 tff(3329,plain,
% 1.54/1.70 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1225, 3328, 3091])).
% 1.54/1.70 tff(3330,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.70 tff(3331,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(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(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3332,plain,
% 1.54/1.70 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3333,plain,
% 1.54/1.70 (((~![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(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(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(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3332])).
% 1.54/1.70 tff(3334,plain,
% 1.54/1.70 (((~![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(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(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(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3333, 3331])).
% 1.54/1.70 tff(3335,plain,
% 1.54/1.70 ((~![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(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3336,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3335, 3334])).
% 1.54/1.70 tff(3337,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3336, 31, 1621, 3330, 1887])).
% 1.54/1.70 tff(3338,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3339,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3338, 3329, 3314, 3281])).
% 1.54/1.70 tff(3340,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(z, s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3341,plain,
% 1.54/1.70 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3340, 430, 478, 3, 3273, 1193, 3267, 257, 3257, 3259])).
% 1.54/1.70 tff(3342,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.54/1.70 tff(3343,plain,
% 1.54/1.70 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[3075])).
% 1.54/1.70 tff(3344,plain,
% 1.54/1.70 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[2096, 3343])).
% 1.54/1.70 tff(3345,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3141, 3344])).
% 1.54/1.70 tff(3346,plain,((~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3347,plain,
% 1.54/1.70 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3346, 3141])).
% 1.54/1.70 tff(3348,assumption,(~(s(z) = s(s(elem!1)))), introduced(assumption)).
% 1.54/1.70 tff(3349,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))), introduced(assumption)).
% 1.54/1.70 tff(3350,assumption,(r(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.70 tff(3351,plain,
% 1.54/1.70 (((~![X0: $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(z, 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(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3352,plain,
% 1.54/1.70 (((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1)))))))) <=> ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3353,plain,
% 1.54/1.70 (((~![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(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), 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(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3352])).
% 1.54/1.70 tff(3354,plain,
% 1.54/1.70 (((~![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(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), 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(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3353, 3351])).
% 1.54/1.70 tff(3355,plain,
% 1.54/1.70 ((~![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(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3356,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.54/1.70 tff(3357,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3356, 31, 302, 3350, 3342])).
% 1.54/1.70 tff(3358,plain,((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3359,plain,
% 1.54/1.70 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3358, 3342, 302])).
% 1.54/1.70 tff(3360,plain,
% 1.54/1.70 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2066, 3359, 3349])).
% 1.54/1.70 tff(3361,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(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(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3362,plain,
% 1.54/1.70 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(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(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3363,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(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(elem!1))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3362])).
% 1.54/1.70 tff(3364,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(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(elem!1)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3363, 3361])).
% 1.54/1.70 tff(3365,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), 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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3366,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(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(elem!1))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3365, 3364])).
% 1.54/1.70 tff(3367,plain,
% 1.54/1.70 (~b(s(z), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3366, 112, 3360, 3142, 3014])).
% 1.54/1.70 tff(3368,plain,
% 1.54/1.70 (r(s(z), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[856, 3367, 3348])).
% 1.54/1.70 tff(3369,plain,
% 1.54/1.70 (((~![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(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(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3370,plain,
% 1.54/1.70 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3371,plain,
% 1.54/1.70 (((~![X0: $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(z, s(s(elem!1)))) | (~r(s(z), 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(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3370])).
% 1.54/1.70 tff(3372,plain,
% 1.54/1.70 (((~![X0: $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(z, s(s(elem!1)))) | (~r(s(z), 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(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3371, 3369])).
% 1.54/1.70 tff(3373,plain,
% 1.54/1.70 ((~![X0: $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(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3374,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3373, 3372])).
% 1.54/1.70 tff(3375,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3374, 31, 162, 3368, 3342])).
% 1.54/1.70 tff(3376,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (s(z) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3377,plain,
% 1.54/1.70 ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3376, 150])).
% 1.54/1.70 tff(3378,plain,
% 1.54/1.70 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3377, 3342, 302, 162, 3347])).
% 1.54/1.70 tff(3379,plain,
% 1.54/1.70 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1025, 3378, 3141])).
% 1.54/1.70 tff(3380,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(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(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3381,plain,
% 1.54/1.70 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3382,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(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(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3381])).
% 1.54/1.70 tff(3383,plain,
% 1.54/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(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(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3382, 3380])).
% 1.54/1.70 tff(3384,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3385,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(elem!1))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.54/1.70 tff(3386,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3385, 31, 302, 3379, 3342])).
% 1.54/1.70 tff(3387,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3388,plain,
% 1.54/1.70 (~r(z, s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3387, 3141, 2533, 162])).
% 1.54/1.70 tff(3389,plain,
% 1.54/1.70 (b(z, s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[841, 3388])).
% 1.54/1.70 tff(3390,plain,
% 1.54/1.70 (((~![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(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), 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(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3391,plain,
% 1.54/1.70 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3392,plain,
% 1.54/1.70 (((~![X0: $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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3391])).
% 1.54/1.70 tff(3393,plain,
% 1.54/1.71 (((~![X0: $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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3392, 3390])).
% 1.54/1.71 tff(3394,plain,
% 1.54/1.71 ((~![X0: $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(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3395,plain,
% 1.54/1.71 ((~![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(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3394, 3393])).
% 1.54/1.71 tff(3396,plain,
% 1.54/1.71 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3395, 31, 162, 2533, 1887])).
% 1.54/1.71 tff(3397,plain,
% 1.54/1.71 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[398, 3396])).
% 1.54/1.71 tff(3398,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(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))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3399,plain,
% 1.54/1.71 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(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(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3400,plain,
% 1.54/1.71 (((~![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(elem!1)))), s(s(s(z))))) | (~r(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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(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))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3399])).
% 1.54/1.71 tff(3401,plain,
% 1.54/1.71 (((~![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(elem!1)))), s(s(s(z))))) | (~r(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(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(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))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3400, 3398])).
% 1.54/1.71 tff(3402,plain,
% 1.54/1.71 ((~![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(elem!1)))), s(s(s(z))))) | (~r(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(elem!1)), s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3403,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3402, 3401])).
% 1.54/1.71 tff(3404,plain,
% 1.54/1.71 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3403, 31, 1887, 249, 1953])).
% 1.54/1.71 tff(3405,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[872, 3404, 248])).
% 1.54/1.71 tff(3406,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1998, 3405, 1987, 2, 1988])).
% 1.54/1.71 tff(3407,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = 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,[]))).
% 1.54/1.71 tff(3408,plain,
% 1.54/1.71 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3407, 3389, 2, 248, 1887, 249])).
% 1.54/1.71 tff(3409,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1008, 78, 1392, 3408])).
% 1.54/1.71 tff(3410,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3411,plain,
% 1.54/1.71 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3412,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3411])).
% 1.54/1.71 tff(3413,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3412, 3410])).
% 1.54/1.71 tff(3414,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3415,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3414, 3413])).
% 1.54/1.71 tff(3416,plain,
% 1.54/1.71 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3415, 112, 859, 803, 3409, 406, 762])).
% 1.54/1.71 tff(3417,plain,
% 1.54/1.71 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1025, 3416, 3141])).
% 1.54/1.71 tff(3418,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.71 tff(3419,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3420,plain,
% 1.54/1.71 (((~r(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))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3421,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3420])).
% 1.54/1.71 tff(3422,plain,
% 1.54/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3421, 3419])).
% 1.54/1.71 tff(3423,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3424,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3423, 3422])).
% 1.54/1.71 tff(3425,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3424, 31, 3418, 1438, 1887])).
% 1.54/1.71 tff(3426,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3427,plain,
% 1.54/1.71 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3426, 3417, 1887])).
% 1.54/1.71 tff(3428,plain,
% 1.54/1.71 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1986, 3427, 1975])).
% 1.54/1.71 tff(3429,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3430,plain,
% 1.54/1.71 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, 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(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3431,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3430])).
% 1.54/1.71 tff(3432,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3431, 3429])).
% 1.54/1.71 tff(3433,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3434,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3433, 3432])).
% 1.54/1.71 tff(3435,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3434, 112, 803, 3428, 3409, 3397, 2, 3389])).
% 1.54/1.71 tff(3436,plain,((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(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))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3437,plain,
% 1.54/1.71 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3436, 3341, 3271, 3279, 3277, 3259, 3257, 3267, 248, 249, 3273])).
% 1.54/1.71 tff(3438,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3437])).
% 1.54/1.71 tff(3439,plain,
% 1.54/1.71 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3438])).
% 1.54/1.71 tff(3440,plain,
% 1.54/1.71 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3439])).
% 1.54/1.71 tff(3441,plain,
% 1.54/1.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3438])).
% 1.54/1.71 tff(3442,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3441, 3440])).
% 1.54/1.71 tff(3443,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3442, 890])).
% 1.54/1.71 tff(3444,plain,
% 1.54/1.71 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3443])).
% 1.54/1.71 tff(3445,plain,
% 1.54/1.71 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3444])).
% 1.54/1.71 tff(3446,plain,
% 1.54/1.71 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[257, 3445])).
% 1.54/1.71 tff(3447,plain,
% 1.54/1.71 (r(s(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))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1736])).
% 1.54/1.71 tff(3448,plain,
% 1.54/1.71 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3447])).
% 1.54/1.71 tff(3449,plain,
% 1.54/1.71 (r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[1887, 3448])).
% 1.54/1.71 tff(3450,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.54/1.71 tff(3451,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3450, 3449])).
% 1.54/1.71 tff(3452,plain,(r(s(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))))))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3453,plain,
% 1.54/1.71 (r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3452, 3279, 3437])).
% 1.54/1.71 tff(3454,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3441])).
% 1.54/1.71 tff(3455,plain,
% 1.54/1.71 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3454, 900])).
% 1.54/1.71 tff(3456,plain,
% 1.54/1.71 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3455])).
% 1.54/1.71 tff(3457,plain,
% 1.54/1.71 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3456])).
% 1.54/1.71 tff(3458,plain,
% 1.54/1.71 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[889, 3457])).
% 1.54/1.71 tff(3459,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2940, 31, 162, 981])).
% 1.54/1.71 tff(3460,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[917, 78, 224, 3459])).
% 1.54/1.71 tff(3461,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[960, 31, 3, 981])).
% 1.54/1.71 tff(3462,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[972, 78, 969, 3461])).
% 1.54/1.71 tff(3463,plain,
% 1.54/1.71 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3464,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3463])).
% 1.54/1.72 tff(3465,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3464, 1685])).
% 1.54/1.72 tff(3466,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3467,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3466, 3465])).
% 1.54/1.72 tff(3468,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3467, 112, 859, 803, 3462, 3460])).
% 1.54/1.72 tff(3469,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3470,plain,
% 1.54/1.72 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3469, 3277, 3, 3267, 3273])).
% 1.54/1.72 tff(3471,plain,
% 1.54/1.72 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1733, 3470])).
% 1.54/1.72 tff(3472,plain,
% 1.54/1.72 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1933, 3273, 3269])).
% 1.54/1.72 tff(3473,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[749, 3472])).
% 1.54/1.72 tff(3474,plain,
% 1.54/1.72 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[536, 3273, 3])).
% 1.54/1.72 tff(3475,plain,
% 1.54/1.72 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[462, 3474])).
% 1.54/1.72 tff(3476,plain,
% 1.54/1.72 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(s(z)))), s(z)))) <=> ((~b(s(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(s(s(s(z)))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3477,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(s(z)))), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3476])).
% 1.54/1.72 tff(3478,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3477, 2958])).
% 1.54/1.72 tff(3479,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(s(z)))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3480,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(s(z)))), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3479, 3478])).
% 1.54/1.72 tff(3481,plain,
% 1.54/1.72 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3480, 112, 3475, 3473, 3471])).
% 1.54/1.72 tff(3482,plain,
% 1.54/1.72 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[936, 78, 3481])).
% 1.54/1.72 tff(3483,plain,
% 1.54/1.72 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3482, 3458])).
% 1.54/1.72 tff(3484,plain,
% 1.54/1.72 (((~![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(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(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(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3485,plain,
% 1.54/1.72 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3486,plain,
% 1.54/1.72 (((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3485])).
% 1.54/1.72 tff(3487,plain,
% 1.54/1.72 (((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~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(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3486, 3484])).
% 1.54/1.72 tff(3488,plain,
% 1.54/1.72 ((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3489,plain,
% 1.54/1.72 ((~![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(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3488, 3487])).
% 1.54/1.72 tff(3490,plain,
% 1.54/1.72 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3489, 31, 3483, 3453])).
% 1.54/1.72 tff(3491,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3440])).
% 1.54/1.72 tff(3492,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[3491])).
% 1.54/1.72 tff(3493,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[478, 3492])).
% 1.54/1.72 tff(3494,plain,
% 1.54/1.72 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3437])).
% 1.54/1.72 tff(3495,plain,
% 1.54/1.72 (s(elem!1) = s(s(z))),
% 1.54/1.72 inference(transitivity,[status(thm)],[145, 3494, 55])).
% 1.54/1.72 tff(3496,plain,
% 1.54/1.72 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3495])).
% 1.54/1.72 tff(3497,plain,
% 1.54/1.72 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.54/1.72 inference(symmetry,[status(thm)],[3496])).
% 1.54/1.72 tff(3498,plain,
% 1.54/1.72 (s(z) = elem!1),
% 1.54/1.72 inference(transitivity,[status(thm)],[138, 3497, 247])).
% 1.54/1.72 tff(3499,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3498])).
% 1.54/1.72 tff(3500,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.72 inference(symmetry,[status(thm)],[3499])).
% 1.54/1.72 tff(3501,plain,
% 1.54/1.72 (elem!1 = s(z)),
% 1.54/1.72 inference(transitivity,[status(thm)],[1073, 3496, 137])).
% 1.54/1.72 tff(3502,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3440, 3501])).
% 1.54/1.72 tff(3503,plain,
% 1.54/1.72 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.72 inference(symmetry,[status(thm)],[3502])).
% 1.54/1.72 tff(3504,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[430, 3503])).
% 1.54/1.72 tff(3505,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3504, 3500])).
% 1.54/1.72 tff(3506,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3507,plain,
% 1.54/1.72 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), 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(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3508,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3507])).
% 1.54/1.72 tff(3509,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3508, 3506])).
% 1.54/1.72 tff(3510,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3511,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 1.54/1.72 tff(3512,plain,
% 1.54/1.72 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3511, 112, 3475, 3473, 3471])).
% 1.54/1.72 tff(3513,plain,
% 1.54/1.72 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3512, 3505, 3493])).
% 1.54/1.72 tff(3514,plain,
% 1.54/1.72 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1778, 78, 3513])).
% 1.54/1.72 tff(3515,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3514, 3490, 3446])).
% 1.54/1.72 tff(3516,plain,((~r(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3517,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3516, 400, 249, 248])).
% 1.54/1.72 tff(3518,plain,
% 1.54/1.72 (b(s(s(s(z))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[83, 3517])).
% 1.54/1.72 tff(3519,plain,
% 1.54/1.72 (((~![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(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3520,plain,
% 1.54/1.73 (((~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(elem!1)))))) | (~r(s(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)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3521,plain,
% 1.54/1.73 (((~![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(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(z))))) <=> ((~![X0: $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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3520])).
% 1.54/1.73 tff(3522,plain,
% 1.54/1.73 (((~![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(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(z))))) <=> ((~![X0: $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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3521, 3519])).
% 1.54/1.73 tff(3523,plain,
% 1.54/1.73 ((~![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(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(z))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3524,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3523, 3522])).
% 1.54/1.73 tff(3525,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3524, 31, 464, 276, 21])).
% 1.54/1.73 tff(3526,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3527,plain,
% 1.54/1.73 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3526, 21, 276])).
% 1.54/1.73 tff(3528,plain,
% 1.54/1.73 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[462, 3527])).
% 1.54/1.73 tff(3529,plain,
% 1.54/1.73 (~r(s(z), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[93, 21, 1])).
% 1.54/1.73 tff(3530,plain,
% 1.54/1.73 (b(s(z), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[99, 3529])).
% 1.54/1.73 tff(3531,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1919, 112, 3530, 101, 3528, 762])).
% 1.54/1.73 tff(3532,plain,((~r(s(z), 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))))) | (~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3533,plain,
% 1.54/1.73 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3532, 3518, 3254, 3244, 400])).
% 1.54/1.73 tff(3534,plain,
% 1.54/1.73 (b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[477, 3533])).
% 1.54/1.73 tff(3535,plain,
% 1.54/1.73 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[284, 276, 249])).
% 1.54/1.73 tff(3536,plain,
% 1.54/1.73 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[386, 3535])).
% 1.54/1.73 tff(3537,plain,
% 1.54/1.73 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(z))) | (~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(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3538,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(elem!1))))), s(s(s(z)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3537])).
% 1.54/1.73 tff(3539,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3538, 1914])).
% 1.54/1.73 tff(3540,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3541,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3540, 3539])).
% 1.54/1.73 tff(3542,plain,
% 1.54/1.73 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3541, 112, 1857, 101, 3536])).
% 1.54/1.73 tff(3543,plain,
% 1.54/1.73 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[462, 3542])).
% 1.54/1.73 tff(3544,plain,
% 1.54/1.73 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3526, 3543, 276])).
% 1.54/1.73 tff(3545,plain,
% 1.54/1.73 ((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)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[330, 78, 1886])).
% 1.54/1.73 tff(3546,plain,
% 1.54/1.73 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3545, 327])).
% 1.54/1.73 tff(3547,plain,
% 1.54/1.73 (~r(s(s(s(z))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1423, 3546, 408, 464])).
% 1.54/1.73 tff(3548,plain,
% 1.54/1.73 (b(s(s(s(z))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[83, 3547])).
% 1.54/1.73 tff(3549,plain,
% 1.54/1.73 (((~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(elem!1)))))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~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(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3550,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3549])).
% 1.54/1.73 tff(3551,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3550, 1655])).
% 1.54/1.73 tff(3552,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)))))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3553,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 1.54/1.73 tff(3554,plain,
% 1.54/1.73 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3553, 112, 1897, 3546, 539])).
% 1.54/1.73 tff(3555,plain,
% 1.54/1.73 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[749, 3554])).
% 1.54/1.73 tff(3556,plain,
% 1.54/1.73 (~r(z, s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1911, 408, 464, 271])).
% 1.54/1.73 tff(3557,plain,
% 1.54/1.73 (b(z, s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[182, 3556])).
% 1.54/1.73 tff(3558,plain,
% 1.54/1.73 (~r(s(z), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1855, 249, 408])).
% 1.54/1.73 tff(3559,plain,
% 1.54/1.73 (b(s(z), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[99, 3558])).
% 1.54/1.73 tff(3560,plain,
% 1.54/1.73 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1875, 31, 20, 408, 249])).
% 1.54/1.73 tff(3561,plain,
% 1.54/1.73 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[356, 3560])).
% 1.54/1.73 tff(3562,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3563,plain,
% 1.54/1.73 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3564,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3563])).
% 1.54/1.73 tff(3565,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3564, 3562])).
% 1.54/1.73 tff(3566,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3567,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3566, 3565])).
% 1.54/1.73 tff(3568,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3567, 112, 1827, 2, 673, 539])).
% 1.54/1.73 tff(3569,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3570,plain,
% 1.54/1.73 (~b(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3569, 399, 539, 3561])).
% 1.54/1.73 tff(3571,plain,
% 1.54/1.73 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3553, 112, 333, 332, 539])).
% 1.54/1.73 tff(3572,plain,
% 1.54/1.73 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[749, 3571])).
% 1.54/1.73 tff(3573,plain,
% 1.54/1.73 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[342, 3561, 333, 271, 301])).
% 1.54/1.73 tff(3574,plain,
% 1.54/1.73 (r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[322, 3573])).
% 1.54/1.73 tff(3575,plain,
% 1.54/1.73 (~r(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1670, 31, 3574, 3572])).
% 1.54/1.73 tff(3576,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[606, 78, 176, 3575, 3570])).
% 1.54/1.73 tff(3577,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3578,plain,
% 1.54/1.73 (~r(z, s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3577, 249, 271, 301, 539, 408, 333])).
% 1.54/1.73 tff(3579,plain,
% 1.54/1.73 (b(z, s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[515, 3578])).
% 1.54/1.73 tff(3580,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1867, 3579, 3559, 18, 101])).
% 1.54/1.73 tff(3581,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3582,plain,
% 1.54/1.73 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3581, 3548, 3557, 271, 1886, 539, 408, 1897])).
% 1.54/1.73 tff(3583,plain,
% 1.54/1.73 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[646, 3582])).
% 1.54/1.73 tff(3584,plain,
% 1.54/1.73 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))) | (~b(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(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(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3585,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3584])).
% 1.54/1.73 tff(3586,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3585, 763])).
% 1.54/1.73 tff(3587,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(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))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3588,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 1.54/1.73 tff(3589,plain,
% 1.54/1.73 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3588, 112, 4, 196, 442])).
% 1.54/1.73 tff(3590,plain,
% 1.54/1.73 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[384, 78, 381, 3589])).
% 1.54/1.73 tff(3591,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3592,plain,
% 1.54/1.74 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), 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(s(s(z))), s(z))) | (~b(s(z), s(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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3593,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3592])).
% 1.54/1.74 tff(3594,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3593, 3591])).
% 1.54/1.74 tff(3595,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3596,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3595, 3594])).
% 1.54/1.74 tff(3597,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3596, 112, 102, 101, 4, 196, 539])).
% 1.54/1.74 tff(3598,plain,((~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3599,plain,
% 1.54/1.74 (~b(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3598, 4, 101, 196, 539])).
% 1.54/1.74 tff(3600,plain,
% 1.54/1.74 (r(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[99, 3599])).
% 1.54/1.74 tff(3601,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2674, 31, 3600, 731, 3590])).
% 1.54/1.74 tff(3602,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(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(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3603,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3602, 3583, 3555, 3546, 3548, 539])).
% 1.54/1.74 tff(3604,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[160, 3603])).
% 1.54/1.74 tff(3605,plain,
% 1.54/1.74 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2708, 101, 332, 569, 333, 18, 3572])).
% 1.54/1.74 tff(3606,plain,
% 1.54/1.74 (b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[322, 3605])).
% 1.54/1.74 tff(3607,plain,
% 1.54/1.74 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3581, 101, 18, 271, 301, 539, 408, 333])).
% 1.54/1.74 tff(3608,plain,
% 1.54/1.74 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[646, 3607])).
% 1.54/1.74 tff(3609,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3602, 3608, 3572, 332, 101, 539])).
% 1.54/1.74 tff(3610,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[160, 3609])).
% 1.54/1.74 tff(3611,plain,
% 1.54/1.74 (~r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[563, 31, 569, 3610])).
% 1.54/1.74 tff(3612,plain,
% 1.54/1.74 (b(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[527, 3611])).
% 1.54/1.74 tff(3613,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(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(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(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(s(elem!1))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3614,plain,
% 1.54/1.74 (((~b(z, s(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(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(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(s(elem!1))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3615,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(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(s(elem!1)))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3614])).
% 1.54/1.74 tff(3616,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(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(s(elem!1))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3615, 3613])).
% 1.54/1.74 tff(3617,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3618,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 1.54/1.74 tff(3619,plain,
% 1.54/1.74 (~b(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3618, 112, 3612, 3608, 3606, 333])).
% 1.54/1.74 tff(3620,plain,
% 1.54/1.74 (r(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[398, 3619])).
% 1.54/1.74 tff(3621,plain,
% 1.54/1.74 (~r(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[600, 3620, 408])).
% 1.54/1.74 tff(3622,plain,
% 1.54/1.74 (b(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[608, 3621])).
% 1.54/1.74 tff(3623,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2685, 112, 3612, 101, 18, 3622])).
% 1.54/1.74 tff(3624,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3625,plain,
% 1.54/1.74 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3624, 3548, 408, 1897, 3557, 539, 271, 1886])).
% 1.54/1.74 tff(3626,plain,
% 1.54/1.74 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[356, 3625])).
% 1.54/1.74 tff(3627,plain,
% 1.54/1.74 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[342, 3626, 1897, 271, 1886])).
% 1.54/1.74 tff(3628,plain,
% 1.54/1.74 (r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[322, 3627])).
% 1.54/1.74 tff(3629,plain,
% 1.54/1.74 (~r(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1670, 31, 3628, 3555])).
% 1.54/1.74 tff(3630,plain,
% 1.54/1.74 (b(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[608, 3629])).
% 1.54/1.74 tff(3631,plain,
% 1.54/1.74 (~b(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3569, 3630, 539, 3626])).
% 1.54/1.74 tff(3632,plain,
% 1.54/1.74 (r(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[398, 3631])).
% 1.54/1.74 tff(3633,plain,
% 1.54/1.74 (~b(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2685, 112, 3548, 3557, 3630])).
% 1.54/1.74 tff(3634,plain,
% 1.54/1.74 (r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[527, 3633])).
% 1.54/1.74 tff(3635,plain,
% 1.54/1.74 (((~![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(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, 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)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3636,plain,
% 1.54/1.74 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), 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(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3637,plain,
% 1.54/1.74 (((~![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)))), z)) | (~r(s(s(s(z))), 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(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3636])).
% 1.54/1.74 tff(3638,plain,
% 1.54/1.74 (((~![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)))), z)) | (~r(s(s(s(z))), 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(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3637, 3635])).
% 1.54/1.74 tff(3639,plain,
% 1.54/1.74 ((~![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)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3640,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3639, 3638])).
% 1.54/1.74 tff(3641,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3640, 31, 3634, 408, 3632, 3604])).
% 1.54/1.74 tff(3642,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3643,plain,
% 1.54/1.74 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3642, 3543, 408, 271])).
% 1.54/1.74 tff(3644,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[477, 3643, 3544])).
% 1.54/1.74 tff(3645,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3646,plain,
% 1.54/1.74 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3645, 3244, 268, 3518, 249])).
% 1.54/1.74 tff(3647,plain,
% 1.54/1.74 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[429, 3646])).
% 1.54/1.74 tff(3648,plain,
% 1.54/1.74 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[547, 18, 19, 539])).
% 1.54/1.74 tff(3649,plain,
% 1.54/1.74 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[356, 3648])).
% 1.54/1.74 tff(3650,plain,
% 1.54/1.74 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[783, 3649, 276])).
% 1.54/1.74 tff(3651,plain,
% 1.54/1.74 (b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[322, 3650])).
% 1.54/1.74 tff(3652,plain,
% 1.54/1.74 (~b(z, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2716, 112, 101, 18, 3651, 3536])).
% 1.54/1.74 tff(3653,plain,
% 1.54/1.74 (r(z, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[515, 3652])).
% 1.54/1.74 tff(3654,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[363, 31, 3653, 3649, 249])).
% 1.54/1.74 tff(3655,plain,((~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3656,plain,
% 1.54/1.74 (~b(z, s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3655, 3518, 249, 3244, 3647, 3534])).
% 1.54/1.74 tff(3657,plain,
% 1.54/1.74 (r(z, s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[182, 3656])).
% 1.54/1.74 tff(3658,plain,
% 1.54/1.74 (~r(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[170, 20, 3657])).
% 1.54/1.74 tff(3659,plain,
% 1.54/1.74 (b(s(z), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[99, 3658])).
% 1.54/1.74 tff(3660,plain,
% 1.54/1.74 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3541, 112, 3659, 3518, 3254])).
% 1.54/1.74 tff(3661,plain,
% 1.54/1.74 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[462, 3660])).
% 1.54/1.74 tff(3662,plain,
% 1.54/1.74 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2579, 112, 3659, 3518, 3252, 3254])).
% 1.54/1.74 tff(3663,plain,
% 1.54/1.74 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[749, 3662])).
% 1.54/1.74 tff(3664,plain,
% 1.54/1.74 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[363, 31, 20, 249])).
% 1.54/1.74 tff(3665,plain,
% 1.54/1.74 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[356, 3664])).
% 1.54/1.74 tff(3666,plain,
% 1.54/1.74 (~b(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3569, 399, 3534, 3665])).
% 1.54/1.74 tff(3667,plain,
% 1.54/1.74 (r(s(z), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[608, 3666])).
% 1.54/1.74 tff(3668,plain,
% 1.54/1.74 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3108, 3667, 3663])).
% 1.54/1.74 tff(3669,plain,
% 1.54/1.74 (b(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[494, 3668])).
% 1.54/1.74 tff(3670,plain,
% 1.54/1.74 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1933, 3663, 3657])).
% 1.54/1.74 tff(3671,plain,
% 1.54/1.74 (b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[322, 3670])).
% 1.54/1.74 tff(3672,plain,
% 1.54/1.74 (~b(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2627, 112, 3671, 3669, 3252])).
% 1.54/1.74 tff(3673,plain,
% 1.54/1.74 (r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[527, 3672])).
% 1.54/1.74 tff(3674,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3675,plain,
% 1.54/1.74 (((~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)))), z)) | (~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~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))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3676,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), z)) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~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)))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3675])).
% 1.54/1.74 tff(3677,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), z)) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3676, 3674])).
% 1.54/1.74 tff(3678,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), z)) | (~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(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3679,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~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)))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3678, 3677])).
% 1.54/1.74 tff(3680,plain,
% 1.54/1.74 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3679, 112, 399, 3671, 3669])).
% 1.54/1.74 tff(3681,plain,
% 1.54/1.74 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[299, 3680, 268])).
% 1.54/1.74 tff(3682,plain,
% 1.54/1.74 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[693, 612, 400])).
% 1.54/1.74 tff(3683,plain,
% 1.54/1.74 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[398, 3682])).
% 1.54/1.74 tff(3684,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3685,plain,
% 1.54/1.74 (((~b(z, s(s(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(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~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)))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3686,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(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(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3685])).
% 1.54/1.74 tff(3687,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(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(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3686, 3684])).
% 1.54/1.74 tff(3688,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(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(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3689,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))), z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3688, 3687])).
% 1.54/1.75 tff(3690,plain,
% 1.54/1.75 (~b(s(s(elem!1)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3689, 112, 1990, 3683, 2])).
% 1.54/1.75 tff(3691,plain,
% 1.54/1.75 (r(s(s(elem!1)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[822, 78, 379, 3690])).
% 1.54/1.75 tff(3692,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~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(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3693,plain,
% 1.54/1.75 (((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3694,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3693])).
% 1.54/1.75 tff(3695,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3694, 3692])).
% 1.54/1.75 tff(3696,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3697,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3696, 3695])).
% 1.54/1.75 tff(3698,plain,
% 1.54/1.75 (~r(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3697, 31, 592, 3691])).
% 1.54/1.75 tff(3699,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1435, 78, 3698, 1421])).
% 1.54/1.75 tff(3700,plain,
% 1.54/1.75 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3701,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3700])).
% 1.54/1.75 tff(3702,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3701, 2003])).
% 1.54/1.75 tff(3703,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3704,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 1.54/1.75 tff(3705,plain,
% 1.54/1.75 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3704, 112, 102, 101, 3699])).
% 1.54/1.75 tff(3706,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3707,plain,
% 1.54/1.75 (((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3708,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3707])).
% 1.54/1.75 tff(3709,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3708, 3706])).
% 1.54/1.75 tff(3710,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3711,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3710, 3709])).
% 1.54/1.75 tff(3712,plain,
% 1.54/1.75 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3711, 31, 612, 3691])).
% 1.54/1.75 tff(3713,plain,
% 1.54/1.75 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1008, 78, 3712])).
% 1.54/1.75 tff(3714,plain,
% 1.54/1.75 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3713, 3705])).
% 1.54/1.75 tff(3715,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3714])).
% 1.54/1.75 tff(3716,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[3715])).
% 1.54/1.75 tff(3717,plain,
% 1.54/1.75 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3716])).
% 1.54/1.75 tff(3718,plain,
% 1.54/1.75 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[155, 3717])).
% 1.54/1.75 tff(3719,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1990, 3718])).
% 1.54/1.75 tff(3720,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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3721,plain,
% 1.54/1.75 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3720, 3673, 155, 3518, 3667, 3659, 3665])).
% 1.54/1.75 tff(3722,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3723,plain,
% 1.54/1.75 (((~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))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~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))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3724,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3723])).
% 1.54/1.75 tff(3725,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3724, 3722])).
% 1.54/1.75 tff(3726,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3727,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3726, 3725])).
% 1.54/1.75 tff(3728,plain,
% 1.54/1.75 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3727, 31, 612, 276, 1])).
% 1.54/1.75 tff(3729,plain,
% 1.54/1.75 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[384, 78, 381, 3728])).
% 1.54/1.75 tff(3730,assumption,(~b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.75 tff(3731,plain,
% 1.54/1.75 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[872, 248, 3730])).
% 1.54/1.75 tff(3732,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(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(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3733,plain,
% 1.54/1.75 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3734,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3733])).
% 1.54/1.75 tff(3735,plain,
% 1.54/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3734, 3732])).
% 1.54/1.75 tff(3736,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3737,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3736, 3735])).
% 1.54/1.75 tff(3738,plain,
% 1.54/1.75 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3737, 31, 3731, 464, 276])).
% 1.54/1.75 tff(3739,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3250, 31, 276, 1])).
% 1.54/1.75 tff(3740,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[710, 78, 3739, 699])).
% 1.54/1.75 tff(3741,plain,
% 1.54/1.75 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3526, 276, 464])).
% 1.54/1.75 tff(3742,plain,
% 1.54/1.75 (b(s(z), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[477, 3741])).
% 1.54/1.75 tff(3743,plain,
% 1.54/1.75 (~b(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[547, 3742, 3665, 19])).
% 1.54/1.75 tff(3744,plain,
% 1.54/1.75 (r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[182, 3743])).
% 1.54/1.75 tff(3745,plain,
% 1.54/1.75 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1933, 162, 302])).
% 1.54/1.75 tff(3746,plain,
% 1.54/1.75 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[749, 3745])).
% 1.54/1.75 tff(3747,plain,
% 1.54/1.75 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1907, 162, 302])).
% 1.54/1.75 tff(3748,plain,
% 1.54/1.75 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[462, 3747])).
% 1.54/1.75 tff(3749,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3275, 162, 612])).
% 1.54/1.75 tff(3750,plain,
% 1.54/1.75 (b(s(s(s(z))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[83, 3749])).
% 1.54/1.75 tff(3751,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3752,plain,
% 1.54/1.75 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), 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))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3753,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3752])).
% 1.54/1.75 tff(3754,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3753, 3751])).
% 1.54/1.75 tff(3755,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3756,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3755, 3754])).
% 1.54/1.75 tff(3757,plain,
% 1.54/1.75 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3756, 112, 3750, 3748, 3746])).
% 1.54/1.75 tff(3758,plain,
% 1.54/1.75 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[710, 78, 3757])).
% 1.54/1.76 tff(3759,plain,
% 1.54/1.76 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3758, 2608])).
% 1.54/1.76 tff(3760,plain,
% 1.54/1.76 (((~![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(s(elem!1))))))) | (~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(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3761,plain,
% 1.54/1.76 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3762,plain,
% 1.54/1.76 (((~![X0: $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(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3761])).
% 1.54/1.76 tff(3763,plain,
% 1.54/1.76 (((~![X0: $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(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(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3762, 3760])).
% 1.54/1.76 tff(3764,plain,
% 1.54/1.76 ((~![X0: $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(z))) | (~r(s(s(s(z))), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3765,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3764, 3763])).
% 1.54/1.76 tff(3766,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3765, 31, 612, 162, 302, 3759])).
% 1.54/1.76 tff(3767,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3768,plain,
% 1.54/1.76 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3767, 3744, 612])).
% 1.54/1.76 tff(3769,plain,
% 1.54/1.76 (b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[322, 3768])).
% 1.54/1.76 tff(3770,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[693, 612, 1])).
% 1.54/1.76 tff(3771,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[398, 3770])).
% 1.54/1.76 tff(3772,assumption,(~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.54/1.76 tff(3773,plain,
% 1.54/1.76 (~b(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[547, 539, 2, 19])).
% 1.54/1.76 tff(3774,plain,
% 1.54/1.76 (r(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[182, 3773])).
% 1.54/1.76 tff(3775,plain,
% 1.54/1.76 (~r(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[170, 3774, 20])).
% 1.54/1.76 tff(3776,plain,
% 1.54/1.76 (b(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[99, 3775])).
% 1.54/1.76 tff(3777,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3778,plain,
% 1.54/1.76 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(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(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3779,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3778])).
% 1.54/1.76 tff(3780,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3779, 3777])).
% 1.54/1.76 tff(3781,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3782,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~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(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 1.54/1.76 tff(3783,plain,
% 1.54/1.76 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3782, 112, 3776, 101, 2130, 406, 762])).
% 1.54/1.76 tff(3784,plain,
% 1.54/1.76 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1025, 3783, 3772])).
% 1.54/1.76 tff(3785,plain,
% 1.54/1.76 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3784])).
% 1.54/1.76 tff(3786,plain,
% 1.54/1.76 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3785])).
% 1.54/1.76 tff(3787,plain,
% 1.54/1.76 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3786])).
% 1.54/1.76 tff(3788,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.54/1.76 inference(symmetry,[status(thm)],[3787])).
% 1.54/1.76 tff(3789,plain,
% 1.54/1.76 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3788])).
% 1.54/1.76 tff(3790,plain,
% 1.54/1.76 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3784])).
% 1.54/1.76 tff(3791,plain,
% 1.54/1.76 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[145, 3790, 262])).
% 1.54/1.76 tff(3792,plain,
% 1.54/1.76 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3791])).
% 1.54/1.76 tff(3793,plain,
% 1.54/1.76 (elem!1 = s(s(s(elem!1)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1073, 3792, 131])).
% 1.54/1.76 tff(3794,plain,
% 1.54/1.76 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3793])).
% 1.54/1.76 tff(3795,plain,
% 1.54/1.76 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1073, 3792, 131, 3785])).
% 1.54/1.76 tff(3796,plain,
% 1.54/1.76 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3795])).
% 1.54/1.76 tff(3797,plain,
% 1.54/1.76 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3796, 775])).
% 1.54/1.76 tff(3798,plain,
% 1.54/1.76 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3797])).
% 1.54/1.76 tff(3799,plain,
% 1.54/1.76 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3798])).
% 1.54/1.76 tff(3800,plain,
% 1.54/1.76 (~(elem!1 = s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1041, 3799])).
% 1.54/1.76 tff(3801,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3784])).
% 1.54/1.76 tff(3802,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3801])).
% 1.54/1.76 tff(3803,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[406, 3802])).
% 1.54/1.76 tff(3804,plain,
% 1.54/1.76 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3784])).
% 1.54/1.76 tff(3805,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3804])).
% 1.54/1.76 tff(3806,plain,
% 1.54/1.76 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3784])).
% 1.54/1.76 tff(3807,plain,
% 1.54/1.76 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3806])).
% 1.54/1.76 tff(3808,plain,
% 1.54/1.76 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2128, 3807])).
% 1.54/1.76 tff(3809,plain,
% 1.54/1.76 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3793])).
% 1.54/1.76 tff(3810,plain,
% 1.54/1.76 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3809, 890])).
% 1.54/1.76 tff(3811,plain,
% 1.54/1.76 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3810])).
% 1.54/1.76 tff(3812,plain,
% 1.54/1.76 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3811])).
% 1.54/1.76 tff(3813,plain,
% 1.54/1.76 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[265, 3812])).
% 1.54/1.76 tff(3814,plain,
% 1.54/1.76 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1621, 2221])).
% 1.54/1.76 tff(3815,plain,
% 1.54/1.76 (~r(elem!1, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2145, 3814, 464, 1068])).
% 1.54/1.76 tff(3816,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.76 tff(3817,plain,
% 1.54/1.76 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3338, 1621, 1887])).
% 1.54/1.76 tff(3818,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1209, 3817, 3816])).
% 1.54/1.76 tff(3819,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3818, 3282])).
% 1.54/1.76 tff(3820,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), 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)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3821,plain,
% 1.54/1.76 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3822,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), 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)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3821])).
% 1.54/1.76 tff(3823,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), 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)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3822, 3820])).
% 1.54/1.76 tff(3824,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3825,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 1.54/1.76 tff(3826,plain,
% 1.54/1.76 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3825, 112, 19, 1827, 2, 539, 3819])).
% 1.54/1.76 tff(3827,plain,
% 1.54/1.76 (~b(elem!1, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2249, 3826, 1068])).
% 1.54/1.76 tff(3828,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1139, 3827, 3815, 1125])).
% 1.54/1.76 tff(3829,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(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)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (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,[]))).
% 1.54/1.76 tff(3830,plain,
% 1.54/1.76 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3829, 3784, 464, 19, 1827, 2, 539, 3813, 1887])).
% 1.54/1.76 tff(3831,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1225, 3830, 3808])).
% 1.54/1.76 tff(3832,plain,
% 1.54/1.76 (b(elem!1, s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3831, 3805])).
% 1.54/1.76 tff(3833,plain,
% 1.54/1.76 (~b(elem!1, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1534, 3832, 2130, 3803])).
% 1.54/1.76 tff(3834,plain,
% 1.54/1.76 (r(elem!1, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1498, 3833, 3800])).
% 1.54/1.76 tff(3835,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3834, 3794])).
% 1.54/1.76 tff(3836,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2464, 3835, 20])).
% 1.54/1.76 tff(3837,plain,
% 1.54/1.76 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3836, 3789])).
% 1.54/1.76 tff(3838,plain,
% 1.54/1.76 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3792])).
% 1.54/1.76 tff(3839,plain,
% 1.54/1.76 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.54/1.76 inference(transitivity,[status(thm)],[3786, 132, 3838, 247])).
% 1.54/1.76 tff(3840,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3839])).
% 1.54/1.76 tff(3841,plain,
% 1.54/1.76 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3840])).
% 1.54/1.76 tff(3842,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3831, 3841])).
% 1.54/1.76 tff(3843,plain,
% 1.54/1.76 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[486, 31, 3774, 464])).
% 1.54/1.76 tff(3844,plain,
% 1.54/1.76 (b(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[494, 3843])).
% 1.54/1.76 tff(3845,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3846,plain,
% 1.54/1.76 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3847,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3846])).
% 1.54/1.77 tff(3848,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3847, 3845])).
% 1.54/1.77 tff(3849,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3850,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 1.54/1.77 tff(3851,plain,
% 1.54/1.77 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3850, 112, 334, 3844])).
% 1.54/1.77 tff(3852,plain,
% 1.54/1.77 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3851, 3842])).
% 1.54/1.77 tff(3853,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 3852, 3837])).
% 1.54/1.77 tff(3854,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(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)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), 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)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3855,plain,
% 1.54/1.77 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3854, 257, 20, 464, 19, 3771, 3665, 3742, 1887, 3769, 1193, 3740, 3738, 101, 3729])).
% 1.54/1.77 tff(3856,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3857,plain,
% 1.54/1.77 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3858,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3857])).
% 1.54/1.77 tff(3859,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3858, 3856])).
% 1.54/1.77 tff(3860,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3861,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3860, 3859])).
% 1.54/1.77 tff(3862,plain,
% 1.54/1.77 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3861, 31, 612, 3731, 1])).
% 1.54/1.77 tff(3863,plain,
% 1.54/1.77 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1008, 78, 3862])).
% 1.54/1.77 tff(3864,plain,
% 1.54/1.77 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3863, 3855])).
% 1.54/1.77 tff(3865,plain,
% 1.54/1.77 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3864])).
% 1.54/1.77 tff(3866,plain,
% 1.54/1.77 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3865])).
% 1.54/1.77 tff(3867,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3866])).
% 1.54/1.77 tff(3868,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3867, 890])).
% 1.54/1.77 tff(3869,plain,
% 1.54/1.77 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3868])).
% 1.54/1.77 tff(3870,plain,
% 1.54/1.77 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3869])).
% 1.54/1.77 tff(3871,plain,
% 1.54/1.77 (~(s(s(s(s(z)))) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[257, 3870])).
% 1.54/1.77 tff(3872,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3866])).
% 1.54/1.77 tff(3873,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3872])).
% 1.54/1.77 tff(3874,plain,
% 1.54/1.77 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3864])).
% 1.54/1.77 tff(3875,plain,
% 1.54/1.77 (s(elem!1) = s(s(z))),
% 1.54/1.77 inference(transitivity,[status(thm)],[145, 3874, 55])).
% 1.54/1.77 tff(3876,plain,
% 1.54/1.77 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3875])).
% 1.54/1.77 tff(3877,plain,
% 1.54/1.77 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3876])).
% 1.54/1.77 tff(3878,plain,
% 1.54/1.77 (s(z) = elem!1),
% 1.54/1.77 inference(transitivity,[status(thm)],[138, 3877, 247])).
% 1.54/1.77 tff(3879,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3865, 3878])).
% 1.54/1.77 tff(3880,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[3879])).
% 1.54/1.77 tff(3881,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(3882,plain,
% 1.54/1.77 (elem!1 = s(z)),
% 1.54/1.77 inference(transitivity,[status(thm)],[1073, 3876, 137])).
% 1.54/1.77 tff(3883,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3882])).
% 1.54/1.77 tff(3884,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = elem!1) <=> (s(z) = s(s(s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3883, 3881])).
% 1.54/1.77 tff(3885,plain,
% 1.54/1.77 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[3884])).
% 1.54/1.77 tff(3886,plain,
% 1.54/1.77 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3885])).
% 1.54/1.77 tff(3887,plain,
% 1.54/1.77 (~(s(s(s(s(z)))) = elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[948, 3886])).
% 1.54/1.77 tff(3888,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3882])).
% 1.54/1.77 tff(3889,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[3888])).
% 1.54/1.77 tff(3890,plain,
% 1.54/1.77 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3889])).
% 1.54/1.77 tff(3891,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3892,plain,
% 1.54/1.77 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3893,plain,
% 1.54/1.77 (((~![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(s(s(s(z)))), 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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3892])).
% 1.54/1.77 tff(3894,plain,
% 1.54/1.77 (((~![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(s(s(s(z)))), 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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3893, 3891])).
% 1.54/1.77 tff(3895,plain,
% 1.54/1.77 ((~![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(s(s(s(z)))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3896,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 1.54/1.77 tff(3897,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3896, 31, 20, 162, 981])).
% 1.54/1.77 tff(3898,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[917, 78, 224, 3897])).
% 1.54/1.77 tff(3899,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3900,plain,
% 1.54/1.77 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3901,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3900])).
% 1.54/1.77 tff(3902,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3901, 3899])).
% 1.54/1.77 tff(3903,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3904,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3903, 3902])).
% 1.54/1.77 tff(3905,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3904, 112, 1827, 2, 334, 495, 3898])).
% 1.54/1.77 tff(3906,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2386, 3905, 905])).
% 1.54/1.77 tff(3907,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3908,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3907, 889, 3665, 3769, 3771, 3864, 464, 20, 3744])).
% 1.54/1.77 tff(3909,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3908, 3890])).
% 1.54/1.77 tff(3910,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1335, 3909, 3887])).
% 1.54/1.77 tff(3911,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3910, 3880])).
% 1.54/1.77 tff(3912,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3911, 3873])).
% 1.54/1.77 tff(3913,plain,
% 1.54/1.77 (~r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[170, 3744, 20])).
% 1.54/1.77 tff(3914,plain,
% 1.54/1.77 (b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[99, 3913])).
% 1.54/1.77 tff(3915,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2437, 112, 3914, 101, 3912])).
% 1.54/1.77 tff(3916,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[972, 78, 969, 3915])).
% 1.54/1.77 tff(3917,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(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))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(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))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3918,plain,
% 1.54/1.77 (((~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(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3919,plain,
% 1.54/1.77 (((~![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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3918])).
% 1.54/1.77 tff(3920,plain,
% 1.54/1.77 (((~![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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(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(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3919, 3917])).
% 1.54/1.77 tff(3921,plain,
% 1.54/1.77 ((~![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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3922,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(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))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3921, 3920])).
% 1.54/1.77 tff(3923,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3922, 31, 1887, 249, 3916])).
% 1.54/1.78 tff(3924,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3925,plain,
% 1.54/1.78 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(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(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3926,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3925])).
% 1.54/1.78 tff(3927,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3926, 3924])).
% 1.54/1.78 tff(3928,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3929,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 1.54/1.78 tff(3930,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3929, 112, 3914, 101, 19, 3742, 3912])).
% 1.54/1.78 tff(3931,plain,
% 1.54/1.78 ((s(s(s(s(z)))) = s(s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[994, 78, 3930])).
% 1.54/1.78 tff(3932,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3931, 3923, 3871])).
% 1.54/1.78 tff(3933,plain,((s(s(elem!1)) = 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))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), 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)))))) | b(s(s(elem!1)), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3934,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3933, 3721, 3681, 248, 249, 3244, 3518, 3647, 3673, 400, 20, 3661])).
% 1.54/1.78 tff(3935,plain,((~r(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3936,plain,
% 1.54/1.78 (~r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3935, 155, 249, 248])).
% 1.54/1.78 tff(3937,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[515, 3936])).
% 1.54/1.78 tff(3938,plain,
% 1.54/1.78 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2531, 112, 3937, 3252, 3254])).
% 1.54/1.78 tff(3939,plain,
% 1.54/1.78 (r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[322, 3938])).
% 1.54/1.78 tff(3940,plain,
% 1.54/1.78 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1933, 3939, 3657])).
% 1.54/1.78 tff(3941,plain,
% 1.54/1.78 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[749, 3940])).
% 1.54/1.78 tff(3942,plain,
% 1.54/1.78 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1907, 3939, 3657])).
% 1.54/1.78 tff(3943,plain,
% 1.54/1.78 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[462, 3942])).
% 1.54/1.78 tff(3944,plain,
% 1.54/1.78 (((~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(elem!1))))), 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(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))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3945,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(elem!1))))), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3944])).
% 1.54/1.78 tff(3946,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(elem!1))))), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3945, 3751])).
% 1.54/1.78 tff(3947,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(s(s(elem!1))))), 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))))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3948,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3947, 3946])).
% 1.54/1.78 tff(3949,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3948, 112, 3518, 3943, 3941, 3252])).
% 1.54/1.78 tff(3950,plain,(b(s(s(s(z))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3951,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3950, 249, 248])).
% 1.54/1.78 tff(3952,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3953,plain,
% 1.54/1.78 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~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)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3954,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3953])).
% 1.54/1.78 tff(3955,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3954, 3952])).
% 1.54/1.78 tff(3956,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3957,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3956, 3955])).
% 1.54/1.78 tff(3958,plain,
% 1.54/1.78 (~b(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3957, 112, 399, 3951, 3665])).
% 1.54/1.78 tff(3959,plain,
% 1.54/1.78 (r(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[527, 3958])).
% 1.54/1.78 tff(3960,plain,
% 1.54/1.78 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2471, 275, 249])).
% 1.54/1.78 tff(3961,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[299, 3960, 271])).
% 1.54/1.78 tff(3962,plain,
% 1.54/1.78 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[404, 285, 2474])).
% 1.54/1.78 tff(3963,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2703, 112, 196, 3961, 3962])).
% 1.54/1.78 tff(3964,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2752, 3963])).
% 1.54/1.78 tff(3965,plain,
% 1.54/1.78 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[739, 3964, 3])).
% 1.54/1.78 tff(3966,plain,
% 1.54/1.78 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[749, 3965])).
% 1.54/1.78 tff(3967,plain,
% 1.54/1.78 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[472, 275, 3])).
% 1.54/1.78 tff(3968,plain,
% 1.54/1.78 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[462, 3967])).
% 1.54/1.78 tff(3969,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[636, 31, 3, 408, 249])).
% 1.54/1.78 tff(3970,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3971,plain,
% 1.54/1.78 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3970, 3, 249])).
% 1.54/1.78 tff(3972,plain,
% 1.54/1.78 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[429, 3971])).
% 1.54/1.78 tff(3973,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3021, 112, 3972, 3968, 3966, 3961])).
% 1.54/1.78 tff(3974,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), 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(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3975,plain,
% 1.54/1.78 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3974, 3, 196, 271, 249])).
% 1.54/1.78 tff(3976,plain,
% 1.54/1.78 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[386, 3975])).
% 1.54/1.78 tff(3977,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2752, 1465])).
% 1.54/1.78 tff(3978,plain,
% 1.54/1.78 (~r(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[536, 464, 3])).
% 1.54/1.78 tff(3979,plain,
% 1.54/1.78 (b(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[182, 3978])).
% 1.54/1.78 tff(3980,plain,
% 1.54/1.78 (~b(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1835, 399, 3972, 18])).
% 1.54/1.78 tff(3981,plain,
% 1.54/1.78 (r(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[608, 3980])).
% 1.54/1.78 tff(3982,plain,
% 1.54/1.78 (~b(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3957, 112, 399, 196, 3665])).
% 1.54/1.78 tff(3983,plain,
% 1.54/1.78 (r(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[527, 3982])).
% 1.54/1.78 tff(3984,plain,
% 1.54/1.78 (((~![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(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3985,plain,
% 1.54/1.78 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3986,plain,
% 1.54/1.78 (((~![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(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3985])).
% 1.54/1.78 tff(3987,plain,
% 1.54/1.78 (((~![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(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[3986, 3984])).
% 1.54/1.78 tff(3988,plain,
% 1.54/1.78 ((~![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))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(3989,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[3988, 3987])).
% 1.54/1.78 tff(3990,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3989, 31, 3983, 3, 3981])).
% 1.54/1.78 tff(3991,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(3992,plain,
% 1.54/1.78 (~r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3991, 3979, 196, 3, 249])).
% 1.54/1.78 tff(3993,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[515, 3992])).
% 1.54/1.78 tff(3994,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3995,plain,
% 1.54/1.78 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(3996,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[3995])).
% 1.54/1.78 tff(3997,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[3996, 3994])).
% 1.54/1.79 tff(3998,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(3999,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 1.54/1.79 tff(4000,plain,
% 1.54/1.79 ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3999, 112, 3979, 3972, 196])).
% 1.54/1.79 tff(4001,plain,
% 1.54/1.79 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4000, 3993])).
% 1.54/1.79 tff(4002,plain,
% 1.54/1.79 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[356, 4001])).
% 1.54/1.79 tff(4003,plain,
% 1.54/1.79 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2531, 112, 3993, 3977, 3976])).
% 1.54/1.79 tff(4004,plain,
% 1.54/1.79 (r(z, s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[322, 4003])).
% 1.54/1.79 tff(4005,plain,
% 1.54/1.79 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[783, 4004, 4002])).
% 1.54/1.79 tff(4006,plain,
% 1.54/1.79 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[404, 4005, 2474])).
% 1.54/1.79 tff(4007,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2551, 31, 302, 569, 1887])).
% 1.54/1.79 tff(4008,plain,((~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4009,plain,
% 1.54/1.79 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4008, 4004, 4002])).
% 1.54/1.79 tff(4010,plain,
% 1.54/1.79 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[299, 4009, 271])).
% 1.54/1.79 tff(4011,plain,
% 1.54/1.79 (((~b(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))))))) | (~b(s(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(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(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4012,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(s(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(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4011])).
% 1.54/1.79 tff(4013,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(s(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(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4012, 2698])).
% 1.54/1.79 tff(4014,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1))))))) | (~b(s(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(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(z))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4015,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4014, 4013])).
% 1.54/1.79 tff(4016,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4015, 112, 196, 4010, 4006, 3977])).
% 1.54/1.79 tff(4017,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(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,[]))).
% 1.54/1.79 tff(4018,plain,
% 1.54/1.79 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4017, 3, 271, 196, 249])).
% 1.54/1.79 tff(4019,plain,
% 1.54/1.79 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[462, 4018])).
% 1.54/1.79 tff(4020,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4021,plain,
% 1.54/1.79 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(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(z))), 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(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4022,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(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(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4021])).
% 1.54/1.79 tff(4023,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(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(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4022, 4020])).
% 1.54/1.79 tff(4024,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4025,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4024, 4023])).
% 1.54/1.79 tff(4026,plain,
% 1.54/1.79 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4025, 112, 3972, 196, 4019, 3976])).
% 1.54/1.79 tff(4027,plain,
% 1.54/1.79 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[404, 4026, 2474])).
% 1.54/1.79 tff(4028,plain,
% 1.54/1.79 (~b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3991, 20, 196, 3, 249])).
% 1.54/1.79 tff(4029,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[182, 4028, 3260])).
% 1.54/1.79 tff(4030,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4031,plain,
% 1.54/1.79 (~r(z, s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4030, 3, 196, 249])).
% 1.54/1.79 tff(4032,plain,
% 1.54/1.79 (b(z, s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[515, 4031])).
% 1.54/1.79 tff(4033,plain,
% 1.54/1.79 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3999, 112, 803, 18, 19, 196])).
% 1.54/1.79 tff(4034,plain,
% 1.54/1.79 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[356, 4033])).
% 1.54/1.79 tff(4035,plain,
% 1.54/1.79 (~b(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[683, 4034, 276, 443, 18])).
% 1.54/1.79 tff(4036,plain,
% 1.54/1.79 (r(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[608, 4035])).
% 1.54/1.79 tff(4037,plain,
% 1.54/1.79 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[759, 18, 443, 334])).
% 1.54/1.79 tff(4038,plain,
% 1.54/1.79 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[749, 4037])).
% 1.54/1.79 tff(4039,plain,
% 1.54/1.79 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3108, 4036, 4038])).
% 1.54/1.79 tff(4040,plain,
% 1.54/1.79 (b(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[494, 4039])).
% 1.54/1.79 tff(4041,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[534, 112, 859, 803, 2604, 762])).
% 1.54/1.79 tff(4042,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4043,plain,
% 1.54/1.79 (~b(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4042, 4040, 803, 762])).
% 1.54/1.79 tff(4044,plain,
% 1.54/1.79 (r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[527, 4043])).
% 1.54/1.79 tff(4045,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3989, 31, 4044, 3, 4036])).
% 1.54/1.79 tff(4046,plain,((~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, 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(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(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4047,plain,
% 1.54/1.79 (~b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4046, 334, 4032, 3976, 4027, 4019, 3972, 196, 3])).
% 1.54/1.79 tff(4048,plain,
% 1.54/1.79 (r(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[182, 4047])).
% 1.54/1.79 tff(4049,plain,
% 1.54/1.79 (~r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3275, 4048, 3])).
% 1.54/1.79 tff(4050,plain,
% 1.54/1.79 (b(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[527, 4049])).
% 1.54/1.79 tff(4051,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(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(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4052,plain,
% 1.54/1.79 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4053,plain,
% 1.54/1.79 (((~![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(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4052])).
% 1.54/1.79 tff(4054,plain,
% 1.54/1.79 (((~![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(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4053, 4051])).
% 1.54/1.79 tff(4055,plain,
% 1.54/1.79 ((~![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(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4056,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4055, 4054])).
% 1.54/1.79 tff(4057,plain,
% 1.54/1.79 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4056, 31, 162, 276, 569])).
% 1.54/1.79 tff(4058,plain,
% 1.54/1.79 (b(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[494, 4057])).
% 1.54/1.79 tff(4059,plain,
% 1.54/1.79 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3115, 112, 859, 803, 4058])).
% 1.54/1.79 tff(4060,plain,
% 1.54/1.79 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[384, 78, 381, 4059])).
% 1.54/1.79 tff(4061,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[282, 31, 276, 249, 4060])).
% 1.54/1.79 tff(4062,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4063,plain,
% 1.54/1.79 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4062, 4050, 4027, 249, 4032, 4048])).
% 1.54/1.79 tff(4064,plain,
% 1.54/1.79 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[356, 4063])).
% 1.54/1.79 tff(4065,plain,
% 1.54/1.79 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4042, 4050, 4032, 3976])).
% 1.54/1.79 tff(4066,plain,
% 1.54/1.79 (r(s(s(s(s(s(elem!1))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[494, 4065])).
% 1.54/1.79 tff(4067,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4068,plain,
% 1.54/1.79 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4069,plain,
% 1.54/1.79 (((~![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)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4068])).
% 1.54/1.79 tff(4070,plain,
% 1.54/1.79 (((~![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)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4069, 4067])).
% 1.54/1.79 tff(4071,plain,
% 1.54/1.79 ((~![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)))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4072,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4071, 4070])).
% 1.54/1.79 tff(4073,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4072, 31, 568, 276, 714])).
% 1.54/1.79 tff(4074,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4075,plain,
% 1.54/1.79 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4074, 4066, 4027])).
% 1.54/1.79 tff(4076,plain,
% 1.54/1.79 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[398, 4075])).
% 1.54/1.79 tff(4077,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(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(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4078,plain,
% 1.64/1.80 (((~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(z))) | (~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(elem!1)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(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(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4079,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(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(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4078])).
% 1.64/1.80 tff(4080,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(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(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4079, 4077])).
% 1.64/1.80 tff(4081,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~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)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4082,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4081, 4080])).
% 1.64/1.80 tff(4083,plain,
% 1.64/1.80 ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4082, 112, 3972, 4019, 334])).
% 1.64/1.80 tff(4084,plain,
% 1.64/1.80 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4083, 4076, 4064])).
% 1.64/1.80 tff(4085,plain,
% 1.64/1.80 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[299, 4084, 271])).
% 1.64/1.80 tff(4086,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2618, 4085, 249])).
% 1.64/1.80 tff(4087,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2752, 4086])).
% 1.64/1.80 tff(4088,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1389, 112, 4050, 4032, 334, 4087, 3976])).
% 1.64/1.80 tff(4089,plain,((~b(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4090,plain,
% 1.64/1.80 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4089, 3, 271, 249, 196])).
% 1.64/1.80 tff(4091,plain,
% 1.64/1.80 (r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[322, 4090])).
% 1.64/1.80 tff(4092,plain,
% 1.64/1.80 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[783, 4091, 4027])).
% 1.64/1.80 tff(4093,plain,
% 1.64/1.80 (b(z, s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[356, 4092])).
% 1.64/1.80 tff(4094,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3999, 112, 803, 18, 19, 196, 2])).
% 1.64/1.80 tff(4095,plain,((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4096,plain,
% 1.64/1.80 (~b(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4095, 4032, 3972, 196, 4093])).
% 1.64/1.80 tff(4097,plain,
% 1.64/1.80 (r(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[182, 4096])).
% 1.64/1.80 tff(4098,plain,
% 1.64/1.80 (~r(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3275, 4097, 3])).
% 1.64/1.80 tff(4099,plain,
% 1.64/1.80 (b(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[527, 4098])).
% 1.64/1.80 tff(4100,plain,
% 1.64/1.80 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4042, 4099, 4032, 3976])).
% 1.64/1.80 tff(4101,plain,
% 1.64/1.80 (r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[494, 4100])).
% 1.64/1.80 tff(4102,plain,
% 1.64/1.80 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4074, 4101, 4027])).
% 1.64/1.80 tff(4103,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[398, 4102])).
% 1.64/1.80 tff(4104,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4105,plain,
% 1.64/1.80 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4106,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4105])).
% 1.64/1.80 tff(4107,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4106, 4104])).
% 1.64/1.80 tff(4108,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4109,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4108, 4107])).
% 1.64/1.80 tff(4110,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4109, 112, 4099, 4032, 4103, 196, 4093])).
% 1.64/1.80 tff(4111,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), 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(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4112,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4111, 3951, 268, 249])).
% 1.64/1.80 tff(4113,plain,
% 1.64/1.80 (b(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[83, 4112])).
% 1.64/1.80 tff(4114,plain,
% 1.64/1.80 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3645, 408, 268, 4113, 249])).
% 1.64/1.80 tff(4115,plain,
% 1.64/1.80 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2467, 4114, 4113, 408, 249, 248])).
% 1.64/1.80 tff(4116,plain,
% 1.64/1.80 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2752, 4115])).
% 1.64/1.80 tff(4117,plain,
% 1.64/1.80 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[404, 4114, 274])).
% 1.64/1.80 tff(4118,plain,
% 1.64/1.80 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2182, 112, 1827, 2, 4117])).
% 1.64/1.80 tff(4119,plain,
% 1.64/1.80 (r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[494, 4118])).
% 1.64/1.80 tff(4120,plain,
% 1.64/1.80 (~b(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3957, 112, 1827, 3951, 2])).
% 1.64/1.80 tff(4121,plain,
% 1.64/1.80 (r(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[527, 4120])).
% 1.64/1.80 tff(4122,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[720, 31, 4121, 4119, 4116])).
% 1.64/1.80 tff(4123,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4124,plain,
% 1.64/1.80 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4123, 399, 3665, 249, 248])).
% 1.64/1.80 tff(4125,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[429, 4124])).
% 1.64/1.80 tff(4126,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[720, 31, 612, 714])).
% 1.64/1.80 tff(4127,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2752, 4126])).
% 1.64/1.80 tff(4128,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[170, 162, 20])).
% 1.64/1.80 tff(4129,plain,
% 1.64/1.80 (b(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[99, 4128])).
% 1.64/1.80 tff(4130,plain,
% 1.64/1.80 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3541, 112, 4129, 101, 762])).
% 1.64/1.80 tff(4131,plain,
% 1.64/1.80 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[462, 4130])).
% 1.64/1.80 tff(4132,plain,
% 1.64/1.80 (((~![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(z))))) | (~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(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4133,plain,
% 1.64/1.80 (((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4134,plain,
% 1.64/1.80 (((~![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(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(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(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4133])).
% 1.64/1.80 tff(4135,plain,
% 1.64/1.80 (((~![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(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(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(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4134, 4132])).
% 1.64/1.80 tff(4136,plain,
% 1.64/1.80 ((~![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(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4137,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4136, 4135])).
% 1.64/1.80 tff(4138,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4137, 31, 20, 162, 4131, 714])).
% 1.64/1.80 tff(4139,plain,((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4140,plain,
% 1.64/1.80 (~r(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4139, 714, 20, 101, 762])).
% 1.64/1.80 tff(4141,plain,
% 1.64/1.80 (b(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[182, 4140])).
% 1.64/1.80 tff(4142,plain,
% 1.64/1.80 (~b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1835, 4141, 19, 399])).
% 1.64/1.80 tff(4143,plain,
% 1.64/1.80 (r(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[608, 4142])).
% 1.64/1.80 tff(4144,plain,
% 1.64/1.80 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3108, 4143, 714])).
% 1.64/1.80 tff(4145,plain,
% 1.64/1.80 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[749, 4144])).
% 1.64/1.80 tff(4146,plain,
% 1.64/1.80 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[547, 4141, 19, 3665])).
% 1.64/1.80 tff(4147,plain,
% 1.64/1.80 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[477, 4146])).
% 1.64/1.80 tff(4148,plain,
% 1.64/1.80 (((~![X0: $i, 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))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4149,plain,
% 1.64/1.80 (((~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))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4150,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4149])).
% 1.64/1.80 tff(4151,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4150, 4148])).
% 1.64/1.80 tff(4152,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4153,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 1.64/1.80 tff(4154,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4153, 31, 85, 21, 249])).
% 1.64/1.80 tff(4155,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,[]))).
% 1.64/1.80 tff(4156,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4155, 4147, 249])).
% 1.64/1.80 tff(4157,plain,
% 1.64/1.80 (b(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[99, 4156])).
% 1.64/1.80 tff(4158,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2579, 112, 4157, 101, 4145, 4127, 762])).
% 1.64/1.80 tff(4159,plain,((~r(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4160,plain,
% 1.64/1.80 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4159, 387, 4113, 249, 4125, 20, 3959])).
% 1.64/1.80 tff(4161,plain,
% 1.64/1.80 (b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[494, 4160])).
% 1.64/1.80 tff(4162,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4163,plain,
% 1.64/1.80 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(z))), s(s(s(s(elem!1)))))) | (~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(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4164,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4163])).
% 1.64/1.81 tff(4165,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4164, 4162])).
% 1.64/1.81 tff(4166,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4167,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4166, 4165])).
% 1.64/1.81 tff(4168,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4167, 112, 1827, 196, 442, 2604, 762])).
% 1.64/1.81 tff(4169,plain,((~b(s(s(s(s(s(elem!1))))), 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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4170,plain,
% 1.64/1.81 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4169, 4161, 3951, 399, 387])).
% 1.64/1.81 tff(4171,plain,
% 1.64/1.81 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[404, 4170, 274])).
% 1.64/1.81 tff(4172,plain,
% 1.64/1.81 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3655, 18, 249, 101, 19, 276])).
% 1.64/1.81 tff(4173,plain,
% 1.64/1.81 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[477, 4172])).
% 1.64/1.81 tff(4174,plain,
% 1.64/1.81 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3526, 4173, 276])).
% 1.64/1.81 tff(4175,plain,
% 1.64/1.81 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[462, 4174])).
% 1.64/1.81 tff(4176,plain,
% 1.64/1.81 (~r(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4155, 4173, 249])).
% 1.64/1.81 tff(4177,plain,
% 1.64/1.81 (b(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[99, 4176])).
% 1.64/1.81 tff(4178,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4179,plain,
% 1.64/1.81 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4180,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4179])).
% 1.64/1.81 tff(4181,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4180, 4178])).
% 1.64/1.81 tff(4182,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4183,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 1.64/1.81 tff(4184,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4183, 112, 4177, 18, 4175, 2604, 762])).
% 1.64/1.81 tff(4185,plain,((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4186,plain,
% 1.64/1.81 (~b(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4185, 4161, 387, 4171, 249, 4113, 4125])).
% 1.64/1.81 tff(4187,plain,
% 1.64/1.81 (r(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[182, 4186])).
% 1.64/1.81 tff(4188,plain,
% 1.64/1.81 (~r(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[170, 4187, 20])).
% 1.64/1.81 tff(4189,plain,
% 1.64/1.81 (b(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[99, 4188])).
% 1.64/1.81 tff(4190,plain,
% 1.64/1.81 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3541, 112, 4189, 4113, 387])).
% 1.64/1.81 tff(4191,plain,
% 1.64/1.81 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[462, 4190])).
% 1.64/1.81 tff(4192,plain,
% 1.64/1.81 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3526, 4191, 4171])).
% 1.64/1.81 tff(4193,plain,
% 1.64/1.81 (b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[477, 4192])).
% 1.64/1.81 tff(4194,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4195,plain,
% 1.64/1.81 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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))))) | (~b(s(s(s(z))), 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))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4196,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(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))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4195])).
% 1.64/1.81 tff(4197,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(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))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4196, 4194])).
% 1.64/1.81 tff(4198,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(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))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4199,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4198, 4197])).
% 1.64/1.81 tff(4200,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4199, 112, 4189, 4113, 4125, 3951, 4193])).
% 1.64/1.81 tff(4201,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4202,plain,
% 1.64/1.81 (~r(z, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4201, 249, 248])).
% 1.64/1.81 tff(4203,plain,
% 1.64/1.81 (b(z, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[515, 4202])).
% 1.64/1.81 tff(4204,plain,
% 1.64/1.81 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1877, 408, 249, 4113])).
% 1.64/1.81 tff(4205,plain,
% 1.64/1.81 (b(z, s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[356, 4204])).
% 1.64/1.81 tff(4206,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4123, 4205, 408, 249, 248])).
% 1.64/1.81 tff(4207,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[398, 4206])).
% 1.64/1.81 tff(4208,plain,
% 1.64/1.81 (~b(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1867, 1857, 4113, 4203])).
% 1.64/1.81 tff(4209,plain,
% 1.64/1.81 (r(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[182, 4208])).
% 1.64/1.81 tff(4210,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1822, 31, 4209, 408, 4207])).
% 1.64/1.81 tff(4211,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4212,plain,
% 1.64/1.81 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4211, 249, 248])).
% 1.64/1.81 tff(4213,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[429, 4212])).
% 1.64/1.81 tff(4214,plain,
% 1.64/1.81 (~r(s(s(s(z))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4111, 196, 271, 249])).
% 1.64/1.81 tff(4215,plain,
% 1.64/1.81 (b(s(s(s(z))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[83, 4214])).
% 1.64/1.81 tff(4216,plain,
% 1.64/1.81 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2676, 85, 275])).
% 1.64/1.81 tff(4217,plain,
% 1.64/1.81 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[749, 4216])).
% 1.64/1.81 tff(4218,plain,
% 1.64/1.81 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4155, 85, 249])).
% 1.64/1.81 tff(4219,plain,
% 1.64/1.81 (b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[477, 4218])).
% 1.64/1.81 tff(4220,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1662, 4219, 4217, 442, 333])).
% 1.64/1.81 tff(4221,plain,((~r(s(z), s(s(s(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(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4222,plain,
% 1.64/1.81 (~r(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4221, 3962, 3961, 249, 275])).
% 1.64/1.81 tff(4223,plain,
% 1.64/1.81 (b(s(z), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[99, 4222])).
% 1.64/1.81 tff(4224,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4199, 112, 102, 101, 19, 196, 539])).
% 1.64/1.81 tff(4225,plain,((~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(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4226,plain,
% 1.64/1.81 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4225, 4223, 4215, 19, 196])).
% 1.64/1.81 tff(4227,plain,
% 1.64/1.81 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[477, 4226])).
% 1.64/1.81 tff(4228,plain,
% 1.64/1.81 (~b(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1867, 4223, 4215, 803])).
% 1.64/1.81 tff(4229,plain,
% 1.64/1.81 (r(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[182, 4228])).
% 1.64/1.81 tff(4230,plain,
% 1.64/1.81 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3023, 4229, 19, 3961])).
% 1.64/1.81 tff(4231,plain,
% 1.64/1.81 (b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[322, 4230])).
% 1.64/1.81 tff(4232,plain,
% 1.64/1.81 (~b(z, s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[342, 4231, 285, 271, 3961])).
% 1.64/1.81 tff(4233,plain,
% 1.64/1.81 (r(z, s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[356, 4232])).
% 1.64/1.81 tff(4234,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4235,plain,
% 1.64/1.81 (((~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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4236,plain,
% 1.64/1.81 (((~![X0: $i, 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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4235])).
% 1.64/1.81 tff(4237,plain,
% 1.64/1.81 (((~![X0: $i, 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(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4236, 4234])).
% 1.64/1.81 tff(4238,plain,
% 1.64/1.81 ((~![X0: $i, 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))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4239,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 1.64/1.81 tff(4240,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4239, 31, 4229, 4233, 4227])).
% 1.64/1.81 tff(4241,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4242,plain,
% 1.64/1.81 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4241, 4213, 3951, 268, 4203, 249])).
% 1.64/1.81 tff(4243,plain,
% 1.64/1.81 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[386, 4242])).
% 1.64/1.81 tff(4244,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4245,plain,
% 1.64/1.81 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4246,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4245])).
% 1.64/1.82 tff(4247,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4246, 4244])).
% 1.64/1.82 tff(4248,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4249,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4248, 4247])).
% 1.64/1.82 tff(4250,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4249, 112, 101, 19, 196, 539])).
% 1.64/1.82 tff(4251,plain,((~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(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4252,plain,
% 1.64/1.82 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4251, 4113, 4213, 3951])).
% 1.64/1.82 tff(4253,plain,
% 1.64/1.82 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[477, 4252])).
% 1.64/1.82 tff(4254,plain,
% 1.64/1.82 (~r(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4155, 4253, 249])).
% 1.64/1.82 tff(4255,plain,
% 1.64/1.82 (b(s(z), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[99, 4254])).
% 1.64/1.82 tff(4256,plain,
% 1.64/1.82 (~b(z, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1867, 4255, 4113, 4203])).
% 1.64/1.82 tff(4257,plain,
% 1.64/1.82 (r(z, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[182, 4256])).
% 1.64/1.82 tff(4258,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4239, 31, 162, 569, 21])).
% 1.64/1.82 tff(4259,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,[]))).
% 1.64/1.82 tff(4260,plain,
% 1.64/1.82 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4259, 4257, 4253])).
% 1.64/1.82 tff(4261,plain,
% 1.64/1.82 (b(z, s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[356, 4260])).
% 1.64/1.82 tff(4262,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4263,plain,
% 1.64/1.82 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), 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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4264,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4263])).
% 1.64/1.82 tff(4265,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4264, 4262])).
% 1.64/1.82 tff(4266,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4267,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 1.64/1.82 tff(4268,plain,
% 1.64/1.82 (~b(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4267, 112, 4203, 4113, 4213, 3951, 4261])).
% 1.64/1.82 tff(4269,plain,
% 1.64/1.82 (r(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[527, 4268])).
% 1.64/1.82 tff(4270,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[620, 4269, 249])).
% 1.64/1.82 tff(4271,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[398, 4270])).
% 1.64/1.82 tff(4272,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1919, 112, 102, 101, 443, 762])).
% 1.64/1.82 tff(4273,plain,((~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(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4274,plain,
% 1.64/1.82 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4273, 4255, 4113, 4243])).
% 1.64/1.82 tff(4275,plain,
% 1.64/1.82 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[462, 4274])).
% 1.64/1.82 tff(4276,plain,
% 1.64/1.82 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3526, 4275, 4253])).
% 1.64/1.82 tff(4277,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[404, 4276, 274])).
% 1.64/1.82 tff(4278,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[486, 31, 162, 464, 714])).
% 1.64/1.82 tff(4279,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4280,plain,
% 1.64/1.82 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4279, 4275, 4257])).
% 1.64/1.82 tff(4281,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[494, 4280])).
% 1.64/1.82 tff(4282,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4169, 4281, 4277, 3951, 4271, 4243])).
% 1.64/1.82 tff(4283,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4284,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4283, 248])).
% 1.64/1.82 tff(4285,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[646, 4284])).
% 1.64/1.82 tff(4286,plain,
% 1.64/1.82 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[416, 581, 3])).
% 1.64/1.82 tff(4287,plain,
% 1.64/1.82 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[160, 4286])).
% 1.64/1.82 tff(4288,plain,
% 1.64/1.82 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3526, 464, 276])).
% 1.64/1.82 tff(4289,plain,
% 1.64/1.82 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3642, 464, 408, 271])).
% 1.64/1.82 tff(4290,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[477, 4289, 4288])).
% 1.64/1.82 tff(4291,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4292,plain,
% 1.64/1.82 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4291, 276, 271, 581])).
% 1.64/1.82 tff(4293,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[462, 4292])).
% 1.64/1.82 tff(4294,plain,
% 1.64/1.82 (~b(s(z), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[683, 569, 276, 4293, 18])).
% 1.64/1.82 tff(4295,plain,
% 1.64/1.82 (r(s(z), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[608, 4294])).
% 1.64/1.82 tff(4296,plain,
% 1.64/1.82 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[783, 569, 276])).
% 1.64/1.82 tff(4297,plain,
% 1.64/1.82 (b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[322, 4296])).
% 1.64/1.82 tff(4298,plain,
% 1.64/1.82 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[759, 4297, 18, 4293])).
% 1.64/1.82 tff(4299,plain,
% 1.64/1.82 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[749, 4298])).
% 1.64/1.82 tff(4300,plain,
% 1.64/1.82 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3108, 4299, 4295])).
% 1.64/1.82 tff(4301,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[494, 4300])).
% 1.64/1.82 tff(4302,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2028, 4299, 581])).
% 1.64/1.82 tff(4303,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[299, 4302, 271])).
% 1.64/1.82 tff(4304,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1362, 569, 580, 4293])).
% 1.64/1.82 tff(4305,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[398, 4304])).
% 1.64/1.82 tff(4306,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3679, 112, 4305, 4297, 4303, 4301])).
% 1.64/1.82 tff(4307,plain,((~r(z, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4308,plain,
% 1.64/1.82 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4307, 569, 18, 271, 580])).
% 1.64/1.82 tff(4309,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[404, 4308, 2474])).
% 1.64/1.82 tff(4310,plain,
% 1.64/1.82 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[770, 4309, 4, 4287])).
% 1.64/1.82 tff(4311,plain,
% 1.64/1.82 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[386, 4310])).
% 1.64/1.82 tff(4312,plain,
% 1.64/1.82 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1423, 4309, 3, 581])).
% 1.64/1.82 tff(4313,plain,
% 1.64/1.82 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[462, 4312])).
% 1.64/1.82 tff(4314,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1362, 4313, 580, 569])).
% 1.64/1.82 tff(4315,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[398, 4314])).
% 1.64/1.82 tff(4316,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4317,plain,
% 1.64/1.82 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~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(z))) | (~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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4318,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4317])).
% 1.64/1.82 tff(4319,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4318, 4316])).
% 1.64/1.82 tff(4320,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4321,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~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(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4320, 4319])).
% 1.64/1.82 tff(4322,plain,
% 1.64/1.82 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4321, 112, 18, 4315, 4313, 4309])).
% 1.64/1.82 tff(4323,plain,
% 1.64/1.82 (r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[494, 4322])).
% 1.64/1.82 tff(4324,plain,
% 1.64/1.82 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4321, 112, 18, 1827, 443, 442])).
% 1.64/1.82 tff(4325,plain,
% 1.64/1.82 (r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[494, 4324])).
% 1.64/1.82 tff(4326,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4327,plain,
% 1.64/1.82 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(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(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4328,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4327])).
% 1.64/1.82 tff(4329,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(elem!1)))), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4328, 4326])).
% 1.64/1.82 tff(4330,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4331,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 1.64/1.82 tff(4332,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4331, 112, 859, 803, 4, 1827])).
% 1.64/1.82 tff(4333,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4334,plain,
% 1.64/1.82 (~b(z, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4333, 1827, 4, 859])).
% 1.64/1.82 tff(4335,plain,
% 1.64/1.82 (r(z, s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[515, 4334])).
% 1.64/1.82 tff(4336,plain,
% 1.64/1.82 (((~![X0: $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(elem!1))))), 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(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4337,plain,
% 1.64/1.82 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4338,plain,
% 1.64/1.82 (((~![X0: $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(elem!1))))), s(s(s(z))))) | (~r(z, s(s(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(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4337])).
% 1.64/1.82 tff(4339,plain,
% 1.64/1.82 (((~![X0: $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(elem!1))))), s(s(s(z))))) | (~r(z, s(s(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(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4338, 4336])).
% 1.64/1.82 tff(4340,plain,
% 1.64/1.82 ((~![X0: $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(elem!1))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4341,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4340, 4339])).
% 1.64/1.82 tff(4342,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4341, 31, 4335, 4325, 275])).
% 1.64/1.82 tff(4343,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(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(s(z))), z)) | (~b(z, 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))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4344,plain,
% 1.64/1.82 (~b(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4343, 4315, 4, 4309, 18, 4313, 4311])).
% 1.64/1.82 tff(4345,plain,
% 1.64/1.82 (r(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[527, 4344])).
% 1.64/1.82 tff(4346,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(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(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4347,plain,
% 1.64/1.82 (((~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(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4348,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4347])).
% 1.64/1.83 tff(4349,plain,
% 1.64/1.83 (((~![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))), 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(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4348, 4346])).
% 1.64/1.83 tff(4350,plain,
% 1.64/1.83 ((~![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))), 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))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4351,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4350, 4349])).
% 1.64/1.83 tff(4352,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4351, 31, 4345, 4323, 4311])).
% 1.64/1.83 tff(4353,plain,((~r(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(s(elem!1)))), s(z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4354,plain,
% 1.64/1.83 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4353, 580, 4285, 18, 3, 268])).
% 1.64/1.83 tff(4355,plain,
% 1.64/1.83 (b(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[356, 4354])).
% 1.64/1.83 tff(4356,plain,
% 1.64/1.83 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2676, 275, 85])).
% 1.64/1.83 tff(4357,plain,
% 1.64/1.83 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[749, 4356])).
% 1.64/1.83 tff(4358,plain,
% 1.64/1.83 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[759, 4357, 18, 3968])).
% 1.64/1.83 tff(4359,plain,
% 1.64/1.83 (r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[322, 4358])).
% 1.64/1.83 tff(4360,plain,
% 1.64/1.83 (~r(z, s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[310, 4359, 275])).
% 1.64/1.83 tff(4361,plain,
% 1.64/1.83 (b(z, s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[515, 4360])).
% 1.64/1.83 tff(4362,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4363,plain,
% 1.64/1.83 (((~b(s(s(s(s(elem!1)))), s(s(s(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4364,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4363])).
% 1.64/1.83 tff(4365,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4364, 4362])).
% 1.64/1.83 tff(4366,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(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)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4367,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4366, 4365])).
% 1.64/1.83 tff(4368,plain,
% 1.64/1.83 (~b(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4367, 112, 4361, 4, 4287])).
% 1.64/1.83 tff(4369,plain,
% 1.64/1.83 (r(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[356, 4368])).
% 1.64/1.83 tff(4370,plain,
% 1.64/1.83 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[783, 4369, 4359])).
% 1.64/1.83 tff(4371,plain,
% 1.64/1.83 (b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[404, 4370, 2474])).
% 1.64/1.83 tff(4372,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4008, 4369, 4359])).
% 1.64/1.83 tff(4373,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[299, 4372, 271])).
% 1.64/1.83 tff(4374,plain,
% 1.64/1.83 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[712, 4373, 4, 4287, 4371])).
% 1.64/1.83 tff(4375,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1362, 4369, 580, 3968])).
% 1.64/1.83 tff(4376,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[398, 4375])).
% 1.64/1.83 tff(4377,plain,
% 1.64/1.83 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4321, 112, 18, 4376, 3968, 4371])).
% 1.64/1.83 tff(4378,plain,
% 1.64/1.83 (r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[494, 4377])).
% 1.64/1.83 tff(4379,plain,
% 1.64/1.83 (~b(s(s(s(z))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4333, 4376, 4, 4361])).
% 1.64/1.83 tff(4380,plain,
% 1.64/1.83 (r(s(s(s(z))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[527, 4379])).
% 1.64/1.83 tff(4381,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[720, 31, 4380, 4378, 4374])).
% 1.64/1.83 tff(4382,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(elem!1)))), s(z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(4383,plain,
% 1.64/1.83 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4382, 85, 4285, 268, 580, 3, 18])).
% 1.64/1.83 tff(4384,plain,
% 1.64/1.83 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[386, 4383])).
% 1.64/1.83 tff(4385,plain,
% 1.64/1.83 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[770, 4384, 4285, 4287])).
% 1.64/1.83 tff(4386,plain,
% 1.64/1.83 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[404, 4385, 274])).
% 1.64/1.83 tff(4387,plain,
% 1.64/1.83 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4307, 4386, 18, 268, 580])).
% 1.64/1.83 tff(4388,plain,
% 1.64/1.83 (b(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[356, 4387])).
% 1.64/1.83 tff(4389,plain,
% 1.64/1.83 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(z))))) | (~b(z, s(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(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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4390,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4389])).
% 1.64/1.83 tff(4391,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4390, 4362])).
% 1.64/1.83 tff(4392,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4393,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4392, 4391])).
% 1.64/1.83 tff(4394,plain,
% 1.64/1.83 (~b(z, s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4393, 112, 4285, 4287, 4388])).
% 1.64/1.83 tff(4395,plain,
% 1.64/1.83 (r(z, s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[515, 4394])).
% 1.64/1.83 tff(4396,plain,
% 1.64/1.83 (~r(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2569, 31, 85, 4395])).
% 1.64/1.83 tff(4397,plain,
% 1.64/1.83 (b(s(z), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[608, 4396])).
% 1.64/1.83 tff(4398,plain,
% 1.64/1.83 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4291, 4386, 268, 581])).
% 1.64/1.83 tff(4399,plain,
% 1.64/1.83 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[462, 4398])).
% 1.64/1.83 tff(4400,plain,
% 1.64/1.83 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[653, 112, 18, 4399, 4397])).
% 1.64/1.83 tff(4401,plain,
% 1.64/1.83 (r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[494, 4400])).
% 1.64/1.83 tff(4402,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4074, 4401, 4386])).
% 1.64/1.83 tff(4403,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[398, 4402])).
% 1.64/1.83 tff(4404,plain,
% 1.64/1.83 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3569, 4403, 4397, 4388])).
% 1.64/1.83 tff(4405,plain,
% 1.64/1.83 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[477, 4404])).
% 1.64/1.83 tff(4406,plain,
% 1.64/1.83 (((~![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(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(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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4407,plain,
% 1.64/1.83 (((~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(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4408,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4407])).
% 1.64/1.83 tff(4409,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4408, 4406])).
% 1.64/1.83 tff(4410,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4411,plain,
% 1.64/1.83 ((~![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(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(elem!1))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4410, 4409])).
% 1.64/1.83 tff(4412,plain,
% 1.64/1.83 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4411, 31, 4386, 4405])).
% 1.64/1.83 tff(4413,plain,
% 1.64/1.83 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[749, 4412])).
% 1.64/1.83 tff(4414,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4415,plain,
% 1.64/1.83 (((~b(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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), 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(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)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(4416,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[4415])).
% 1.64/1.83 tff(4417,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[4416, 4414])).
% 1.64/1.83 tff(4418,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(4419,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4418, 4417])).
% 1.64/1.83 tff(4420,plain,
% 1.64/1.83 (~b(s(s(s(z))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4419, 112, 4285, 4403, 4287, 4388])).
% 1.64/1.83 tff(4421,plain,
% 1.64/1.83 (r(s(s(s(z))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[527, 4420])).
% 1.64/1.83 tff(4422,plain,
% 1.64/1.83 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[720, 31, 4421, 4401])).
% 1.64/1.83 tff(4423,plain,
% 1.64/1.83 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2752, 4422])).
% 1.64/1.83 tff(4424,plain,
% 1.64/1.83 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[759, 4413, 18, 4399])).
% 1.64/1.83 tff(4425,plain,
% 1.64/1.83 (r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[322, 4424])).
% 1.64/1.83 tff(4426,plain,
% 1.64/1.83 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[3315])).
% 1.64/1.83 tff(4427,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(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(s(elem!1))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4428,plain,
% 1.64/1.84 (((~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(s(s(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~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(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), 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(s(elem!1))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4429,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(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(s(elem!1)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4428])).
% 1.64/1.84 tff(4430,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(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(s(elem!1))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4429, 4427])).
% 1.64/1.84 tff(4431,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4432,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(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(s(elem!1)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4431, 4430])).
% 1.64/1.84 tff(4433,plain,
% 1.64/1.84 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4432, 112, 4, 196, 406, 762])).
% 1.64/1.84 tff(4434,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[299, 4433, 3064])).
% 1.64/1.84 tff(4435,plain,
% 1.64/1.84 (~b(z, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4393, 112, 4, 196, 2])).
% 1.64/1.84 tff(4436,plain,
% 1.64/1.84 (r(z, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[515, 4435])).
% 1.64/1.84 tff(4437,plain,
% 1.64/1.84 (((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(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(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4438,plain,
% 1.64/1.84 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4439,plain,
% 1.64/1.84 (((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(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(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4438])).
% 1.64/1.84 tff(4440,plain,
% 1.64/1.84 (((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(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(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4439, 4437])).
% 1.64/1.84 tff(4441,plain,
% 1.64/1.84 ((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4442,plain,
% 1.64/1.84 ((~![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(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4441, 4440])).
% 1.64/1.84 tff(4443,plain,
% 1.64/1.84 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4442, 31, 4436, 302, 3814])).
% 1.64/1.84 tff(4444,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4445,plain,
% 1.64/1.84 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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))), 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4446,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4445])).
% 1.64/1.84 tff(4447,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4446, 4444])).
% 1.64/1.84 tff(4448,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4449,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4448, 4447])).
% 1.64/1.84 tff(4450,plain,
% 1.64/1.84 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4449, 112, 4, 1827, 196, 2, 3819])).
% 1.64/1.84 tff(4451,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 4450, 4443])).
% 1.64/1.84 tff(4452,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~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)))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (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,[]))).
% 1.64/1.84 tff(4453,plain,
% 1.64/1.84 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4452, 1068, 1827, 196, 2, 302, 4, 3069, 4434])).
% 1.64/1.84 tff(4454,plain,
% 1.64/1.84 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1225, 4453, 3091])).
% 1.64/1.84 tff(4455,plain,
% 1.64/1.84 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4454, 4426])).
% 1.64/1.84 tff(4456,plain,
% 1.64/1.84 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1068])).
% 1.64/1.84 tff(4457,plain,
% 1.64/1.84 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(elem!1)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[4456])).
% 1.64/1.84 tff(4458,plain,
% 1.64/1.84 (b(elem!1, s(s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4454, 4457])).
% 1.64/1.84 tff(4459,plain,
% 1.64/1.84 (~b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1534, 4458, 2229, 2226])).
% 1.64/1.84 tff(4460,plain,
% 1.64/1.84 (r(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1498, 4459, 2234])).
% 1.64/1.84 tff(4461,plain,
% 1.64/1.84 (~r(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1568, 4460, 3])).
% 1.64/1.84 tff(4462,plain,
% 1.64/1.84 (b(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1139, 4461, 1125])).
% 1.64/1.84 tff(4463,plain,
% 1.64/1.84 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2249, 4462, 1068])).
% 1.64/1.84 tff(4464,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))), s(z))) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4465,plain,
% 1.64/1.84 (((~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(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), 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(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(4466,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[4465])).
% 1.64/1.84 tff(4467,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[4466, 4464])).
% 1.64/1.84 tff(4468,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(4469,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4468, 4467])).
% 1.64/1.84 tff(4470,plain,
% 1.64/1.84 ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4469, 112, 443, 751])).
% 1.64/1.84 tff(4471,plain,
% 1.64/1.84 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4470, 4463])).
% 1.64/1.84 tff(4472,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4471, 4455])).
% 1.64/1.84 tff(4473,plain,((~(s(s(elem!1)) = 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))))))) | (~r(s(s(s(z))), 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)))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (elem!1 = 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)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4474,plain,
% 1.64/1.84 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4473, 4399, 4413, 3, 4403, 4287, 4388, 4425, 4285, 257, 1193, 4384, 4423])).
% 1.64/1.84 tff(4475,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1736])).
% 1.64/1.84 tff(4476,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[4475])).
% 1.64/1.84 tff(4477,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4, 4476])).
% 1.64/1.84 tff(4478,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[230, 4477])).
% 1.64/1.84 tff(4479,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(4480,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4479, 891, 4])).
% 1.64/1.84 tff(4481,plain,
% 1.64/1.84 (elem!1 = s(z)),
% 1.64/1.84 inference(transitivity,[status(thm)],[1073, 1742, 137])).
% 1.64/1.84 tff(4482,plain,
% 1.64/1.84 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1736, 4481])).
% 1.64/1.84 tff(4483,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.84 inference(symmetry,[status(thm)],[4482])).
% 1.64/1.84 tff(4484,plain,
% 1.64/1.84 (r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[408, 4483])).
% 1.64/1.84 tff(4485,plain,
% 1.64/1.84 (r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4484, 2342])).
% 1.64/1.84 tff(4486,plain,
% 1.64/1.84 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[939, 891, 18, 443, 673, 751, 899])).
% 1.64/1.84 tff(4487,plain,
% 1.64/1.84 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1733, 4486])).
% 1.64/1.84 tff(4488,plain,
% 1.64/1.84 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2350, 31, 4487])).
% 1.64/1.84 tff(4489,plain,
% 1.64/1.84 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4488, 4485])).
% 1.64/1.84 tff(4490,plain,
% 1.64/1.84 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4489, 2340])).
% 1.64/1.84 tff(4491,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2360, 4490, 265])).
% 1.64/1.84 tff(4492,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[4491, 2338])).
% 1.64/1.84 tff(4493,plain,
% 1.64/1.84 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.64/1.84 inference(commutativity,[status(thm)],[])).
% 1.64/1.85 tff(4494,plain,
% 1.64/1.85 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[4493])).
% 1.64/1.85 tff(4495,plain,
% 1.64/1.85 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4494])).
% 1.64/1.85 tff(4496,plain,
% 1.64/1.85 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[969, 4495])).
% 1.64/1.85 tff(4497,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(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)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4498,plain,
% 1.64/1.85 (((~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)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4499,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(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))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4498])).
% 1.64/1.85 tff(4500,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(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)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4499, 4497])).
% 1.64/1.85 tff(4501,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4502,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4501, 4500])).
% 1.64/1.85 tff(4503,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4502, 31, 3, 4487])).
% 1.64/1.85 tff(4504,plain,
% 1.64/1.85 (((~![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))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4505,plain,
% 1.64/1.85 ((~![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))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4506,plain,
% 1.64/1.85 ((~![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)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4505, 4504])).
% 1.64/1.85 tff(4507,plain,
% 1.64/1.85 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4506, 78, 4503])).
% 1.64/1.85 tff(4508,plain,
% 1.64/1.85 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4507, 4496])).
% 1.64/1.85 tff(4509,plain,
% 1.64/1.85 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[990, 4487, 408])).
% 1.64/1.85 tff(4510,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1781, 4509, 891, 265])).
% 1.64/1.85 tff(4511,plain,
% 1.64/1.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1728, 4487, 85])).
% 1.64/1.85 tff(4512,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1718, 4511])).
% 1.64/1.85 tff(4513,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4514,plain,
% 1.64/1.85 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4515,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4514])).
% 1.64/1.85 tff(4516,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4515, 4513])).
% 1.64/1.85 tff(4517,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4518,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4517, 4516])).
% 1.64/1.85 tff(4519,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4518, 112, 4512, 4510, 4508, 4492, 4480])).
% 1.64/1.85 tff(4520,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (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(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4521,plain,
% 1.64/1.85 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4520, 85, 257, 3, 581, 4285, 18, 4399, 4397, 4413, 889])).
% 1.64/1.85 tff(4522,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4523,plain,
% 1.64/1.85 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4524,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4523])).
% 1.64/1.85 tff(4525,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4524, 4522])).
% 1.64/1.85 tff(4526,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4527,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~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))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4526, 4525])).
% 1.64/1.85 tff(4528,plain,
% 1.64/1.85 (~b(s(s(elem!1)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4527, 112, 1990, 4, 1827, 196, 2])).
% 1.64/1.85 tff(4529,plain,
% 1.64/1.85 (r(s(s(elem!1)), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[822, 78, 379, 4528])).
% 1.64/1.85 tff(4530,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1004, 112, 1990, 4, 196])).
% 1.64/1.85 tff(4531,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1008, 78, 4530, 1392])).
% 1.64/1.85 tff(4532,plain,
% 1.64/1.85 (((~![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(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4533,plain,
% 1.64/1.85 (((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4534,plain,
% 1.64/1.85 (((~![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(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(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(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4533])).
% 1.64/1.85 tff(4535,plain,
% 1.64/1.85 (((~![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(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(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(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4534, 4532])).
% 1.64/1.85 tff(4536,plain,
% 1.64/1.85 ((~![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(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4537,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4536, 4535])).
% 1.64/1.85 tff(4538,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4537, 31, 20, 4531, 4529])).
% 1.64/1.85 tff(4539,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (s(s(elem!1)) = 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))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(4540,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4539, 4521, 4285, 4395, 4403, 4287, 4388])).
% 1.64/1.85 tff(4541,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[872, 4540, 248])).
% 1.64/1.85 tff(4542,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(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(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4543,plain,
% 1.64/1.85 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4544,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[4543])).
% 1.64/1.85 tff(4545,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(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)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[4544, 4542])).
% 1.64/1.85 tff(4546,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(4547,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4546, 4545])).
% 1.64/1.85 tff(4548,plain,
% 1.64/1.85 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4547, 31, 4541, 4386])).
% 1.64/1.85 tff(4549,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1025, 4548, 4474])).
% 1.64/1.85 tff(4550,plain,
% 1.64/1.85 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3346, 4474])).
% 1.64/1.85 tff(4551,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(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(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4552,plain,
% 1.64/1.85 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(4553,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4552])).
% 1.64/1.86 tff(4554,plain,
% 1.64/1.86 (((~![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(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(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(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4553, 4551])).
% 1.64/1.86 tff(4555,plain,
% 1.64/1.86 ((~![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(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4556,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 1.64/1.86 tff(4557,plain,
% 1.64/1.86 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4556, 31, 4541, 4386])).
% 1.64/1.86 tff(4558,plain,
% 1.64/1.86 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2066, 4557, 4550])).
% 1.64/1.86 tff(4559,plain,
% 1.64/1.86 (~r(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[851, 4541, 4405])).
% 1.64/1.86 tff(4560,plain,
% 1.64/1.86 (b(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[857, 4559])).
% 1.64/1.86 tff(4561,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3366, 112, 4560, 4558, 4549, 4413])).
% 1.64/1.86 tff(4562,plain,((~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | b(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4563,plain,
% 1.64/1.86 (~r(s(z), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4562, 580, 3, 18, 248])).
% 1.64/1.86 tff(4564,plain,
% 1.64/1.86 (b(s(z), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[99, 4563])).
% 1.64/1.86 tff(4565,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4566,plain,
% 1.64/1.86 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4567,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4566])).
% 1.64/1.86 tff(4568,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4567, 4565])).
% 1.64/1.86 tff(4569,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4570,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4569, 4568])).
% 1.64/1.86 tff(4571,plain,
% 1.64/1.86 (~b(z, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4570, 112, 4564, 18, 4287, 4355])).
% 1.64/1.86 tff(4572,plain,
% 1.64/1.86 (r(z, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[515, 4571])).
% 1.64/1.86 tff(4573,plain,
% 1.64/1.86 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1423, 2475, 3, 408])).
% 1.64/1.86 tff(4574,plain,
% 1.64/1.86 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[462, 4573])).
% 1.64/1.86 tff(4575,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[416, 408, 3])).
% 1.64/1.86 tff(4576,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[160, 4575])).
% 1.64/1.86 tff(4577,plain,
% 1.64/1.86 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[770, 2475, 4, 4576])).
% 1.64/1.86 tff(4578,plain,
% 1.64/1.86 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[386, 4577])).
% 1.64/1.86 tff(4579,plain,
% 1.64/1.86 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[310, 4578, 20])).
% 1.64/1.86 tff(4580,plain,
% 1.64/1.86 (b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[322, 4579])).
% 1.64/1.86 tff(4581,plain,
% 1.64/1.86 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[759, 4580, 18, 4574])).
% 1.64/1.86 tff(4582,plain,
% 1.64/1.86 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[749, 4581])).
% 1.64/1.86 tff(4583,plain,
% 1.64/1.86 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[342, 4580, 2, 271, 301])).
% 1.64/1.86 tff(4584,plain,
% 1.64/1.86 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[299, 4583, 271])).
% 1.64/1.86 tff(4585,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2028, 4584, 4582, 408])).
% 1.64/1.86 tff(4586,plain,(r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4587,plain,
% 1.64/1.86 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4586, 581, 268, 4355, 18, 4572, 4285, 3])).
% 1.64/1.86 tff(4588,plain,
% 1.64/1.86 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4291, 4587, 268, 581])).
% 1.64/1.86 tff(4589,plain,
% 1.64/1.86 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[462, 4588])).
% 1.64/1.86 tff(4590,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4591,plain,
% 1.64/1.86 (((~b(s(s(s(s(elem!1)))), s(s(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(s(s(s(elem!1)))))) | (~b(s(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)))))) <=> ((~b(s(z), 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(z), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4592,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(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(s(s(s(elem!1)))))) | (~b(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4591])).
% 1.64/1.86 tff(4593,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(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(s(s(s(elem!1)))))) | (~b(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4592, 4590])).
% 1.64/1.86 tff(4594,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(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(s(s(s(elem!1)))))) | (~b(s(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))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4595,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4594, 4593])).
% 1.64/1.86 tff(4596,plain,
% 1.64/1.86 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4595, 112, 4564, 4285, 4287])).
% 1.64/1.86 tff(4597,plain,
% 1.64/1.86 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[477, 4596])).
% 1.64/1.86 tff(4598,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4411, 31, 731, 276, 21])).
% 1.64/1.86 tff(4599,plain,((~r(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(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4600,plain,
% 1.64/1.86 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4599, 4587, 4597])).
% 1.64/1.86 tff(4601,plain,
% 1.64/1.86 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[749, 4600])).
% 1.64/1.86 tff(4602,plain,
% 1.64/1.86 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[759, 4601, 18, 4589])).
% 1.64/1.86 tff(4603,plain,
% 1.64/1.86 (r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[322, 4602])).
% 1.64/1.86 tff(4604,plain,
% 1.64/1.86 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[310, 4603, 4572])).
% 1.64/1.86 tff(4605,plain,
% 1.64/1.86 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[386, 4604])).
% 1.64/1.86 tff(4606,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4183, 112, 102, 18, 443, 2604, 762])).
% 1.64/1.86 tff(4607,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(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)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4608,plain,
% 1.64/1.86 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4607, 4564, 18, 4589, 4605])).
% 1.64/1.86 tff(4609,plain,
% 1.64/1.86 (r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[494, 4608])).
% 1.64/1.86 tff(4610,plain,
% 1.64/1.86 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4074, 4609, 4587])).
% 1.64/1.86 tff(4611,plain,
% 1.64/1.86 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[398, 4610])).
% 1.64/1.86 tff(4612,plain,
% 1.64/1.86 (~b(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4419, 112, 4285, 4611, 4287, 4355])).
% 1.64/1.86 tff(4613,plain,
% 1.64/1.86 (r(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[527, 4612])).
% 1.64/1.86 tff(4614,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[720, 31, 4613, 4609])).
% 1.64/1.86 tff(4615,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2752, 4614])).
% 1.64/1.86 tff(4616,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), 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))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4617,plain,
% 1.64/1.86 (((~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(z), 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(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(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4618,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), 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(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), 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)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4617])).
% 1.64/1.86 tff(4619,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), 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(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), 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))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4618, 4616])).
% 1.64/1.86 tff(4620,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z), 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4621,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4620, 4619])).
% 1.64/1.86 tff(4622,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4621, 112, 4564, 4285, 4287, 4601, 4615, 4605])).
% 1.64/1.86 tff(4623,plain,(b(s(s(s(s(elem!1)))), s(z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4624,plain,
% 1.64/1.86 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4623, 18, 3, 248])).
% 1.64/1.86 tff(4625,plain,
% 1.64/1.86 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[386, 1459])).
% 1.64/1.86 tff(4626,plain,
% 1.64/1.86 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[770, 4625, 4, 442])).
% 1.64/1.86 tff(4627,plain,
% 1.64/1.86 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[160, 4626])).
% 1.64/1.86 tff(4628,plain,
% 1.64/1.86 (~r(z, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2660, 31, 569, 4627])).
% 1.64/1.86 tff(4629,plain,
% 1.64/1.86 (b(z, s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[515, 4628])).
% 1.64/1.86 tff(4630,plain,
% 1.64/1.86 (~r(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[563, 31, 569, 4627])).
% 1.64/1.86 tff(4631,plain,
% 1.64/1.86 (b(s(s(s(z))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[527, 4630])).
% 1.64/1.86 tff(4632,plain,
% 1.64/1.86 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1389, 112, 4631, 4629, 3977, 4625])).
% 1.64/1.86 tff(4633,plain,
% 1.64/1.86 (r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[322, 4632])).
% 1.64/1.86 tff(4634,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(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(s(elem!1))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4635,plain,
% 1.64/1.86 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(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(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(s(elem!1))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(4636,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(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(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(s(elem!1)))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[4635])).
% 1.64/1.86 tff(4637,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(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(z))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(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(s(elem!1))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[4636, 4634])).
% 1.64/1.86 tff(4638,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(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(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(4639,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[4638, 4637])).
% 1.64/1.86 tff(4640,plain,
% 1.64/1.86 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4639, 112, 4631, 4629, 4, 3977, 4625])).
% 1.64/1.86 tff(4641,plain,
% 1.64/1.86 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[299, 4640, 271])).
% 1.64/1.86 tff(4642,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4008, 4641, 4633, 569])).
% 1.64/1.86 tff(4643,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(4644,plain,
% 1.64/1.86 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4643, 569, 271, 4, 3, 442])).
% 1.64/1.86 tff(4645,plain,
% 1.64/1.86 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[462, 4644])).
% 1.64/1.86 tff(4646,plain,
% 1.64/1.86 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[451, 4645, 19, 442])).
% 1.64/1.87 tff(4647,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[39, 4646, 3])).
% 1.64/1.87 tff(4648,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[160, 4647])).
% 1.64/1.87 tff(4649,plain,
% 1.64/1.87 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[759, 751, 18, 443])).
% 1.64/1.87 tff(4650,plain,
% 1.64/1.87 (r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[322, 4649])).
% 1.64/1.87 tff(4651,plain,
% 1.64/1.87 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4008, 4650, 569])).
% 1.64/1.87 tff(4652,plain,
% 1.64/1.87 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[299, 4651, 271])).
% 1.64/1.87 tff(4653,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3021, 112, 19, 443, 751, 4652])).
% 1.64/1.87 tff(4654,plain,((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4655,plain,
% 1.64/1.87 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4654, 4645, 19, 271, 569, 18])).
% 1.64/1.87 tff(4656,plain,
% 1.64/1.87 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[749, 4655])).
% 1.64/1.87 tff(4657,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[739, 4656, 3])).
% 1.64/1.87 tff(4658,plain,
% 1.64/1.87 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[712, 4657, 4, 442, 4648])).
% 1.64/1.87 tff(4659,plain,
% 1.64/1.87 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[299, 4658, 271])).
% 1.64/1.87 tff(4660,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2587, 31, 4656, 4659, 4646])).
% 1.64/1.87 tff(4661,plain,((~r(z, s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(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(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4662,plain,
% 1.64/1.87 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4661, 2475, 4, 271, 3, 19, 18])).
% 1.64/1.87 tff(4663,plain,
% 1.64/1.87 (b(z, s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[356, 4662])).
% 1.64/1.87 tff(4664,plain,
% 1.64/1.87 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[547, 4663, 18, 19])).
% 1.64/1.87 tff(4665,plain,
% 1.64/1.87 (r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[477, 4664])).
% 1.64/1.87 tff(4666,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[39, 4665, 3])).
% 1.64/1.87 tff(4667,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[160, 4666])).
% 1.64/1.87 tff(4668,plain,
% 1.64/1.87 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[770, 4667, 4, 2475])).
% 1.64/1.87 tff(4669,plain,
% 1.64/1.87 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[386, 4668])).
% 1.64/1.87 tff(4670,plain,
% 1.64/1.87 (~b(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4095, 4667, 18, 19, 4663])).
% 1.64/1.87 tff(4671,plain,
% 1.64/1.87 (r(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[515, 4670])).
% 1.64/1.87 tff(4672,plain,
% 1.64/1.87 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[310, 4671, 4669])).
% 1.64/1.87 tff(4673,plain,
% 1.64/1.87 (b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[322, 4672])).
% 1.64/1.87 tff(4674,plain,
% 1.64/1.87 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[342, 4673, 301, 271, 4663])).
% 1.64/1.87 tff(4675,plain,
% 1.64/1.87 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[299, 4674, 271])).
% 1.64/1.87 tff(4676,plain,
% 1.64/1.87 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[472, 4669, 3])).
% 1.64/1.87 tff(4677,plain,
% 1.64/1.87 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[462, 4676])).
% 1.64/1.87 tff(4678,plain,
% 1.64/1.87 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[759, 4673, 18, 4677])).
% 1.64/1.87 tff(4679,plain,
% 1.64/1.87 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[749, 4678])).
% 1.64/1.87 tff(4680,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2587, 31, 4679, 4675, 4665])).
% 1.64/1.87 tff(4681,plain,(r(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)))))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4682,plain,
% 1.64/1.87 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4681, 18, 268, 3, 4285, 4624])).
% 1.64/1.87 tff(4683,plain,
% 1.64/1.87 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3526, 464, 4682])).
% 1.64/1.87 tff(4684,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[477, 4683])).
% 1.64/1.87 tff(4685,plain,
% 1.64/1.87 (~b(z, s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[547, 4684, 18, 4624])).
% 1.64/1.87 tff(4686,plain,
% 1.64/1.87 (r(z, s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[356, 4685])).
% 1.64/1.87 tff(4687,plain,
% 1.64/1.87 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[783, 4686, 4682])).
% 1.64/1.87 tff(4688,plain,
% 1.64/1.87 (b(z, s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[322, 4687])).
% 1.64/1.87 tff(4689,plain,
% 1.64/1.87 (((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4690,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4689])).
% 1.64/1.87 tff(4691,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4690, 2526])).
% 1.64/1.87 tff(4692,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4693,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4692, 4691])).
% 1.64/1.87 tff(4694,plain,
% 1.64/1.87 (~b(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4693, 112, 4688, 3977, 4625])).
% 1.64/1.87 tff(4695,plain,
% 1.64/1.87 (r(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[515, 4694])).
% 1.64/1.87 tff(4696,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2660, 31, 20, 569, 1])).
% 1.64/1.87 tff(4697,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(4698,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4697, 4695, 4686])).
% 1.64/1.87 tff(4699,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[160, 4698])).
% 1.64/1.87 tff(4700,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4701,plain,
% 1.64/1.87 (((~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(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4702,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4701])).
% 1.64/1.87 tff(4703,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4702, 4700])).
% 1.64/1.87 tff(4704,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4705,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4704, 4703])).
% 1.64/1.87 tff(4706,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4705, 112, 4285, 2130, 4699, 3977, 4625])).
% 1.64/1.87 tff(4707,plain,
% 1.64/1.87 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4708,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4707])).
% 1.64/1.87 tff(4709,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4708, 999])).
% 1.64/1.87 tff(4710,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(elem!1)), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(4711,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 1.64/1.87 tff(4712,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4711, 112, 4285, 2130, 4699])).
% 1.64/1.87 tff(4713,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[872, 4712, 248])).
% 1.64/1.87 tff(4714,plain,
% 1.64/1.87 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3737, 31, 4713, 464, 4682])).
% 1.64/1.87 tff(4715,plain,
% 1.64/1.87 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1025, 4714, 4706])).
% 1.64/1.87 tff(4716,plain,
% 1.64/1.87 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4715])).
% 1.64/1.87 tff(4717,plain,
% 1.64/1.87 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4715])).
% 1.64/1.87 tff(4718,plain,
% 1.64/1.87 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[145, 4717, 262])).
% 1.64/1.87 tff(4719,plain,
% 1.64/1.87 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4718])).
% 1.64/1.87 tff(4720,plain,
% 1.64/1.87 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1073, 4719, 131, 4716])).
% 1.64/1.87 tff(4721,plain,
% 1.64/1.87 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4720])).
% 1.64/1.87 tff(4722,plain,
% 1.64/1.87 (elem!1 = s(s(s(elem!1)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1073, 4719, 131])).
% 1.64/1.87 tff(4723,plain,
% 1.64/1.87 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4722])).
% 1.64/1.87 tff(4724,plain,
% 1.64/1.87 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[4723, 890])).
% 1.64/1.87 tff(4725,plain,
% 1.64/1.87 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[4724])).
% 1.64/1.87 tff(4726,plain,
% 1.64/1.87 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[4725])).
% 1.64/1.87 tff(4727,plain,
% 1.64/1.87 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[257, 4726])).
% 1.64/1.87 tff(4728,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(elem!1))))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4729,plain,
% 1.64/1.87 (((~b(s(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(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~b(s(s(s(z))), s(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(s(z))))) | (~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(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(4730,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4729])).
% 1.64/1.88 tff(4731,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4730, 4728])).
% 1.64/1.88 tff(4732,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1)))), s(s(s(z))))) | (~b(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))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4733,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4732, 4731])).
% 1.64/1.88 tff(4734,plain,
% 1.64/1.88 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4733, 112, 4285, 3977, 4625])).
% 1.64/1.88 tff(4735,plain,
% 1.64/1.88 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[299, 4734, 268])).
% 1.64/1.88 tff(4736,plain,
% 1.64/1.88 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4715])).
% 1.64/1.88 tff(4737,plain,
% 1.64/1.88 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4736])).
% 1.64/1.88 tff(4738,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1193, 4737])).
% 1.64/1.88 tff(4739,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4715])).
% 1.64/1.88 tff(4740,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4739])).
% 1.64/1.88 tff(4741,plain,
% 1.64/1.88 (b(s(s(s(z))), s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[3977, 4740])).
% 1.64/1.88 tff(4742,plain,
% 1.64/1.88 (((~![X0: $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(elem!1))))), z)) | (~r(z, s(s(s(s(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(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4743,plain,
% 1.64/1.88 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4744,plain,
% 1.64/1.88 (((~![X0: $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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(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(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4743])).
% 1.64/1.88 tff(4745,plain,
% 1.64/1.88 (((~![X0: $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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(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(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4744, 4742])).
% 1.64/1.88 tff(4746,plain,
% 1.64/1.88 ((~![X0: $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(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4747,plain,
% 1.64/1.88 ((~![X0: $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(elem!1))))), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4746, 4745])).
% 1.64/1.88 tff(4748,plain,
% 1.64/1.88 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4747, 31, 4695, 4682, 4686])).
% 1.64/1.88 tff(4749,plain,
% 1.64/1.88 (b(s(s(s(s(s(elem!1))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[494, 4748])).
% 1.64/1.88 tff(4750,plain,
% 1.64/1.88 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1093])).
% 1.64/1.88 tff(4751,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.88 inference(symmetry,[status(thm)],[4750])).
% 1.64/1.88 tff(4752,plain,
% 1.64/1.88 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4751])).
% 1.64/1.88 tff(4753,plain,
% 1.64/1.88 (b(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1211, 4457])).
% 1.64/1.88 tff(4754,plain,
% 1.64/1.88 (~b(elem!1, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1534, 4753, 2130, 2129])).
% 1.64/1.88 tff(4755,plain,
% 1.64/1.88 (r(elem!1, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1498, 4754, 2234])).
% 1.64/1.88 tff(4756,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2856, 4755, 3076])).
% 1.64/1.88 tff(4757,plain,
% 1.64/1.88 (~r(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2464, 4756, 20])).
% 1.64/1.88 tff(4758,plain,
% 1.64/1.88 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4757, 4752])).
% 1.64/1.88 tff(4759,plain,
% 1.64/1.88 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1211, 4426])).
% 1.64/1.88 tff(4760,plain,
% 1.64/1.88 (~r(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1568, 4755, 3])).
% 1.64/1.88 tff(4761,plain,
% 1.64/1.88 (b(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1139, 4760, 1125])).
% 1.64/1.88 tff(4762,plain,
% 1.64/1.88 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2249, 4761, 1068])).
% 1.64/1.88 tff(4763,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4764,plain,
% 1.64/1.88 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4765,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4764])).
% 1.64/1.88 tff(4766,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4765, 4763])).
% 1.64/1.88 tff(4767,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4768,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4767, 4766])).
% 1.64/1.88 tff(4769,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4768, 112, 18, 4762, 2604, 4759])).
% 1.64/1.88 tff(4770,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 4769, 4758])).
% 1.64/1.88 tff(4771,plain,((~b(elem!1, s(s(s(s(s(elem!1))))))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4772,plain,
% 1.64/1.88 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4771, 4715, 18, 4749, 4695, 3, 2130, 4741])).
% 1.64/1.88 tff(4773,plain,
% 1.64/1.88 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1225, 4772, 4738])).
% 1.64/1.88 tff(4774,plain,
% 1.64/1.88 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3338, 4773, 4735])).
% 1.64/1.88 tff(4775,plain,
% 1.64/1.88 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1209, 4774, 4727])).
% 1.64/1.88 tff(4776,plain,
% 1.64/1.88 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4775, 4721])).
% 1.64/1.88 tff(4777,plain,
% 1.64/1.88 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4720])).
% 1.64/1.88 tff(4778,plain,
% 1.64/1.88 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4777, 1113])).
% 1.64/1.88 tff(4779,plain,
% 1.64/1.88 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4778])).
% 1.64/1.88 tff(4780,plain,
% 1.64/1.88 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4779])).
% 1.64/1.88 tff(4781,plain,
% 1.64/1.88 (~(elem!1 = s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1124, 4780])).
% 1.64/1.88 tff(4782,plain,
% 1.64/1.88 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4720])).
% 1.64/1.88 tff(4783,plain,
% 1.64/1.88 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4782, 775])).
% 1.64/1.88 tff(4784,plain,
% 1.64/1.88 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4783])).
% 1.64/1.88 tff(4785,plain,
% 1.64/1.88 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4784])).
% 1.64/1.88 tff(4786,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1041, 4785])).
% 1.64/1.88 tff(4787,plain,
% 1.64/1.88 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4715])).
% 1.64/1.88 tff(4788,plain,
% 1.64/1.88 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[4787])).
% 1.64/1.88 tff(4789,plain,
% 1.64/1.88 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4735, 4788])).
% 1.64/1.88 tff(4790,plain,
% 1.64/1.88 ((~b(elem!1, s(s(s(s(s(elem!1))))))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4457])).
% 1.64/1.88 tff(4791,plain,
% 1.64/1.88 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2265, 4790])).
% 1.64/1.88 tff(4792,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.64/1.88 tff(4793,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4792, 4791])).
% 1.64/1.88 tff(4794,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))) | b(elem!1, s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4795,plain,
% 1.64/1.88 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4794, 4772, 4715])).
% 1.64/1.88 tff(4796,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.64/1.88 tff(4797,plain,
% 1.64/1.88 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(elem!1)))),
% 1.64/1.88 inference(symmetry,[status(thm)],[3089])).
% 1.64/1.88 tff(4798,plain,
% 1.64/1.88 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(commutativity,[status(thm)],[])).
% 1.64/1.88 tff(4799,plain,
% 1.64/1.88 (s(s(s(elem!1))) = elem!1),
% 1.64/1.88 inference(transitivity,[status(thm)],[132, 1092, 247])).
% 1.64/1.88 tff(4800,plain,
% 1.64/1.88 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4799])).
% 1.64/1.88 tff(4801,plain,
% 1.64/1.88 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4800, 4798])).
% 1.64/1.88 tff(4802,plain,
% 1.64/1.88 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4801, 4797])).
% 1.64/1.88 tff(4803,plain,
% 1.64/1.88 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4802])).
% 1.64/1.88 tff(4804,plain,
% 1.64/1.88 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[899, 4803])).
% 1.64/1.88 tff(4805,plain,
% 1.64/1.88 (r(elem!1, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1539, 4804, 4796])).
% 1.64/1.88 tff(4806,plain,
% 1.64/1.88 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(commutativity,[status(thm)],[])).
% 1.64/1.88 tff(4807,plain,
% 1.64/1.88 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.88 inference(symmetry,[status(thm)],[4806])).
% 1.64/1.88 tff(4808,plain,
% 1.64/1.88 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4799])).
% 1.64/1.88 tff(4809,plain,
% 1.64/1.88 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4808, 4806])).
% 1.64/1.88 tff(4810,plain,
% 1.64/1.88 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.88 inference(transitivity,[status(thm)],[4809, 4807])).
% 1.64/1.88 tff(4811,plain,
% 1.64/1.88 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4810])).
% 1.64/1.88 tff(4812,plain,
% 1.64/1.88 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[265, 4811])).
% 1.64/1.88 tff(4813,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.64/1.88 tff(4814,plain,
% 1.64/1.88 (((~![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))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4815,plain,
% 1.64/1.88 ((~![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))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4816,plain,
% 1.64/1.88 ((~![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)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 1.64/1.88 tff(4817,plain,
% 1.64/1.88 ((s(s(s(s(elem!1)))) = elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4816, 78, 4813])).
% 1.64/1.88 tff(4818,plain,
% 1.64/1.88 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4817, 4812])).
% 1.64/1.88 tff(4819,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.64/1.88 tff(4820,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.64/1.88 tff(4821,plain,
% 1.64/1.88 (((~![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(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4822,plain,
% 1.64/1.88 (((~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(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)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4823,plain,
% 1.64/1.88 (((~![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(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))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4822])).
% 1.64/1.88 tff(4824,plain,
% 1.64/1.88 (((~![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(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)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4823, 4821])).
% 1.64/1.88 tff(4825,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(4826,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 1.64/1.88 tff(4827,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4826, 31, 4820, 3418, 4819])).
% 1.64/1.88 tff(4828,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4829,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4828, 4818, 4805, 3418])).
% 1.64/1.88 tff(4830,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | b(s(s(s(s(elem!1)))), elem!1) | b(elem!1, s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(4831,plain,
% 1.64/1.88 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4830, 4795, 889, 4715, 257, 4789])).
% 1.64/1.88 tff(4832,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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)))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4833,plain,
% 1.64/1.88 (((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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)))), elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(4834,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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)))), elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[4833])).
% 1.64/1.88 tff(4835,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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)))), elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[4834, 4832])).
% 1.64/1.88 tff(4836,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4837,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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)))), elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4836, 4835])).
% 1.64/1.89 tff(4838,plain,
% 1.64/1.89 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(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)))), elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4837, 112])).
% 1.64/1.89 tff(4839,plain,
% 1.64/1.89 (~b(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4838, 4775, 4285, 4831, 4699])).
% 1.64/1.89 tff(4840,plain,
% 1.64/1.89 (r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1498, 4839, 4786])).
% 1.64/1.89 tff(4841,plain,
% 1.64/1.89 (~r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1568, 4840, 3])).
% 1.64/1.89 tff(4842,plain,
% 1.64/1.89 (b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1139, 4841, 4781])).
% 1.64/1.89 tff(4843,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2249, 4842, 4715])).
% 1.64/1.89 tff(4844,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4845,plain,
% 1.64/1.89 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4846,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4845])).
% 1.64/1.89 tff(4847,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4846, 4844])).
% 1.64/1.89 tff(4848,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4849,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4848, 4847])).
% 1.64/1.89 tff(4850,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4849, 112, 4624, 4285, 4699, 4843, 4684, 4776])).
% 1.64/1.89 tff(4851,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4852,plain,
% 1.64/1.89 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4851, 464, 18, 3, 248])).
% 1.64/1.89 tff(4853,plain,
% 1.64/1.89 (~r(s(s(elem!1)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4537, 31, 20, 1953])).
% 1.64/1.89 tff(4854,plain,
% 1.64/1.89 (~r(s(z), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2569, 31, 85, 20])).
% 1.64/1.89 tff(4855,plain,
% 1.64/1.89 (b(s(z), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[608, 4854])).
% 1.64/1.89 tff(4856,plain,
% 1.64/1.89 (((~![X0: $i, 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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4857,plain,
% 1.64/1.89 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4858,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4857])).
% 1.64/1.89 tff(4859,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4858, 4856])).
% 1.64/1.89 tff(4860,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4861,plain,
% 1.64/1.89 ((~![X0: $i, 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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4860, 4859])).
% 1.64/1.89 tff(4862,plain,
% 1.64/1.89 (~r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4861, 31, 85, 1953])).
% 1.64/1.89 tff(4863,plain,
% 1.64/1.89 (b(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[857, 4862])).
% 1.64/1.89 tff(4864,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.64/1.89 tff(4865,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.89 tff(4866,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4867,plain,
% 1.64/1.89 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), 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)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4868,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4867])).
% 1.64/1.89 tff(4869,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4868, 4866])).
% 1.64/1.89 tff(4870,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4871,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4870, 4869])).
% 1.64/1.89 tff(4872,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4871, 112, 4865, 673, 1988, 4864])).
% 1.64/1.89 tff(4873,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4874,plain,
% 1.64/1.89 (~b(s(s(elem!1)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4873, 4863, 1969, 4855])).
% 1.64/1.89 tff(4875,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[822, 78, 379, 4874, 4853])).
% 1.64/1.89 tff(4876,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4877,plain,
% 1.64/1.89 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4876, 85, 20])).
% 1.64/1.89 tff(4878,assumption,(~r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.64/1.89 tff(4879,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1008, 78, 3138, 1392, 4878])).
% 1.64/1.89 tff(4880,plain,(b(s(s(elem!1)), s(s(s(z)))) | (s(s(elem!1)) = s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(4881,plain,
% 1.64/1.89 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4880, 4877, 3138])).
% 1.64/1.89 tff(4882,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4881])).
% 1.64/1.89 tff(4883,plain,
% 1.64/1.89 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4882])).
% 1.64/1.89 tff(4884,plain,
% 1.64/1.89 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4883])).
% 1.64/1.89 tff(4885,plain,
% 1.64/1.89 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4884])).
% 1.64/1.89 tff(4886,plain,
% 1.64/1.89 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4885])).
% 1.64/1.89 tff(4887,plain,
% 1.64/1.89 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[899, 4886])).
% 1.64/1.89 tff(4888,plain,
% 1.64/1.89 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4882])).
% 1.64/1.89 tff(4889,plain,
% 1.64/1.89 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4888])).
% 1.64/1.89 tff(4890,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4889])).
% 1.64/1.89 tff(4891,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4890])).
% 1.64/1.89 tff(4892,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[539, 4891])).
% 1.64/1.89 tff(4893,plain,
% 1.64/1.89 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4881])).
% 1.64/1.89 tff(4894,plain,
% 1.64/1.89 (s(elem!1) = s(s(z))),
% 1.64/1.89 inference(transitivity,[status(thm)],[145, 4893, 55])).
% 1.64/1.89 tff(4895,plain,
% 1.64/1.89 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4894])).
% 1.64/1.89 tff(4896,plain,
% 1.64/1.89 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4895])).
% 1.64/1.89 tff(4897,plain,
% 1.64/1.89 (s(z) = elem!1),
% 1.64/1.89 inference(transitivity,[status(thm)],[138, 4896, 247])).
% 1.64/1.89 tff(4898,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4897])).
% 1.64/1.89 tff(4899,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.89 inference(symmetry,[status(thm)],[4898])).
% 1.64/1.89 tff(4900,plain,
% 1.64/1.89 (elem!1 = s(z)),
% 1.64/1.89 inference(transitivity,[status(thm)],[1073, 4895, 137])).
% 1.64/1.89 tff(4901,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4889, 4900])).
% 1.64/1.89 tff(4902,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[4901])).
% 1.64/1.89 tff(4903,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[19, 4902])).
% 1.64/1.89 tff(4904,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4903, 4899])).
% 1.64/1.89 tff(4905,plain,
% 1.64/1.89 (~b(s(s(s(s(elem!1)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1835, 4855, 18, 19])).
% 1.64/1.89 tff(4906,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[398, 4905])).
% 1.64/1.89 tff(4907,plain,
% 1.64/1.89 (r(s(s(s(s(s(z))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1788, 4906, 4881])).
% 1.64/1.89 tff(4908,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.89 tff(4909,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.64/1.89 tff(4910,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4911,plain,
% 1.64/1.89 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(4912,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[4911])).
% 1.64/1.89 tff(4913,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[4912, 4910])).
% 1.64/1.89 tff(4914,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(4915,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[4914, 4913])).
% 1.64/1.89 tff(4916,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4915, 112, 18, 673, 906, 4909, 4908])).
% 1.64/1.89 tff(4917,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1781, 4916, 891, 265])).
% 1.64/1.89 tff(4918,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1800, 4917, 891, 1792])).
% 1.64/1.89 tff(4919,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[912, 112, 18, 673, 906])).
% 1.64/1.89 tff(4920,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[917, 78, 224, 4919, 4918])).
% 1.64/1.89 tff(4921,plain,((~b(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4922,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4921, 4881, 4907, 265, 18, 4855, 4904, 4892])).
% 1.74/1.90 tff(4923,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1733, 4922])).
% 1.74/1.90 tff(4924,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2372, 31, 464, 4923])).
% 1.74/1.90 tff(4925,plain,
% 1.74/1.90 ((s(s(s(s(s(elem!1))))) = s(s(s(s(z))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2376, 78, 4924])).
% 1.74/1.90 tff(4926,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4925, 4887])).
% 1.74/1.90 tff(4927,plain,
% 1.74/1.90 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4883])).
% 1.74/1.90 tff(4928,plain,
% 1.74/1.90 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4927, 900])).
% 1.74/1.90 tff(4929,plain,
% 1.74/1.90 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[4928])).
% 1.74/1.90 tff(4930,plain,
% 1.74/1.90 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4929])).
% 1.74/1.90 tff(4931,plain,
% 1.74/1.90 (~(s(s(s(s(z)))) = s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[899, 4930])).
% 1.74/1.90 tff(4932,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2384, 31, 464, 4923])).
% 1.74/1.90 tff(4933,plain,
% 1.74/1.90 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[936, 78, 4932])).
% 1.74/1.90 tff(4934,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4933, 4931])).
% 1.74/1.90 tff(4935,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4502, 31, 3, 4923])).
% 1.74/1.90 tff(4936,plain,
% 1.74/1.90 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4506, 78, 4935])).
% 1.74/1.90 tff(4937,plain,
% 1.74/1.90 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4936, 4496])).
% 1.74/1.90 tff(4938,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1728, 4923, 85])).
% 1.74/1.90 tff(4939,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1718, 4938])).
% 1.74/1.90 tff(4940,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4941,plain,
% 1.74/1.90 (((~b(s(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(z)))))) | (~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(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(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(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))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4942,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z)))))) | (~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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4941])).
% 1.74/1.90 tff(4943,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z)))))) | (~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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4942, 4940])).
% 1.74/1.90 tff(4944,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z)))))) | (~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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4945,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 1.74/1.90 tff(4946,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4945, 112, 3977, 4939, 4937, 4934, 4926])).
% 1.74/1.90 tff(4947,plain,((~r(s(z), s(s(s(z))))) | (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(s(z))), s(z))) | (s(s(s(s(elem!1)))) = 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))) | (~r(z, s(s(s(z))))) | b(s(s(elem!1)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4948,plain,
% 1.74/1.90 (~r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4947, 464, 889, 3, 257, 18, 4684, 4624, 4695, 4852])).
% 1.74/1.90 tff(4949,plain,
% 1.74/1.90 (b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[99, 4948])).
% 1.74/1.90 tff(4950,plain,
% 1.74/1.90 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), 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(z), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4951,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4950])).
% 1.74/1.90 tff(4952,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4951, 4590])).
% 1.74/1.90 tff(4953,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4954,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4953, 4952])).
% 1.74/1.90 tff(4955,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4954, 112, 4949, 4285, 4699, 4684])).
% 1.74/1.90 tff(4956,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4957,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4956, 18, 3, 248])).
% 1.74/1.90 tff(4958,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[462, 4957])).
% 1.74/1.90 tff(4959,plain,
% 1.74/1.90 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[39, 1, 3])).
% 1.74/1.90 tff(4960,plain,
% 1.74/1.90 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[477, 4959])).
% 1.74/1.90 tff(4961,plain,
% 1.74/1.90 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[547, 4960, 18, 19])).
% 1.74/1.90 tff(4962,plain,
% 1.74/1.90 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[356, 4961])).
% 1.74/1.90 tff(4963,plain,
% 1.74/1.90 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[783, 4962, 276])).
% 1.74/1.90 tff(4964,plain,
% 1.74/1.90 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[322, 4963])).
% 1.74/1.90 tff(4965,plain,
% 1.74/1.90 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4654, 4962, 19, 271, 443, 18])).
% 1.74/1.90 tff(4966,plain,
% 1.74/1.90 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[749, 4965])).
% 1.74/1.90 tff(4967,plain,
% 1.74/1.90 (~b(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[683, 4962, 276, 443, 18])).
% 1.74/1.90 tff(4968,plain,
% 1.74/1.90 (r(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[608, 4967])).
% 1.74/1.90 tff(4969,plain,
% 1.74/1.90 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3108, 4968, 4966])).
% 1.74/1.90 tff(4970,plain,
% 1.74/1.90 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[494, 4969])).
% 1.74/1.90 tff(4971,plain,
% 1.74/1.90 (~r(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[563, 31, 4962, 1])).
% 1.74/1.90 tff(4972,plain,
% 1.74/1.90 (b(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[527, 4971])).
% 1.74/1.90 tff(4973,plain,
% 1.74/1.90 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4042, 4972, 803, 4970])).
% 1.74/1.90 tff(4974,plain,
% 1.74/1.90 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[386, 4973])).
% 1.74/1.90 tff(4975,plain,
% 1.74/1.90 (~r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2676, 4974, 4966])).
% 1.74/1.90 tff(4976,plain,
% 1.74/1.90 (b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[99, 4975])).
% 1.74/1.90 tff(4977,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4978,plain,
% 1.74/1.90 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(4979,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[4978])).
% 1.74/1.90 tff(4980,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[4979, 4977])).
% 1.74/1.90 tff(4981,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(4982,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4981, 4980])).
% 1.74/1.90 tff(4983,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4982, 112, 4976, 803, 18, 443, 4964])).
% 1.74/1.90 tff(4984,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4985,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4984, 803, 18, 443, 276, 19, 271, 3])).
% 1.74/1.90 tff(4986,plain,
% 1.74/1.90 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[160, 4985])).
% 1.74/1.90 tff(4987,plain,
% 1.74/1.90 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4095, 4986, 18, 19, 803])).
% 1.74/1.90 tff(4988,plain,
% 1.74/1.90 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[356, 4987])).
% 1.74/1.90 tff(4989,plain,
% 1.74/1.90 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[783, 4988, 276])).
% 1.74/1.90 tff(4990,plain,
% 1.74/1.90 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[322, 4989])).
% 1.74/1.90 tff(4991,plain,
% 1.74/1.90 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4654, 4988, 19, 271, 443, 18])).
% 1.74/1.90 tff(4992,plain,
% 1.74/1.90 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[749, 4991])).
% 1.74/1.90 tff(4993,plain,
% 1.74/1.90 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4046, 4990, 18, 19, 276, 443, 803, 4986, 3])).
% 1.74/1.90 tff(4994,plain,
% 1.74/1.90 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[386, 4993])).
% 1.74/1.90 tff(4995,plain,
% 1.74/1.90 (~r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2676, 4994, 4992])).
% 1.74/1.90 tff(4996,plain,
% 1.74/1.90 (b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[99, 4995])).
% 1.74/1.90 tff(4997,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4982, 112, 4996, 803, 18, 443, 4990])).
% 1.74/1.90 tff(4998,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), 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(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(4999,plain,
% 1.74/1.90 (~b(z, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4998, 18, 4958, 4624, 4682, 3, 268])).
% 1.74/1.90 tff(5000,plain,
% 1.74/1.90 (r(z, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[515, 4999])).
% 1.74/1.90 tff(5001,plain,
% 1.74/1.90 (~b(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1835, 1827, 18, 19])).
% 1.74/1.90 tff(5002,plain,
% 1.74/1.90 (r(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[608, 5001])).
% 1.74/1.90 tff(5003,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5004,plain,
% 1.74/1.90 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), 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)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5005,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5004])).
% 1.74/1.90 tff(5006,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5005, 5003])).
% 1.74/1.91 tff(5007,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(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(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5008,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5007, 5006])).
% 1.74/1.91 tff(5009,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5008, 112, 102, 18, 19, 4, 1827])).
% 1.74/1.91 tff(5010,plain,((~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)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5011,plain,
% 1.74/1.91 (~b(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5010, 1827, 19, 4, 18])).
% 1.74/1.91 tff(5012,plain,
% 1.74/1.91 (r(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[99, 5011])).
% 1.74/1.91 tff(5013,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2569, 31, 5012, 20, 5002])).
% 1.74/1.91 tff(5014,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(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(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5015,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5014, 5000, 4624, 4285, 18])).
% 1.74/1.91 tff(5016,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[398, 5015])).
% 1.74/1.91 tff(5017,plain,
% 1.74/1.91 (~r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2510, 21, 568])).
% 1.74/1.91 tff(5018,plain,
% 1.74/1.91 (b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[608, 5017])).
% 1.74/1.91 tff(5019,plain,
% 1.74/1.91 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4599, 21, 276])).
% 1.74/1.91 tff(5020,plain,
% 1.74/1.91 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[749, 5019])).
% 1.74/1.91 tff(5021,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), 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(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5022,plain,
% 1.74/1.91 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), 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(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5023,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), 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(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5022])).
% 1.74/1.91 tff(5024,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), 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(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5023, 5021])).
% 1.74/1.91 tff(5025,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(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(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5026,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), 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(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.74/1.91 tff(5027,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5026, 112, 18, 19, 443, 5020, 5018])).
% 1.74/1.91 tff(5028,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[299, 5027, 271])).
% 1.74/1.91 tff(5029,plain,
% 1.74/1.91 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[759, 5020, 18, 443])).
% 1.74/1.91 tff(5030,plain,
% 1.74/1.91 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[322, 5029])).
% 1.74/1.91 tff(5031,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), 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(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5032,plain,
% 1.74/1.91 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5033,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5032])).
% 1.74/1.91 tff(5034,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5033, 5031])).
% 1.74/1.91 tff(5035,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5036,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5035, 5034])).
% 1.74/1.91 tff(5037,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5036, 31, 20, 5030, 568, 5028])).
% 1.74/1.91 tff(5038,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(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(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5039,plain,
% 1.74/1.91 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5038, 5000, 5016, 268, 18, 4624, 4958, 4682])).
% 1.74/1.91 tff(5040,plain,
% 1.74/1.91 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[477, 5039])).
% 1.74/1.91 tff(5041,plain,
% 1.74/1.91 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[547, 5040, 18, 4624])).
% 1.74/1.91 tff(5042,plain,
% 1.74/1.91 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[356, 5041])).
% 1.74/1.91 tff(5043,plain,
% 1.74/1.91 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4654, 5042, 4624, 268, 4958, 18])).
% 1.74/1.91 tff(5044,plain,
% 1.74/1.91 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[749, 5043])).
% 1.74/1.91 tff(5045,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[739, 5044, 3])).
% 1.74/1.91 tff(5046,plain,
% 1.74/1.91 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2752, 5045])).
% 1.74/1.91 tff(5047,plain,
% 1.74/1.91 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4074, 5016, 4682])).
% 1.74/1.91 tff(5048,plain,
% 1.74/1.91 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[494, 5047])).
% 1.74/1.91 tff(5049,plain,
% 1.74/1.91 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[783, 5042, 4682])).
% 1.74/1.91 tff(5050,plain,
% 1.74/1.91 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[322, 5049])).
% 1.74/1.91 tff(5051,plain,
% 1.74/1.91 (~b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[683, 5042, 4682, 4958, 18])).
% 1.74/1.91 tff(5052,plain,
% 1.74/1.91 (r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[608, 5051])).
% 1.74/1.91 tff(5053,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3989, 31, 612, 3, 592])).
% 1.74/1.91 tff(5054,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5055,plain,
% 1.74/1.91 (~r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5054, 5052, 3])).
% 1.74/1.91 tff(5056,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[527, 5055])).
% 1.74/1.91 tff(5057,plain,
% 1.74/1.91 (((~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(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5058,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5057])).
% 1.74/1.91 tff(5059,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5058, 2622])).
% 1.74/1.91 tff(5060,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5061,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5060, 5059])).
% 1.74/1.91 tff(5062,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5061, 112, 5056, 5050, 5048, 5046])).
% 1.74/1.91 tff(5063,plain,((~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5064,plain,
% 1.74/1.91 (~b(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5063, 3, 248])).
% 1.74/1.91 tff(5065,plain,
% 1.74/1.91 (r(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[182, 5064])).
% 1.74/1.91 tff(5066,plain,
% 1.74/1.91 (~r(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[503, 5065, 3])).
% 1.74/1.91 tff(5067,plain,
% 1.74/1.91 (b(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[515, 5066])).
% 1.74/1.91 tff(5068,plain,
% 1.74/1.91 (~r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3275, 5065, 3])).
% 1.74/1.91 tff(5069,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[527, 5068])).
% 1.74/1.91 tff(5070,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4333, 5067, 4285, 5069])).
% 1.74/1.91 tff(5071,plain,
% 1.74/1.91 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[398, 5070])).
% 1.74/1.91 tff(5072,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5073,plain,
% 1.74/1.91 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(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)))))) <=> ((~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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(5074,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5073])).
% 1.74/1.91 tff(5075,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[5074, 5072])).
% 1.74/1.91 tff(5076,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(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))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(5077,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[5076, 5075])).
% 1.74/1.91 tff(5078,plain,
% 1.74/1.91 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5077, 112, 859, 516, 4, 196])).
% 1.74/1.91 tff(5079,plain,
% 1.74/1.91 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[356, 5078])).
% 1.74/1.91 tff(5080,plain,
% 1.74/1.91 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[589, 5079, 162])).
% 1.74/1.91 tff(5081,plain,
% 1.74/1.91 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[429, 5080])).
% 1.74/1.91 tff(5082,plain,
% 1.74/1.91 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[451, 5081, 442, 3320])).
% 1.74/1.91 tff(5083,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4239, 31, 162, 5079, 5082])).
% 1.74/1.91 tff(5084,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), 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(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(5085,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5084, 442, 4, 3, 162, 3286])).
% 1.74/1.91 tff(5086,plain,
% 1.74/1.91 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4333, 516, 4, 3286])).
% 1.74/1.92 tff(5087,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[398, 5086])).
% 1.74/1.92 tff(5088,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1822, 31, 162, 408, 568])).
% 1.74/1.92 tff(5089,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5090,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5089, 162, 5087])).
% 1.74/1.92 tff(5091,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[429, 5090])).
% 1.74/1.92 tff(5092,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[451, 442, 5091, 3320])).
% 1.74/1.92 tff(5093,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[39, 5092, 3])).
% 1.74/1.92 tff(5094,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[160, 5093, 5085])).
% 1.74/1.92 tff(5095,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5096,plain,
% 1.74/1.92 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5095, 3, 4285, 5065])).
% 1.74/1.92 tff(5097,plain,
% 1.74/1.92 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[404, 5096, 274])).
% 1.74/1.92 tff(5098,plain,
% 1.74/1.92 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4074, 5097, 5071])).
% 1.74/1.92 tff(5099,plain,
% 1.74/1.92 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[494, 5098])).
% 1.74/1.92 tff(5100,plain,
% 1.74/1.92 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4042, 5099, 5069, 5067])).
% 1.74/1.92 tff(5101,plain,
% 1.74/1.92 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[386, 5100])).
% 1.74/1.92 tff(5102,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~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))))) | (~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(z))) | (~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))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5103,plain,
% 1.74/1.92 (((~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(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~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))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5104,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(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(z))) | (~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))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5103])).
% 1.74/1.92 tff(5105,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(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(z))) | (~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))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5104, 5102])).
% 1.74/1.92 tff(5106,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5107,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5106, 5105])).
% 1.74/1.92 tff(5108,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5107, 31, 3, 276, 1, 275])).
% 1.74/1.92 tff(5109,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5110,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5109, 3, 5097, 5101])).
% 1.74/1.92 tff(5111,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[160, 5110])).
% 1.74/1.92 tff(5112,plain,
% 1.74/1.92 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5077, 112, 5069, 5067, 4285, 5111])).
% 1.74/1.92 tff(5113,plain,
% 1.74/1.92 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[356, 5112])).
% 1.74/1.92 tff(5114,plain,
% 1.74/1.92 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4259, 5113, 5065])).
% 1.74/1.92 tff(5115,plain,
% 1.74/1.92 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[477, 5114])).
% 1.74/1.92 tff(5116,plain,
% 1.74/1.92 (~b(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4954, 112, 4285, 5111, 5115])).
% 1.74/1.92 tff(5117,plain,
% 1.74/1.92 (r(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[99, 5116])).
% 1.74/1.92 tff(5118,plain,
% 1.74/1.92 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[783, 5113, 5097])).
% 1.74/1.92 tff(5119,plain,
% 1.74/1.92 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[322, 5118])).
% 1.74/1.92 tff(5120,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5061, 112, 5069, 5119, 5099])).
% 1.74/1.92 tff(5121,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2752, 5120])).
% 1.74/1.92 tff(5122,plain,
% 1.74/1.92 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[739, 5121, 3])).
% 1.74/1.92 tff(5123,plain,
% 1.74/1.92 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[749, 5122])).
% 1.74/1.92 tff(5124,plain,
% 1.74/1.92 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[536, 5065, 3])).
% 1.74/1.92 tff(5125,plain,
% 1.74/1.92 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[462, 5124])).
% 1.74/1.92 tff(5126,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5089, 5065, 5071])).
% 1.74/1.92 tff(5127,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[429, 5126])).
% 1.74/1.92 tff(5128,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5129,plain,
% 1.74/1.92 (((~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(z))) | (~b(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5130,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5129])).
% 1.74/1.92 tff(5131,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5130, 5128])).
% 1.74/1.92 tff(5132,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5133,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5132, 5131])).
% 1.74/1.92 tff(5134,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5133, 112, 19, 443, 751, 333, 441])).
% 1.74/1.92 tff(5135,plain,((~b(s(z), 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(elem!1)))), s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5136,plain,
% 1.74/1.92 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5135, 5123, 5127, 5125, 5114])).
% 1.74/1.92 tff(5137,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[299, 5136, 268])).
% 1.74/1.92 tff(5138,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3469, 5067, 3, 5065, 5069])).
% 1.74/1.92 tff(5139,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1733, 5138])).
% 1.74/1.92 tff(5140,plain,
% 1.74/1.92 (r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3452, 891, 1887])).
% 1.74/1.92 tff(5141,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1735])).
% 1.74/1.92 tff(5142,plain,
% 1.74/1.92 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[19, 5141])).
% 1.74/1.92 tff(5143,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3511, 112, 443, 751, 906, 5142, 1739])).
% 1.74/1.92 tff(5144,plain,
% 1.74/1.92 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1778, 78, 5143])).
% 1.74/1.92 tff(5145,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5144, 1774])).
% 1.74/1.92 tff(5146,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3480, 112, 443, 751, 906])).
% 1.74/1.92 tff(5147,plain,
% 1.74/1.92 ((s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[936, 78, 5146])).
% 1.74/1.92 tff(5148,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5147, 905])).
% 1.74/1.92 tff(5149,plain,
% 1.74/1.92 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1788, 891, 568])).
% 1.74/1.92 tff(5150,plain,
% 1.74/1.92 (((~![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(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(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(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5151,plain,
% 1.74/1.92 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5152,plain,
% 1.74/1.92 (((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5151])).
% 1.74/1.92 tff(5153,plain,
% 1.74/1.92 (((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~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)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5152, 5150])).
% 1.74/1.92 tff(5154,plain,
% 1.74/1.92 ((~![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(s(z))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5155,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5154, 5153])).
% 1.74/1.92 tff(5156,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5155, 31, 5149, 5148, 5145, 5140])).
% 1.74/1.92 tff(5157,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = 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(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(5158,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5157, 5125, 889, 257, 5123, 5139, 5115, 5127, 5071, 5137])).
% 1.74/1.92 tff(5159,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(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))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5160,plain,
% 1.74/1.92 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), 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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(5161,plain,
% 1.74/1.92 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(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)), 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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5160])).
% 1.74/1.92 tff(5162,plain,
% 1.74/1.92 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(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)), 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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[5161, 5159])).
% 1.74/1.92 tff(5163,plain,
% 1.74/1.92 ((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(5164,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), 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(s(elem!1))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[5163, 5162])).
% 1.74/1.92 tff(5165,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5164, 31, 276, 275, 1953])).
% 1.74/1.92 tff(5166,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1025, 5165, 3141])).
% 1.74/1.92 tff(5167,plain,
% 1.74/1.92 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2066, 2811, 3347])).
% 1.74/1.92 tff(5168,plain,
% 1.74/1.92 (((~![X0: $i, 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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5169,plain,
% 1.74/1.93 (((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5170,plain,
% 1.74/1.93 (((~![X0: $i, 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(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~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(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5169])).
% 1.74/1.93 tff(5171,plain,
% 1.74/1.93 (((~![X0: $i, 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(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~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(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5170, 5168])).
% 1.74/1.93 tff(5172,plain,
% 1.74/1.93 ((~![X0: $i, 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(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5173,plain,
% 1.74/1.93 ((~![X0: $i, 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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5172, 5171])).
% 1.74/1.93 tff(5174,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5173, 31, 85, 1953])).
% 1.74/1.93 tff(5175,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1435, 78, 5174, 1421])).
% 1.74/1.93 tff(5176,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(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(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5177,plain,
% 1.74/1.93 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(z))) | (~b(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(s(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(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5178,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(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(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5177])).
% 1.74/1.93 tff(5179,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(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(elem!1)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5178, 5176])).
% 1.74/1.93 tff(5180,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5181,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5180, 5179])).
% 1.74/1.93 tff(5182,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5181, 112, 5175, 4863, 5167, 5166, 751])).
% 1.74/1.93 tff(5183,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = 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(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5184,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5183, 3141, 751, 276, 275, 85])).
% 1.74/1.93 tff(5185,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4880, 5184, 1392])).
% 1.74/1.93 tff(5186,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4547, 31, 812, 276])).
% 1.74/1.93 tff(5187,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1025, 5186, 3141])).
% 1.74/1.93 tff(5188,plain,
% 1.74/1.93 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[4556, 31, 812, 276])).
% 1.74/1.93 tff(5189,plain,
% 1.74/1.93 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2066, 5188, 3347])).
% 1.74/1.93 tff(5190,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5191,plain,
% 1.74/1.93 (((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5192,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5191])).
% 1.74/1.93 tff(5193,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5192, 5190])).
% 1.74/1.93 tff(5194,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5195,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5194, 5193])).
% 1.74/1.93 tff(5196,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5195, 112, 4297, 5189, 5187, 2604, 842])).
% 1.74/1.93 tff(5197,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5198,plain,
% 1.74/1.93 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5197, 3141, 2604, 276, 569])).
% 1.74/1.93 tff(5199,plain,
% 1.74/1.93 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[872, 5198, 248])).
% 1.74/1.93 tff(5200,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1004, 112, 5199, 4285, 5185, 196])).
% 1.74/1.93 tff(5201,plain,((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = 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(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5202,plain,
% 1.74/1.93 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5201, 5111, 248, 5099, 5097, 5113, 5158, 5123, 5101, 5117])).
% 1.74/1.93 tff(5203,plain,
% 1.74/1.93 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5202])).
% 1.74/1.93 tff(5204,plain,
% 1.74/1.93 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5203])).
% 1.74/1.93 tff(5205,plain,
% 1.74/1.93 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1193, 5204])).
% 1.74/1.93 tff(5206,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5202])).
% 1.74/1.93 tff(5207,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5206])).
% 1.74/1.93 tff(5208,plain,
% 1.74/1.93 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5137, 5207])).
% 1.74/1.93 tff(5209,plain,
% 1.74/1.93 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5202])).
% 1.74/1.93 tff(5210,plain,
% 1.74/1.93 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[145, 5209, 262])).
% 1.74/1.93 tff(5211,plain,
% 1.74/1.93 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5210])).
% 1.74/1.93 tff(5212,plain,
% 1.74/1.93 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5211])).
% 1.74/1.93 tff(5213,plain,
% 1.74/1.93 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5202])).
% 1.74/1.93 tff(5214,plain,
% 1.74/1.93 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[5213])).
% 1.74/1.93 tff(5215,plain,
% 1.74/1.93 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.74/1.93 inference(transitivity,[status(thm)],[5214, 132, 5212, 247])).
% 1.74/1.93 tff(5216,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5215])).
% 1.74/1.93 tff(5217,plain,
% 1.74/1.93 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) <=> (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5216])).
% 1.74/1.93 tff(5218,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5219,plain,
% 1.74/1.93 (((~b(z, s(s(s(s(s(elem!1))))))) | (~b(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))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5220,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(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))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5219])).
% 1.74/1.93 tff(5221,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(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))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[5220, 5218])).
% 1.74/1.93 tff(5222,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(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))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(5223,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5222, 5221])).
% 1.74/1.93 tff(5224,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5223, 112, 334, 751, 2604, 673])).
% 1.74/1.93 tff(5225,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(5226,plain,
% 1.74/1.93 (~b(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5225, 751, 334, 2604])).
% 1.74/1.93 tff(5227,plain,
% 1.74/1.93 (r(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[608, 5226])).
% 1.74/1.93 tff(5228,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.93 tff(5229,plain,
% 1.74/1.93 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3850, 112, 334, 2604])).
% 1.74/1.93 tff(5230,plain,
% 1.74/1.93 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5229, 5228])).
% 1.74/1.93 tff(5231,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5232,plain,
% 1.74/1.93 (((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(5233,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5232])).
% 1.74/1.93 tff(5234,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5233, 5231])).
% 1.74/1.94 tff(5235,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5236,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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))))), z)) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5235, 5234])).
% 1.74/1.94 tff(5237,plain,
% 1.74/1.94 ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5236, 112, 443, 334, 751, 2604])).
% 1.74/1.94 tff(5238,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5237, 5228])).
% 1.74/1.94 tff(5239,assumption,(~b(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 1.74/1.94 tff(5240,plain,
% 1.74/1.94 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 5239])).
% 1.74/1.94 tff(5241,plain,
% 1.74/1.94 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.74/1.94 inference(symmetry,[status(thm)],[1113])).
% 1.74/1.94 tff(5242,plain,
% 1.74/1.94 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(z)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5241])).
% 1.74/1.94 tff(5243,plain,
% 1.74/1.94 (~(s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1124, 5242])).
% 1.74/1.94 tff(5244,plain,
% 1.74/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5245,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5246,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5245, 5244])).
% 1.74/1.94 tff(5247,plain,
% 1.74/1.94 ((s(s(s(s(s(s(elem!1)))))) = s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5246, 78, 2247])).
% 1.74/1.94 tff(5248,plain,
% 1.74/1.94 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5247, 5243])).
% 1.74/1.94 tff(5249,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(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(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5250,plain,
% 1.74/1.94 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5251,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5250])).
% 1.74/1.94 tff(5252,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5251, 5249])).
% 1.74/1.94 tff(5253,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5254,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5253, 5252])).
% 1.74/1.94 tff(5255,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5254, 31, 85, 592, 5248, 5240])).
% 1.74/1.94 tff(5256,plain,(b(s(s(s(s(s(s(elem!1)))))), z) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | b(s(s(s(s(s(s(elem!1)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5257,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5256, 5238, 5230, 5227, 85])).
% 1.74/1.94 tff(5258,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(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))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5259,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5258, 5117, 5125, 5119, 5123, 5099])).
% 1.74/1.94 tff(5260,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5259, 5217])).
% 1.74/1.94 tff(5261,assumption,(~(elem!1 = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.94 tff(5262,plain,
% 1.74/1.94 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1225, 2265, 5261])).
% 1.74/1.94 tff(5263,plain,
% 1.74/1.94 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3338, 5262, 1887])).
% 1.74/1.94 tff(5264,plain,
% 1.74/1.94 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1209, 5263, 3069])).
% 1.74/1.94 tff(5265,plain,
% 1.74/1.94 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5264, 3282])).
% 1.74/1.94 tff(5266,plain,
% 1.74/1.94 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4794, 2265, 1068])).
% 1.74/1.94 tff(5267,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4830, 5266, 899, 1068, 265, 3418])).
% 1.74/1.94 tff(5268,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4838, 5264, 4, 5267, 196])).
% 1.74/1.94 tff(5269,plain,
% 1.74/1.94 (r(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1498, 5268, 2234])).
% 1.74/1.94 tff(5270,plain,
% 1.74/1.94 (~r(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1568, 5269, 3])).
% 1.74/1.94 tff(5271,plain,
% 1.74/1.94 (b(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1139, 5270, 1125])).
% 1.74/1.94 tff(5272,plain,
% 1.74/1.94 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2249, 5271, 1068])).
% 1.74/1.94 tff(5273,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4849, 112, 19, 4, 196, 5272, 539, 5265])).
% 1.74/1.94 tff(5274,plain,(b(elem!1, s(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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))) | (elem!1 = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5275,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5274, 5260, 5208, 4285, 5111, 5115, 5127, 3, 889, 257, 5202, 5137, 5205])).
% 1.74/1.94 tff(5276,plain,((~r(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5277,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5276, 248])).
% 1.74/1.94 tff(5278,plain,
% 1.74/1.94 (b(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[83, 5277])).
% 1.74/1.94 tff(5279,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(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(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5280,plain,
% 1.74/1.94 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), 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(s(s(elem!1))))), s(s(s(z))))) | (~b(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(s(z))), s(z))) | (~b(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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5281,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5280])).
% 1.74/1.94 tff(5282,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5281, 5279])).
% 1.74/1.94 tff(5283,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(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(s(s(elem!1))))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5284,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(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(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5283, 5282])).
% 1.74/1.94 tff(5285,plain,
% 1.74/1.94 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5284, 112, 101, 4, 1913, 442])).
% 1.74/1.94 tff(5286,plain,
% 1.74/1.94 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[386, 5285])).
% 1.74/1.94 tff(5287,plain,
% 1.74/1.94 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5089, 162, 408])).
% 1.74/1.94 tff(5288,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[398, 5287])).
% 1.74/1.94 tff(5289,plain,
% 1.74/1.94 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2182, 112, 5288, 1899, 442])).
% 1.74/1.94 tff(5290,plain,
% 1.74/1.94 (r(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[494, 5289])).
% 1.74/1.94 tff(5291,plain,
% 1.74/1.94 (~b(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4333, 803, 4, 1827])).
% 1.74/1.94 tff(5292,plain,
% 1.74/1.94 (r(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[527, 5291])).
% 1.74/1.94 tff(5293,plain,
% 1.74/1.94 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3767, 5292, 162])).
% 1.74/1.94 tff(5294,plain,
% 1.74/1.94 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[322, 5293])).
% 1.74/1.94 tff(5295,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5296,plain,
% 1.74/1.94 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(z, s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(5297,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5296])).
% 1.74/1.94 tff(5298,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[5297, 5295])).
% 1.74/1.94 tff(5299,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), 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(z, s(s(s(s(s(elem!1))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(5300,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5299, 5298])).
% 1.74/1.94 tff(5301,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5300, 112, 803, 4, 2, 5294, 442])).
% 1.74/1.94 tff(5302,plain,((~b(z, s(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(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5303,plain,
% 1.74/1.94 (~b(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5302, 1899, 4, 442, 162, 5288])).
% 1.74/1.94 tff(5304,plain,
% 1.74/1.94 (r(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[515, 5303])).
% 1.74/1.94 tff(5305,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4341, 31, 5304, 5290, 5286])).
% 1.74/1.94 tff(5306,plain,((~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(5307,plain,
% 1.74/1.94 (~r(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5306, 408, 405, 5278, 4285, 268])).
% 1.74/1.94 tff(5308,plain,
% 1.74/1.94 (b(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[182, 5307])).
% 1.74/1.94 tff(5309,plain,
% 1.74/1.94 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2028, 731, 408])).
% 1.74/1.94 tff(5310,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[299, 5309, 268])).
% 1.74/1.94 tff(5311,plain,
% 1.74/1.94 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[299, 5309, 271])).
% 1.74/1.94 tff(5312,plain,
% 1.74/1.94 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1933, 162, 731])).
% 1.74/1.94 tff(5313,plain,
% 1.74/1.94 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[322, 5312])).
% 1.74/1.94 tff(5314,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[342, 5313, 1899, 301, 271, 5311])).
% 1.74/1.94 tff(5315,plain,((~r(z, s(z))) | r(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(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5316,plain,
% 1.74/1.95 (~r(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5315, 731, 268, 301, 408])).
% 1.74/1.95 tff(5317,plain,
% 1.74/1.95 (b(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[182, 5316])).
% 1.74/1.95 tff(5318,plain,
% 1.74/1.95 (~r(z, s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2718, 5317, 5278, 405, 5310, 1])).
% 1.74/1.95 tff(5319,plain,
% 1.74/1.95 (~r(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1911, 464, 408, 268])).
% 1.74/1.95 tff(5320,plain,
% 1.74/1.95 (b(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[182, 5319])).
% 1.74/1.95 tff(5321,plain,
% 1.74/1.95 (~r(z, s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2718, 5320, 5278, 405, 5310, 1])).
% 1.74/1.95 tff(5322,plain,
% 1.74/1.95 (b(z, s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[356, 5321])).
% 1.74/1.95 tff(5323,plain,
% 1.74/1.95 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[342, 5322, 301, 268, 5310])).
% 1.74/1.95 tff(5324,plain,
% 1.74/1.95 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[322, 5323])).
% 1.74/1.95 tff(5325,plain,
% 1.74/1.95 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3642, 464, 408, 268])).
% 1.74/1.95 tff(5326,plain,
% 1.74/1.95 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[477, 5325])).
% 1.74/1.95 tff(5327,plain,
% 1.74/1.95 (~r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[93, 5326, 1])).
% 1.74/1.95 tff(5328,plain,
% 1.74/1.95 (b(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[99, 5327])).
% 1.74/1.95 tff(5329,plain,
% 1.74/1.95 (~b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1867, 5328, 5278, 5320])).
% 1.74/1.95 tff(5330,plain,
% 1.74/1.95 (r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[515, 5329])).
% 1.74/1.95 tff(5331,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), 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(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5332,plain,
% 1.74/1.95 (((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5333,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(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(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5332])).
% 1.74/1.95 tff(5334,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(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(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5333, 5331])).
% 1.74/1.95 tff(5335,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5336,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5335, 5334])).
% 1.74/1.95 tff(5337,plain,
% 1.74/1.95 (~r(s(s(elem!1)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5336, 31, 20, 302, 1438])).
% 1.74/1.95 tff(5338,plain,
% 1.74/1.95 (~r(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1672, 302, 731])).
% 1.74/1.95 tff(5339,plain,
% 1.74/1.95 (b(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[608, 5338])).
% 1.74/1.95 tff(5340,plain,
% 1.74/1.95 (~r(z, s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3385, 31, 302, 1438])).
% 1.74/1.95 tff(5341,plain,
% 1.74/1.95 (b(z, s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[841, 5340])).
% 1.74/1.95 tff(5342,plain,
% 1.74/1.95 (((~![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(elem!1)))) | (~r(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5343,plain,
% 1.74/1.95 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(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(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5344,plain,
% 1.74/1.95 (((~![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)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5343])).
% 1.74/1.95 tff(5345,plain,
% 1.74/1.95 (((~![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)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5344, 5342])).
% 1.74/1.95 tff(5346,plain,
% 1.74/1.95 ((~![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)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(elem!1)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5347,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 1.74/1.95 tff(5348,plain,
% 1.74/1.95 (~r(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5347, 31, 1438, 731])).
% 1.74/1.95 tff(5349,plain,
% 1.74/1.95 (b(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[857, 5348])).
% 1.74/1.95 tff(5350,plain,
% 1.74/1.95 (~b(s(s(elem!1)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4873, 5349, 5341, 5339])).
% 1.74/1.95 tff(5351,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[822, 78, 379, 5350, 5337])).
% 1.74/1.95 tff(5352,plain,((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5353,plain,
% 1.74/1.95 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5352, 5330, 5324, 731])).
% 1.74/1.95 tff(5354,plain,
% 1.74/1.95 (~r(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1672, 5324, 731])).
% 1.74/1.95 tff(5355,plain,
% 1.74/1.95 (b(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[608, 5354])).
% 1.74/1.95 tff(5356,plain,
% 1.74/1.95 (b(s(s(elem!1)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[822, 78, 379, 4853])).
% 1.74/1.95 tff(5357,plain,
% 1.74/1.95 (~b(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4873, 1969, 673, 5356])).
% 1.74/1.95 tff(5358,plain,
% 1.74/1.95 (r(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[857, 5357])).
% 1.74/1.95 tff(5359,plain,
% 1.74/1.95 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[851, 5358, 21])).
% 1.74/1.95 tff(5360,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[872, 5359, 248])).
% 1.74/1.95 tff(5361,plain,
% 1.74/1.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1998, 5360, 2, 1969])).
% 1.74/1.95 tff(5362,plain,
% 1.74/1.95 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1986, 5361, 1975])).
% 1.74/1.95 tff(5363,plain,
% 1.74/1.95 (((~![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(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5364,plain,
% 1.74/1.95 (((~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(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)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5365,plain,
% 1.74/1.95 (((~![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(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(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))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5364])).
% 1.74/1.95 tff(5366,plain,
% 1.74/1.95 (((~![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(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(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)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5365, 5363])).
% 1.74/1.95 tff(5367,plain,
% 1.74/1.95 ((~![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(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))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5368,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 1.74/1.95 tff(5369,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5368, 31, 408, 5362, 5358])).
% 1.74/1.95 tff(5370,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5371,plain,
% 1.74/1.95 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5370, 5355, 408, 248, 5326, 5322, 5330])).
% 1.74/1.95 tff(5372,plain,
% 1.74/1.95 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[892])).
% 1.74/1.95 tff(5373,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.74/1.95 inference(symmetry,[status(thm)],[5372])).
% 1.74/1.95 tff(5374,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2335, 891, 333])).
% 1.74/1.95 tff(5375,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2396, 4484, 464, 265, 899, 891, 5374])).
% 1.74/1.95 tff(5376,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1733, 5375])).
% 1.74/1.95 tff(5377,plain,
% 1.74/1.95 (~r(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1911, 464, 408, 3064])).
% 1.74/1.95 tff(5378,plain,
% 1.74/1.95 (b(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[182, 5377])).
% 1.74/1.95 tff(5379,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2428, 112, 102, 101, 5378, 673, 5376])).
% 1.74/1.95 tff(5380,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[917, 78, 224, 5379])).
% 1.74/1.95 tff(5381,plain,
% 1.74/1.95 (r(s(s(s(elem!1))), z)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5380, 5373])).
% 1.74/1.95 tff(5382,plain,
% 1.74/1.95 (~b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1867, 102, 101, 5378])).
% 1.74/1.95 tff(5383,plain,
% 1.74/1.95 (r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[515, 5382])).
% 1.74/1.95 tff(5384,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2440, 5376, 101, 102])).
% 1.74/1.95 tff(5385,plain,
% 1.74/1.95 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2454, 5384, 891])).
% 1.74/1.95 tff(5386,plain,
% 1.74/1.95 (~r(s(s(s(elem!1))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2464, 5385, 5383])).
% 1.74/1.95 tff(5387,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5386, 5381])).
% 1.74/1.95 tff(5388,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5389,plain,
% 1.74/1.95 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5388, 5328, 5278, 5355, 464, 257, 889, 408, 5310])).
% 1.74/1.95 tff(5390,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4880, 5389, 5371])).
% 1.74/1.95 tff(5391,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.74/1.95 tff(5392,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3704, 112, 102, 101, 5391, 2130])).
% 1.74/1.95 tff(5393,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(5394,plain,
% 1.74/1.95 (~b(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5393, 5328, 5278, 5390])).
% 1.74/1.95 tff(5395,plain,
% 1.74/1.95 (r(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1435, 78, 5394, 1421])).
% 1.74/1.95 tff(5396,plain,
% 1.74/1.95 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2053, 31, 408, 5395])).
% 1.74/1.95 tff(5397,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[872, 5396, 248])).
% 1.74/1.95 tff(5398,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5399,plain,
% 1.74/1.95 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(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(z))))) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(5400,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5399])).
% 1.74/1.95 tff(5401,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5400, 5398])).
% 1.74/1.95 tff(5402,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(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))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(5403,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(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(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[5402, 5401])).
% 1.74/1.95 tff(5404,plain,
% 1.74/1.95 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5403, 112, 4285, 5390, 405])).
% 1.74/1.95 tff(5405,plain,
% 1.74/1.95 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5404, 5397])).
% 1.74/1.95 tff(5406,plain,
% 1.74/1.95 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1025, 5405, 5353])).
% 1.74/1.95 tff(5407,plain,
% 1.74/1.95 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5406])).
% 1.74/1.95 tff(5408,plain,
% 1.74/1.95 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5407])).
% 1.74/1.95 tff(5409,plain,
% 1.74/1.95 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5408])).
% 1.74/1.95 tff(5410,plain,
% 1.74/1.95 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5407])).
% 1.74/1.95 tff(5411,plain,
% 1.74/1.95 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5410, 775])).
% 1.74/1.95 tff(5412,plain,
% 1.74/1.95 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[5411])).
% 1.74/1.95 tff(5413,plain,
% 1.74/1.95 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5412])).
% 1.74/1.95 tff(5414,plain,
% 1.74/1.95 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1041, 5413])).
% 1.74/1.95 tff(5415,plain,
% 1.74/1.95 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.74/1.95 inference(symmetry,[status(thm)],[5407])).
% 1.74/1.95 tff(5416,plain,
% 1.74/1.95 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5415])).
% 1.74/1.95 tff(5417,plain,
% 1.74/1.95 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5416])).
% 1.74/1.95 tff(5418,plain,
% 1.74/1.95 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5406])).
% 1.74/1.95 tff(5419,plain,
% 1.74/1.95 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[145, 5418, 262])).
% 1.74/1.95 tff(5420,plain,
% 1.74/1.95 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5419])).
% 1.74/1.95 tff(5421,plain,
% 1.74/1.95 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1073, 5420, 131, 5407])).
% 1.74/1.95 tff(5422,plain,
% 1.74/1.95 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5421])).
% 1.74/1.95 tff(5423,plain,
% 1.74/1.95 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1073, 5420, 131])).
% 1.74/1.95 tff(5424,plain,
% 1.74/1.95 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5423])).
% 1.74/1.95 tff(5425,plain,
% 1.74/1.95 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[5424, 890])).
% 1.74/1.95 tff(5426,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[5425])).
% 1.74/1.95 tff(5427,plain,
% 1.74/1.95 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5426])).
% 1.74/1.95 tff(5428,plain,
% 1.74/1.95 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[257, 5427])).
% 1.74/1.95 tff(5429,plain,
% 1.74/1.95 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5406])).
% 1.74/1.95 tff(5430,plain,
% 1.74/1.95 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5429])).
% 1.74/1.95 tff(5431,plain,
% 1.74/1.95 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1193, 5430])).
% 1.74/1.95 tff(5432,plain,
% 1.74/1.95 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.74/1.95 inference(symmetry,[status(thm)],[5420])).
% 1.74/1.95 tff(5433,plain,
% 1.74/1.95 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.74/1.95 inference(transitivity,[status(thm)],[5415, 132, 5432, 247])).
% 1.74/1.95 tff(5434,plain,
% 1.74/1.95 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5433])).
% 1.74/1.95 tff(5435,plain,
% 1.74/1.95 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5434])).
% 1.74/1.95 tff(5436,plain,
% 1.74/1.95 (~b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1867, 102, 101, 18])).
% 1.74/1.95 tff(5437,plain,
% 1.74/1.95 (r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[515, 5436])).
% 1.74/1.95 tff(5438,plain,
% 1.74/1.95 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4442, 31, 5437, 302, 2136])).
% 1.74/1.95 tff(5439,plain,
% 1.74/1.95 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 5438])).
% 1.74/1.95 tff(5440,plain,
% 1.74/1.95 (~r(elem!1, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2145, 2136, 464, 1068])).
% 1.74/1.95 tff(5441,plain,
% 1.74/1.95 (b(elem!1, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1139, 5440, 1125])).
% 1.74/1.95 tff(5442,plain,
% 1.74/1.95 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2249, 5441, 1068])).
% 1.74/1.95 tff(5443,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5444,plain,
% 1.74/1.96 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5445,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5444])).
% 1.74/1.96 tff(5446,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5445, 5443])).
% 1.74/1.96 tff(5447,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5448,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5447, 5446])).
% 1.74/1.96 tff(5449,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5448, 112, 102, 101, 18, 5442, 673, 5439])).
% 1.74/1.96 tff(5450,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5451,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5450, 5328, 5278, 5320, 5355, 5406, 464, 5324])).
% 1.74/1.96 tff(5452,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5451, 5435])).
% 1.74/1.96 tff(5453,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1225, 5452, 5431])).
% 1.74/1.96 tff(5454,plain,
% 1.74/1.96 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1220, 5453, 268, 5310, 301])).
% 1.74/1.96 tff(5455,plain,
% 1.74/1.96 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1209, 5454, 5428])).
% 1.74/1.96 tff(5456,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5455, 5422])).
% 1.74/1.96 tff(5457,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5458,plain,
% 1.74/1.96 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5459,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5458])).
% 1.74/1.96 tff(5460,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5459, 5457])).
% 1.74/1.96 tff(5461,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5462,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5461, 5460])).
% 1.74/1.96 tff(5463,plain,
% 1.74/1.96 (~b(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5462, 112, 5328, 5278, 5320, 5355])).
% 1.74/1.96 tff(5464,plain,
% 1.74/1.96 (r(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[527, 5463])).
% 1.74/1.96 tff(5465,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5466,plain,
% 1.74/1.96 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5467,plain,
% 1.74/1.96 (((~![X0: $i, X3: $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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5466])).
% 1.74/1.96 tff(5468,plain,
% 1.74/1.96 (((~![X0: $i, X3: $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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5467, 5465])).
% 1.74/1.96 tff(5469,plain,
% 1.74/1.96 ((~![X0: $i, X3: $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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5470,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5469, 5468])).
% 1.74/1.96 tff(5471,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5470, 31, 5464, 5456, 1])).
% 1.74/1.96 tff(5472,plain,
% 1.74/1.96 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5471, 5417])).
% 1.74/1.96 tff(5473,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1243, 5472, 5414])).
% 1.74/1.96 tff(5474,plain,
% 1.74/1.96 (~b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2217, 5473, 5278, 5328])).
% 1.74/1.96 tff(5475,plain,
% 1.74/1.96 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5474, 5409])).
% 1.74/1.96 tff(5476,plain,
% 1.74/1.96 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5421])).
% 1.74/1.96 tff(5477,plain,
% 1.74/1.96 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5476, 1113])).
% 1.74/1.96 tff(5478,plain,
% 1.74/1.96 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.74/1.96 inference(symmetry,[status(thm)],[5477])).
% 1.74/1.96 tff(5479,plain,
% 1.74/1.96 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5478])).
% 1.74/1.96 tff(5480,plain,
% 1.74/1.96 (~(elem!1 = s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1124, 5479])).
% 1.74/1.96 tff(5481,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(elem!1, s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5433])).
% 1.74/1.96 tff(5482,plain,
% 1.74/1.96 ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) <=> (~r(elem!1, s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5481])).
% 1.74/1.96 tff(5483,plain,
% 1.74/1.96 (((~![X0: $i, 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(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5484,plain,
% 1.74/1.96 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(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(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5485,plain,
% 1.74/1.96 (((~![X0: $i, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(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), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5484])).
% 1.74/1.96 tff(5486,plain,
% 1.74/1.96 (((~![X0: $i, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(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), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[5485, 5483])).
% 1.74/1.96 tff(5487,plain,
% 1.74/1.96 ((~![X0: $i, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(5488,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5487, 5486])).
% 1.74/1.96 tff(5489,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5488, 31, 731, 5456, 5326])).
% 1.74/1.96 tff(5490,plain,
% 1.74/1.96 (~r(elem!1, s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[5489, 5482])).
% 1.74/1.96 tff(5491,plain,
% 1.74/1.96 (b(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1139, 5490, 5480])).
% 1.74/1.96 tff(5492,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2249, 5491, 5406])).
% 1.74/1.96 tff(5493,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5492, 5475])).
% 1.74/1.96 tff(5494,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5495,plain,
% 1.74/1.96 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5494, 731, 1, 301, 248, 408])).
% 1.74/1.96 tff(5496,plain,
% 1.74/1.96 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[462, 5495])).
% 1.74/1.96 tff(5497,plain,
% 1.74/1.96 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5284, 112, 5278, 4285, 5496, 405])).
% 1.74/1.96 tff(5498,plain,
% 1.74/1.96 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[386, 5497])).
% 1.74/1.96 tff(5499,plain,
% 1.74/1.96 (~r(s(z), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2676, 5498, 731])).
% 1.74/1.96 tff(5500,plain,
% 1.74/1.96 (b(s(z), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[99, 5499])).
% 1.74/1.96 tff(5501,plain,
% 1.74/1.96 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2030, 5317, 268, 5278, 408, 301, 5496, 5500])).
% 1.74/1.96 tff(5502,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[356, 5501, 5318])).
% 1.74/1.96 tff(5503,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5504,plain,
% 1.74/1.96 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5503, 408, 301, 400, 248])).
% 1.74/1.96 tff(5505,plain,
% 1.74/1.96 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[749, 5504])).
% 1.74/1.96 tff(5506,plain,
% 1.74/1.96 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[342, 334, 301, 271, 2])).
% 1.74/1.96 tff(5507,plain,
% 1.74/1.96 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[299, 5506, 271])).
% 1.74/1.96 tff(5508,plain,
% 1.74/1.96 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[759, 334, 751, 18])).
% 1.74/1.96 tff(5509,plain,
% 1.74/1.96 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[462, 5508])).
% 1.74/1.96 tff(5510,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1895, 5509, 5507, 408])).
% 1.74/1.96 tff(5511,plain,((~b(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(5512,plain,
% 1.74/1.96 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5511, 2, 268, 5505, 5308, 301, 408])).
% 1.74/1.96 tff(5513,plain,
% 1.74/1.96 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[322, 5512])).
% 1.74/1.96 tff(5514,plain,
% 1.74/1.96 (~r(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5306, 408, 442, 5278, 4285, 268])).
% 1.74/1.96 tff(5515,plain,
% 1.74/1.96 (b(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[182, 5514])).
% 1.74/1.96 tff(5516,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5517,plain,
% 1.74/1.96 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(5518,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5517])).
% 1.74/1.96 tff(5519,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5518, 5516])).
% 1.74/1.97 tff(5520,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5521,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5520, 5519])).
% 1.74/1.97 tff(5522,plain,
% 1.74/1.97 ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5521, 112, 5278, 5515, 4285])).
% 1.74/1.97 tff(5523,plain,
% 1.74/1.97 (~b(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5522, 2])).
% 1.74/1.97 tff(5524,plain,
% 1.74/1.97 (r(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[515, 5523])).
% 1.74/1.97 tff(5525,plain,
% 1.74/1.97 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[310, 302, 5524])).
% 1.74/1.97 tff(5526,plain,
% 1.74/1.97 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[386, 5525])).
% 1.74/1.97 tff(5527,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5284, 112, 101, 4, 443, 442, 762])).
% 1.74/1.97 tff(5528,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5529,plain,
% 1.74/1.97 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5528, 5526, 4285, 442, 5278])).
% 1.74/1.97 tff(5530,plain,
% 1.74/1.97 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[462, 5529])).
% 1.74/1.97 tff(5531,plain,
% 1.74/1.97 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3642, 5530, 408, 268])).
% 1.74/1.97 tff(5532,plain,
% 1.74/1.97 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[477, 5531])).
% 1.74/1.97 tff(5533,plain,
% 1.74/1.97 (~r(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[93, 5532, 400])).
% 1.74/1.97 tff(5534,plain,
% 1.74/1.97 (b(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[99, 5533])).
% 1.74/1.97 tff(5535,plain,
% 1.74/1.97 (((~![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(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(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5536,plain,
% 1.74/1.97 (((~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))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5537,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5536])).
% 1.74/1.97 tff(5538,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5537, 5535])).
% 1.74/1.97 tff(5539,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~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(z))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5540,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5539, 5538])).
% 1.74/1.97 tff(5541,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5540, 31, 20, 302, 730])).
% 1.74/1.97 tff(5542,plain,((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5543,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5542, 20, 302])).
% 1.74/1.97 tff(5544,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2752, 5543])).
% 1.74/1.97 tff(5545,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[891])).
% 1.74/1.97 tff(5546,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5545])).
% 1.74/1.97 tff(5547,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[406, 5546])).
% 1.74/1.97 tff(5548,assumption,(b(s(s(s(s(s(elem!1))))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.97 tff(5549,plain,
% 1.74/1.97 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[891])).
% 1.74/1.97 tff(5550,plain,
% 1.74/1.97 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5549])).
% 1.74/1.97 tff(5551,plain,
% 1.74/1.97 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4481])).
% 1.74/1.97 tff(5552,plain,
% 1.74/1.97 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5551])).
% 1.74/1.97 tff(5553,plain,
% 1.74/1.97 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5552, 5550])).
% 1.74/1.97 tff(5554,plain,
% 1.74/1.97 (b(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[102, 5553])).
% 1.74/1.97 tff(5555,plain,
% 1.74/1.97 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[4481])).
% 1.74/1.97 tff(5556,plain,
% 1.74/1.97 (b(s(z), s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5555])).
% 1.74/1.97 tff(5557,plain,
% 1.74/1.97 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[751, 5556])).
% 1.74/1.97 tff(5558,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5559,plain,
% 1.74/1.97 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(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)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5560,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5559])).
% 1.74/1.97 tff(5561,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(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(elem!1)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5560, 5558])).
% 1.74/1.97 tff(5562,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5563,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 1.74/1.97 tff(5564,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5563, 112, 4792, 1211, 5548, 3142])).
% 1.74/1.97 tff(5565,plain,((~b(s(s(elem!1)), s(s(s(s(s(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))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5566,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5565, 5557, 5554, 5548, 5547])).
% 1.74/1.97 tff(5567,plain,((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5568,plain,
% 1.74/1.97 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5567, 891, 751, 102, 5544])).
% 1.74/1.97 tff(5569,plain,
% 1.74/1.97 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[891])).
% 1.74/1.97 tff(5570,plain,
% 1.74/1.97 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5569])).
% 1.74/1.97 tff(5571,plain,
% 1.74/1.97 (r(z, s(s(elem!1)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[20, 5570])).
% 1.74/1.97 tff(5572,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[836, 5571])).
% 1.74/1.97 tff(5573,plain,((~(s(s(elem!1)) = s(s(s(z))))) | r(z, s(s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5574,plain,
% 1.74/1.97 (r(z, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5573, 891, 20])).
% 1.74/1.97 tff(5575,plain,
% 1.74/1.97 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3358, 5574, 302])).
% 1.74/1.97 tff(5576,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2066, 5575, 5568, 3349])).
% 1.74/1.97 tff(5577,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | (~r(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))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5578,plain,
% 1.74/1.97 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5577, 3347, 302, 751, 5534, 5524])).
% 1.74/1.97 tff(5579,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5542, 5524, 302])).
% 1.74/1.97 tff(5580,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2752, 5579])).
% 1.74/1.97 tff(5581,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5582,plain,
% 1.74/1.97 (((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5583,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5582])).
% 1.74/1.97 tff(5584,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5583, 5581])).
% 1.74/1.97 tff(5585,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5586,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5585, 5584])).
% 1.74/1.97 tff(5587,plain,
% 1.74/1.97 (~b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5586, 112, 5278, 5515, 751, 5580])).
% 1.74/1.97 tff(5588,plain,
% 1.74/1.97 (r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[527, 5587])).
% 1.74/1.97 tff(5589,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5590,plain,
% 1.74/1.97 (((~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(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(5591,plain,
% 1.74/1.97 (((~![X0: $i, 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(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5590])).
% 1.74/1.97 tff(5592,plain,
% 1.74/1.97 (((~![X0: $i, 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(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[5591, 5589])).
% 1.74/1.97 tff(5593,plain,
% 1.74/1.97 ((~![X0: $i, 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))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(5594,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[5593, 5592])).
% 1.74/1.97 tff(5595,plain,
% 1.74/1.97 (~r(s(s(elem!1)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5594, 31, 812, 21])).
% 1.74/1.97 tff(5596,plain,
% 1.74/1.97 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3861, 31, 612, 812, 1])).
% 1.74/1.97 tff(5597,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4880, 5596, 1392])).
% 1.74/1.97 tff(5598,plain,
% 1.74/1.97 (~b(s(s(elem!1)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5393, 5597, 101, 3530])).
% 1.74/1.97 tff(5599,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1435, 78, 5598, 5595, 1421])).
% 1.74/1.97 tff(5600,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5601,plain,
% 1.74/1.97 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5600, 5578, 5278, 5588, 400, 5532])).
% 1.74/1.97 tff(5602,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[872, 5601, 248])).
% 1.74/1.97 tff(5603,plain,
% 1.74/1.97 (~r(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3720, 5602, 155, 5278, 5588, 5534, 2])).
% 1.74/1.97 tff(5604,plain,
% 1.74/1.97 (b(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[608, 5603])).
% 1.74/1.97 tff(5605,plain,
% 1.74/1.97 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5370, 5604, 408, 248, 5532, 2, 5524])).
% 1.74/1.97 tff(5606,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4880, 5605, 5578])).
% 1.74/1.97 tff(5607,plain,
% 1.74/1.97 (~b(s(s(elem!1)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5393, 5606, 5278, 5534])).
% 1.74/1.97 tff(5608,plain,
% 1.74/1.97 (r(s(s(elem!1)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1435, 78, 5607, 1421])).
% 1.74/1.97 tff(5609,plain,
% 1.74/1.97 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1895, 5530, 408])).
% 1.74/1.97 tff(5610,plain,
% 1.74/1.97 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[299, 5609, 268])).
% 1.74/1.97 tff(5611,plain,
% 1.74/1.97 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1416, 112, 5602, 5610, 442])).
% 1.74/1.97 tff(5612,plain,
% 1.74/1.97 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1025, 5611, 3141])).
% 1.74/1.97 tff(5613,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1446, 5612, 5608, 5530])).
% 1.74/1.97 tff(5614,plain,((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)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(5615,plain,
% 1.74/1.97 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5614, 2, 408, 248, 405, 155, 5513, 5505])).
% 1.74/1.97 tff(5616,plain,
% 1.74/1.97 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5615])).
% 1.74/1.97 tff(5617,plain,
% 1.74/1.97 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5616])).
% 1.74/1.97 tff(5618,plain,
% 1.74/1.97 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[5617])).
% 1.74/1.97 tff(5619,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[5618])).
% 1.74/1.97 tff(5620,plain,
% 1.74/1.97 ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5521, 112, 5278, 5308, 4285])).
% 1.74/1.97 tff(5621,plain,
% 1.74/1.97 (~b(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5620, 2])).
% 1.74/1.97 tff(5622,plain,
% 1.74/1.97 (r(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[515, 5621])).
% 1.74/1.97 tff(5623,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5542, 5622, 5513])).
% 1.74/1.97 tff(5624,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2752, 5623])).
% 1.74/1.97 tff(5625,plain,
% 1.74/1.97 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[310, 5513, 5622])).
% 1.74/1.97 tff(5626,plain,
% 1.74/1.97 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[386, 5625])).
% 1.74/1.97 tff(5627,plain,
% 1.74/1.97 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5528, 5626, 4285, 405, 5278])).
% 1.74/1.97 tff(5628,plain,
% 1.74/1.97 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[462, 5627])).
% 1.74/1.97 tff(5629,plain,
% 1.74/1.97 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3642, 5628, 408, 268])).
% 1.74/1.97 tff(5630,plain,
% 1.74/1.97 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[477, 5629])).
% 1.74/1.97 tff(5631,plain,
% 1.74/1.97 (~r(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[93, 5630, 400])).
% 1.74/1.97 tff(5632,plain,
% 1.74/1.97 (b(s(z), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[99, 5631])).
% 1.74/1.97 tff(5633,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2252, 5615, 1193, 5278, 5626, 5632, 5628, 5624])).
% 1.74/1.98 tff(5634,plain,
% 1.74/1.98 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5633, 5619])).
% 1.74/1.98 tff(5635,plain,
% 1.74/1.98 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5615])).
% 1.74/1.98 tff(5636,plain,
% 1.74/1.98 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[145, 5635, 262])).
% 1.74/1.98 tff(5637,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5616, 5636])).
% 1.74/1.98 tff(5638,plain,
% 1.74/1.98 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5636])).
% 1.74/1.98 tff(5639,plain,
% 1.74/1.98 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5638, 890])).
% 1.74/1.98 tff(5640,plain,
% 1.74/1.98 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5639])).
% 1.74/1.98 tff(5641,plain,
% 1.74/1.98 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5640])).
% 1.74/1.98 tff(5642,plain,
% 1.74/1.98 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[257, 5641])).
% 1.74/1.98 tff(5643,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5636])).
% 1.74/1.98 tff(5644,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5643])).
% 1.74/1.98 tff(5645,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5617])).
% 1.74/1.98 tff(5646,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5645, 5644])).
% 1.74/1.98 tff(5647,plain,
% 1.74/1.98 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5646])).
% 1.74/1.98 tff(5648,plain,
% 1.74/1.98 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5617])).
% 1.74/1.98 tff(5649,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.98 inference(symmetry,[status(thm)],[5648])).
% 1.74/1.98 tff(5650,plain,
% 1.74/1.98 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5649])).
% 1.74/1.98 tff(5651,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2464, 5633, 5622])).
% 1.74/1.98 tff(5652,plain,
% 1.74/1.98 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5651, 5650])).
% 1.74/1.98 tff(5653,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 5652])).
% 1.74/1.98 tff(5654,plain,
% 1.74/1.98 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5636])).
% 1.74/1.98 tff(5655,plain,
% 1.74/1.98 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[1073, 5654, 131, 5616])).
% 1.74/1.98 tff(5656,plain,
% 1.74/1.98 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5655])).
% 1.74/1.98 tff(5657,plain,
% 1.74/1.98 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5656, 1113])).
% 1.74/1.98 tff(5658,plain,
% 1.74/1.98 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5657])).
% 1.74/1.98 tff(5659,plain,
% 1.74/1.98 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5658])).
% 1.74/1.98 tff(5660,plain,
% 1.74/1.98 (~(elem!1 = s(z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1124, 5659])).
% 1.74/1.98 tff(5661,plain,
% 1.74/1.98 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5617])).
% 1.74/1.98 tff(5662,plain,
% 1.74/1.98 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[5661])).
% 1.74/1.98 tff(5663,plain,
% 1.74/1.98 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5662])).
% 1.74/1.98 tff(5664,plain,
% 1.74/1.98 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[257, 5663])).
% 1.74/1.98 tff(5665,plain,
% 1.74/1.98 (b(z, elem!1) <=> b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5655])).
% 1.74/1.98 tff(5666,plain,
% 1.74/1.98 (~(z = elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1090, 5615])).
% 1.74/1.98 tff(5667,plain,
% 1.74/1.98 (r(z, elem!1) <=> r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5655])).
% 1.74/1.98 tff(5668,plain,
% 1.74/1.98 (r(z, s(s(s(s(s(s(elem!1))))))) <=> r(z, elem!1)),
% 1.74/1.98 inference(symmetry,[status(thm)],[5667])).
% 1.74/1.98 tff(5669,plain,
% 1.74/1.98 ((~r(z, s(s(s(s(s(s(elem!1)))))))) <=> (~r(z, elem!1))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5668])).
% 1.74/1.98 tff(5670,plain,
% 1.74/1.98 (((~![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(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5671,plain,
% 1.74/1.98 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5672,plain,
% 1.74/1.98 (((~![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(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5671])).
% 1.74/1.98 tff(5673,plain,
% 1.74/1.98 (((~![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(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5672, 5670])).
% 1.74/1.98 tff(5674,plain,
% 1.74/1.98 ((~![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(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5675,plain,
% 1.74/1.98 ((~![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(z))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5674, 5673])).
% 1.74/1.98 tff(5676,plain,
% 1.74/1.98 ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5675, 31, 5622])).
% 1.74/1.98 tff(5677,plain,
% 1.74/1.98 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5676, 5634])).
% 1.74/1.98 tff(5678,plain,
% 1.74/1.98 (~r(z, elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5677, 5669])).
% 1.74/1.98 tff(5679,plain,
% 1.74/1.98 (b(z, elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1109, 5678, 5666])).
% 1.74/1.98 tff(5680,plain,
% 1.74/1.98 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5679, 5665])).
% 1.74/1.98 tff(5681,plain,
% 1.74/1.98 (~b(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5586, 112, 5278, 5308, 5505, 5624])).
% 1.74/1.98 tff(5682,plain,
% 1.74/1.98 (r(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[527, 5681])).
% 1.74/1.98 tff(5683,plain,
% 1.74/1.98 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[693, 5682, 400])).
% 1.74/1.98 tff(5684,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[398, 5683])).
% 1.74/1.98 tff(5685,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5686,plain,
% 1.74/1.98 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5687,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5686])).
% 1.74/1.98 tff(5688,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5687, 5685])).
% 1.74/1.98 tff(5689,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5690,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5689, 5688])).
% 1.74/1.98 tff(5691,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5690, 112, 5684, 5680, 5653])).
% 1.74/1.98 tff(5692,plain,
% 1.74/1.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5693,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5694,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5693, 5692])).
% 1.74/1.98 tff(5695,plain,
% 1.74/1.98 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5694, 78, 5691])).
% 1.74/1.98 tff(5696,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5695, 5664])).
% 1.74/1.98 tff(5697,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.74/1.98 tff(5698,plain,
% 1.74/1.98 (((~![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(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, 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(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5699,plain,
% 1.74/1.98 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(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(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5700,plain,
% 1.74/1.98 (((~![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(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5699])).
% 1.74/1.98 tff(5701,plain,
% 1.74/1.98 (((~![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(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5700, 5698])).
% 1.74/1.98 tff(5702,plain,
% 1.74/1.98 ((~![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(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(5703,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[5702, 5701])).
% 1.74/1.98 tff(5704,plain,
% 1.74/1.98 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5703, 31, 408, 5697])).
% 1.74/1.98 tff(5705,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5704, 2135])).
% 1.74/1.98 tff(5706,plain,((~r(elem!1, s(z))) | (~(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(elem!1)))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(5707,plain,
% 1.74/1.98 (~r(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5706, 5615, 408, 5696])).
% 1.74/1.98 tff(5708,plain,
% 1.74/1.98 (b(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1139, 5707, 5660])).
% 1.74/1.98 tff(5709,plain,
% 1.74/1.98 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2249, 5708, 5615])).
% 1.74/1.98 tff(5710,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), 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(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5711,plain,
% 1.74/1.98 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), 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(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(5712,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5711])).
% 1.74/1.98 tff(5713,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), 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(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[5712, 5710])).
% 1.74/1.98 tff(5714,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5715,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5714, 5713])).
% 1.74/1.99 tff(5716,plain,
% 1.74/1.99 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5715, 112, 5278, 5308, 4285, 5684, 5709, 5653])).
% 1.74/1.99 tff(5717,plain,
% 1.74/1.99 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5716, 5647])).
% 1.74/1.99 tff(5718,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1166, 5717, 5642])).
% 1.74/1.99 tff(5719,plain,
% 1.74/1.99 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5718, 5637])).
% 1.74/1.99 tff(5720,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5470, 31, 5682, 5719, 400, 5634])).
% 1.74/1.99 tff(5721,plain,((~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5722,plain,
% 1.74/1.99 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5721, 408, 248, 155, 301])).
% 1.74/1.99 tff(5723,plain,
% 1.74/1.99 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[356, 5722])).
% 1.74/1.99 tff(5724,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2718, 5723, 5278, 405, 5308, 400])).
% 1.74/1.99 tff(5725,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[299, 5724, 268])).
% 1.74/1.99 tff(5726,plain,
% 1.74/1.99 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4008, 5725, 5723])).
% 1.74/1.99 tff(5727,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[322, 5726])).
% 1.74/1.99 tff(5728,plain,
% 1.74/1.99 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1895, 5725, 408])).
% 1.74/1.99 tff(5729,plain,
% 1.74/1.99 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[462, 5728])).
% 1.74/1.99 tff(5730,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[759, 5729, 5727, 5505, 5308])).
% 1.74/1.99 tff(5731,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5732,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5731, 155, 248, 301])).
% 1.74/1.99 tff(5733,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[429, 5732])).
% 1.74/1.99 tff(5734,plain,
% 1.74/1.99 (~b(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[120, 5733, 5278, 4285])).
% 1.74/1.99 tff(5735,plain,
% 1.74/1.99 (r(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[99, 5734])).
% 1.74/1.99 tff(5736,plain,
% 1.74/1.99 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[93, 5735, 400])).
% 1.74/1.99 tff(5737,plain,
% 1.74/1.99 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[477, 5736])).
% 1.74/1.99 tff(5738,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[451, 5736, 405, 5733])).
% 1.74/1.99 tff(5739,plain,
% 1.74/1.99 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[462, 5738])).
% 1.74/1.99 tff(5740,plain,
% 1.74/1.99 (~b(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[120, 19, 101, 4])).
% 1.74/1.99 tff(5741,plain,
% 1.74/1.99 (r(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[99, 5740])).
% 1.74/1.99 tff(5742,plain,
% 1.74/1.99 (~r(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[170, 162, 5741])).
% 1.74/1.99 tff(5743,plain,
% 1.74/1.99 (b(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[515, 5742])).
% 1.74/1.99 tff(5744,plain,
% 1.74/1.99 (((~![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(s(elem!1))))), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5745,plain,
% 1.74/1.99 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5746,plain,
% 1.74/1.99 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5745])).
% 1.74/1.99 tff(5747,plain,
% 1.74/1.99 (((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5746, 5744])).
% 1.74/1.99 tff(5748,plain,
% 1.74/1.99 ((~![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(s(elem!1))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5749,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 1.74/1.99 tff(5750,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5749, 31, 85, 464, 275])).
% 1.74/1.99 tff(5751,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5752,plain,
% 1.74/1.99 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5751, 464, 5741])).
% 1.74/1.99 tff(5753,plain,
% 1.74/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[386, 5752])).
% 1.74/1.99 tff(5754,plain,
% 1.74/1.99 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4279, 162, 464])).
% 1.74/1.99 tff(5755,plain,
% 1.74/1.99 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[494, 5754])).
% 1.74/1.99 tff(5756,plain,
% 1.74/1.99 (~b(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4042, 5755, 5753, 5743])).
% 1.74/1.99 tff(5757,plain,
% 1.74/1.99 (r(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[527, 5756])).
% 1.74/1.99 tff(5758,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[693, 5757, 1])).
% 1.74/1.99 tff(5759,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[398, 5758])).
% 1.74/1.99 tff(5760,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5761,plain,
% 1.74/1.99 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5762,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5761])).
% 1.74/1.99 tff(5763,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5762, 5760])).
% 1.74/1.99 tff(5764,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5765,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[5764, 5763])).
% 1.74/1.99 tff(5766,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5765, 112, 5743, 101, 19, 4, 5759])).
% 1.74/1.99 tff(5767,plain,((~r(z, 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))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5768,plain,
% 1.74/1.99 (~r(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5767, 5733, 5278, 4285, 400, 5739])).
% 1.74/1.99 tff(5769,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[182, 5768])).
% 1.74/1.99 tff(5770,plain,
% 1.74/1.99 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[547, 5769, 5733, 5737])).
% 1.74/1.99 tff(5771,plain,
% 1.74/1.99 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[356, 5770])).
% 1.74/1.99 tff(5772,plain,
% 1.74/1.99 (~r(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4697, 5771, 400])).
% 1.74/1.99 tff(5773,plain,
% 1.74/1.99 (b(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[515, 5772])).
% 1.74/1.99 tff(5774,plain,
% 1.74/1.99 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5751, 5739, 5735])).
% 1.74/1.99 tff(5775,plain,
% 1.74/1.99 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[386, 5774])).
% 1.74/1.99 tff(5776,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5765, 112, 5773, 5278, 5733, 4285])).
% 1.74/1.99 tff(5777,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[398, 5776])).
% 1.74/1.99 tff(5778,plain,
% 1.74/1.99 (~r(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[693, 5777, 400])).
% 1.74/1.99 tff(5779,plain,
% 1.74/1.99 (b(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[527, 5778])).
% 1.74/1.99 tff(5780,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4042, 5779, 5775, 5773])).
% 1.74/1.99 tff(5781,plain,
% 1.74/1.99 (r(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[494, 5780])).
% 1.74/1.99 tff(5782,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2718, 5771, 5278, 405, 5769, 400])).
% 1.74/1.99 tff(5783,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[299, 5782, 268])).
% 1.74/1.99 tff(5784,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[661, 31, 5777, 5783, 5781])).
% 1.74/1.99 tff(5785,plain,(b(s(s(s(z))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5786,plain,
% 1.74/1.99 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5785, 301, 248])).
% 1.74/1.99 tff(5787,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[770, 5786, 4285, 405])).
% 1.74/1.99 tff(5788,plain,
% 1.74/1.99 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[386, 5787])).
% 1.74/1.99 tff(5789,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[770, 196, 4, 2475])).
% 1.74/1.99 tff(5790,plain,
% 1.74/1.99 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[386, 5789])).
% 1.74/1.99 tff(5791,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[770, 196, 4, 442])).
% 1.74/1.99 tff(5792,plain,
% 1.74/1.99 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[386, 5791])).
% 1.74/1.99 tff(5793,plain,
% 1.74/1.99 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2676, 85, 5792])).
% 1.74/1.99 tff(5794,plain,
% 1.74/1.99 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[749, 5793])).
% 1.74/1.99 tff(5795,plain,
% 1.74/1.99 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3756, 112, 101, 443, 5794])).
% 1.74/1.99 tff(5796,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2752, 5795])).
% 1.74/1.99 tff(5797,plain,
% 1.74/1.99 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4259, 162, 569])).
% 1.74/1.99 tff(5798,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[589, 162, 569])).
% 1.74/1.99 tff(5799,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[429, 5798])).
% 1.74/1.99 tff(5800,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[451, 5799, 5797, 442, 443])).
% 1.74/1.99 tff(5801,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5802,plain,
% 1.74/1.99 (~r(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5801, 569, 443, 442])).
% 1.74/1.99 tff(5803,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[182, 5802])).
% 1.74/1.99 tff(5804,plain,
% 1.74/1.99 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[759, 5803, 443, 751])).
% 1.74/1.99 tff(5805,plain,
% 1.74/1.99 (r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[322, 5804])).
% 1.74/1.99 tff(5806,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4654, 5803, 443, 271, 751, 569])).
% 1.74/1.99 tff(5807,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1362, 5806, 443, 569])).
% 1.74/1.99 tff(5808,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[398, 5807])).
% 1.74/1.99 tff(5809,plain,
% 1.74/1.99 (~b(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4343, 5808, 4, 442, 5803, 443, 275])).
% 1.74/1.99 tff(5810,plain,
% 1.74/1.99 (r(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[527, 5809])).
% 1.74/1.99 tff(5811,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[809, 31, 5810, 5805, 730])).
% 1.74/1.99 tff(5812,plain,((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5813,plain,
% 1.74/1.99 (~r(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5812, 5796, 4, 442, 443, 5792, 271, 5794])).
% 1.74/1.99 tff(5814,plain,
% 1.74/1.99 (b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[356, 5813])).
% 1.74/1.99 tff(5815,plain,
% 1.74/1.99 (~b(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4393, 112, 4, 196, 5814])).
% 1.74/1.99 tff(5816,plain,
% 1.74/1.99 (r(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[515, 5815])).
% 1.74/1.99 tff(5817,plain,
% 1.74/1.99 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5542, 5816, 5796])).
% 1.74/1.99 tff(5818,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[322, 5817])).
% 1.74/1.99 tff(5819,plain,
% 1.74/1.99 (~r(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[170, 5816, 85])).
% 1.74/1.99 tff(5820,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[182, 5819])).
% 1.74/1.99 tff(5821,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[759, 5820, 5818, 443, 5794])).
% 1.74/1.99 tff(5822,plain,((~r(s(z), 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(s(s(s(elem!1)))))) | (~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)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5823,plain,
% 1.74/1.99 (~r(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5822, 443, 4, 196, 2475, 271, 101])).
% 1.74/1.99 tff(5824,plain,
% 1.74/1.99 (b(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[99, 5823])).
% 1.74/1.99 tff(5825,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[120, 5824, 101, 4])).
% 1.74/1.99 tff(5826,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[429, 5825])).
% 1.74/1.99 tff(5827,plain,
% 1.74/1.99 (~r(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5306, 5826, 2475, 101, 4, 271])).
% 1.74/1.99 tff(5828,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[182, 5827])).
% 1.74/1.99 tff(5829,plain,
% 1.74/1.99 (~b(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1867, 5828, 101, 5824])).
% 1.74/1.99 tff(5830,plain,
% 1.74/1.99 (r(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[515, 5829])).
% 1.74/1.99 tff(5831,plain,
% 1.74/1.99 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4341, 31, 5830, 5790])).
% 1.74/1.99 tff(5832,plain,
% 1.74/1.99 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2030, 5828, 271, 101, 443, 301, 5824, 5826])).
% 1.74/1.99 tff(5833,plain,
% 1.74/1.99 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[356, 5832])).
% 1.74/1.99 tff(5834,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1362, 5833, 443, 5825])).
% 1.74/1.99 tff(5835,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[398, 5834])).
% 1.74/1.99 tff(5836,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4321, 112, 5828, 5835, 443, 2475])).
% 1.74/1.99 tff(5837,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[494, 5836, 5831])).
% 1.74/1.99 tff(5838,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | r(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))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(5839,plain,
% 1.74/1.99 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5838, 301, 5278, 268, 4285, 5786])).
% 1.74/1.99 tff(5840,plain,
% 1.74/1.99 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[462, 5839])).
% 1.74/1.99 tff(5841,plain,
% 1.74/1.99 (~r(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5751, 5840, 5788])).
% 1.74/1.99 tff(5842,plain,
% 1.74/1.99 (b(s(z), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[99, 5841])).
% 1.74/1.99 tff(5843,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[120, 5842, 5278, 4285])).
% 1.74/1.99 tff(5844,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[429, 5843])).
% 1.74/1.99 tff(5845,plain,
% 1.74/1.99 (~r(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5306, 5844, 405, 5278, 4285, 268])).
% 1.74/1.99 tff(5846,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[182, 5845])).
% 1.74/1.99 tff(5847,plain,
% 1.74/1.99 (~b(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1867, 5846, 5278, 5842])).
% 1.74/1.99 tff(5848,plain,
% 1.74/1.99 (r(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[515, 5847])).
% 1.74/1.99 tff(5849,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1895, 5844, 5840])).
% 1.74/1.99 tff(5850,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[299, 5849, 268])).
% 1.74/1.99 tff(5851,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[712, 5850, 4285, 405, 5786])).
% 1.74/1.99 tff(5852,plain,
% 1.74/1.99 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5542, 5851, 5848])).
% 1.74/1.99 tff(5853,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[322, 5852])).
% 1.74/1.99 tff(5854,plain,
% 1.74/1.99 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3598, 5842, 4285, 5278, 5786])).
% 1.74/1.99 tff(5855,plain,
% 1.74/1.99 (r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[477, 5854])).
% 1.74/1.99 tff(5856,plain,
% 1.74/1.99 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[342, 5853, 301, 268, 5850])).
% 1.74/1.99 tff(5857,plain,
% 1.74/1.99 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[356, 5856])).
% 1.74/1.99 tff(5858,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5859,plain,
% 1.74/1.99 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(5860,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[5859])).
% 1.74/1.99 tff(5861,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[5860, 5858])).
% 1.74/1.99 tff(5862,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(5863,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5862, 5861])).
% 1.74/2.00 tff(5864,plain,
% 1.74/2.00 (~r(s(z), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5863, 31, 5848, 5857, 5855])).
% 1.74/2.00 tff(5865,plain,
% 1.74/2.00 (b(s(z), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[608, 5864])).
% 1.74/2.00 tff(5866,plain,
% 1.74/2.00 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5388, 5865, 5278, 5842, 5840, 257, 889, 5844, 5850])).
% 1.74/2.00 tff(5867,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5868,plain,
% 1.74/2.00 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5869,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5868])).
% 1.74/2.00 tff(5870,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5869, 5867])).
% 1.74/2.00 tff(5871,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5872,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5871, 5870])).
% 1.74/2.00 tff(5873,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5872, 112, 102, 5278, 4285, 2130, 196])).
% 1.74/2.00 tff(5874,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5393, 2130, 5278, 102])).
% 1.74/2.00 tff(5875,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1435, 78, 5874, 1421])).
% 1.74/2.00 tff(5876,plain,
% 1.74/2.00 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[120, 102, 5278, 4285])).
% 1.74/2.00 tff(5877,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[429, 5876])).
% 1.74/2.00 tff(5878,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2053, 31, 5877, 5875])).
% 1.74/2.00 tff(5879,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[872, 5878, 5873, 248])).
% 1.74/2.00 tff(5880,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5881,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5880, 5842, 248, 5786])).
% 1.74/2.00 tff(5882,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4880, 5881, 5866])).
% 1.74/2.00 tff(5883,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4341, 31, 20, 275])).
% 1.74/2.00 tff(5884,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[494, 5883])).
% 1.74/2.00 tff(5885,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3184, 31, 464, 275, 1953])).
% 1.74/2.00 tff(5886,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1025, 5885, 3141])).
% 1.74/2.00 tff(5887,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5195, 112, 334, 5167, 5886, 5884, 1969])).
% 1.74/2.00 tff(5888,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(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(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5889,plain,
% 1.74/2.00 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5888, 5882, 5853, 5840, 5788, 5848])).
% 1.74/2.00 tff(5890,plain,
% 1.74/2.00 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5889])).
% 1.74/2.00 tff(5891,plain,
% 1.74/2.00 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5890])).
% 1.74/2.00 tff(5892,plain,
% 1.74/2.00 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5891, 775])).
% 1.74/2.00 tff(5893,plain,
% 1.74/2.00 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5892])).
% 1.74/2.00 tff(5894,plain,
% 1.74/2.00 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5893])).
% 1.74/2.00 tff(5895,plain,
% 1.74/2.00 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[1041, 5894])).
% 1.74/2.00 tff(5896,plain,
% 1.74/2.00 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5890])).
% 1.74/2.00 tff(5897,plain,
% 1.74/2.00 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5896])).
% 1.74/2.00 tff(5898,plain,
% 1.74/2.00 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5897])).
% 1.74/2.00 tff(5899,plain,
% 1.74/2.00 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5896])).
% 1.74/2.00 tff(5900,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5899])).
% 1.74/2.00 tff(5901,plain,
% 1.74/2.00 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5889])).
% 1.74/2.00 tff(5902,plain,
% 1.74/2.00 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[145, 5901, 262])).
% 1.74/2.00 tff(5903,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5902])).
% 1.74/2.00 tff(5904,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5903, 5900])).
% 1.74/2.00 tff(5905,plain,
% 1.74/2.00 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5902])).
% 1.74/2.00 tff(5906,plain,
% 1.74/2.00 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5905, 890])).
% 1.74/2.00 tff(5907,plain,
% 1.74/2.00 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5906])).
% 1.74/2.00 tff(5908,plain,
% 1.74/2.00 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5907])).
% 1.74/2.00 tff(5909,plain,
% 1.74/2.00 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[257, 5908])).
% 1.74/2.00 tff(5910,plain,
% 1.74/2.00 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5890, 5902])).
% 1.74/2.00 tff(5911,plain,
% 1.74/2.00 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5910])).
% 1.74/2.00 tff(5912,plain,
% 1.74/2.00 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5911])).
% 1.74/2.00 tff(5913,plain,
% 1.74/2.00 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1160, 5889, 5857, 5855, 5846])).
% 1.74/2.00 tff(5914,plain,
% 1.74/2.00 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5913, 5912])).
% 1.74/2.00 tff(5915,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1166, 5914, 5909])).
% 1.74/2.00 tff(5916,plain,
% 1.74/2.00 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5915, 5904])).
% 1.74/2.00 tff(5917,plain,
% 1.74/2.00 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1174, 112, 4285, 5786, 5916])).
% 1.74/2.00 tff(5918,plain,
% 1.74/2.00 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5917, 5898])).
% 1.74/2.00 tff(5919,plain,
% 1.74/2.00 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5896])).
% 1.74/2.00 tff(5920,plain,
% 1.74/2.00 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5919])).
% 1.74/2.00 tff(5921,plain,
% 1.74/2.00 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5902])).
% 1.74/2.00 tff(5922,plain,
% 1.74/2.00 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5921])).
% 1.74/2.00 tff(5923,plain,
% 1.74/2.00 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.74/2.00 inference(transitivity,[status(thm)],[5896, 132, 5922, 247])).
% 1.74/2.00 tff(5924,plain,
% 1.74/2.00 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5923])).
% 1.74/2.00 tff(5925,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5924])).
% 1.74/2.00 tff(5926,plain,
% 1.74/2.00 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5889])).
% 1.74/2.00 tff(5927,plain,
% 1.74/2.00 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5926])).
% 1.74/2.00 tff(5928,plain,
% 1.74/2.00 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[1193, 5927])).
% 1.74/2.00 tff(5929,plain,
% 1.74/2.00 (elem!1 = s(s(s(elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[1073, 5921, 131])).
% 1.74/2.00 tff(5930,plain,
% 1.74/2.00 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5929])).
% 1.74/2.00 tff(5931,plain,
% 1.74/2.00 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5930, 890])).
% 1.74/2.00 tff(5932,plain,
% 1.74/2.00 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5931])).
% 1.74/2.00 tff(5933,plain,
% 1.74/2.00 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5932])).
% 1.74/2.00 tff(5934,plain,
% 1.74/2.00 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[257, 5933])).
% 1.74/2.00 tff(5935,plain,
% 1.74/2.00 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[1073, 5921, 131, 5890])).
% 1.74/2.00 tff(5936,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5935])).
% 1.74/2.00 tff(5937,plain,
% 1.74/2.00 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[5936])).
% 1.74/2.00 tff(5938,plain,
% 1.74/2.00 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5937])).
% 1.74/2.00 tff(5939,plain,
% 1.74/2.00 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5913, 5938])).
% 1.74/2.00 tff(5940,plain,
% 1.74/2.00 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1209, 5939, 5934])).
% 1.74/2.00 tff(5941,plain,
% 1.74/2.00 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1220, 5940, 268, 5850, 301])).
% 1.74/2.00 tff(5942,plain,
% 1.74/2.00 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1225, 5941, 5928])).
% 1.74/2.00 tff(5943,plain,
% 1.74/2.00 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5942, 5925])).
% 1.74/2.00 tff(5944,plain,
% 1.74/2.00 (~b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5462, 112, 5842, 5278, 5846, 5865])).
% 1.74/2.00 tff(5945,plain,
% 1.74/2.00 (r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[527, 5944])).
% 1.74/2.00 tff(5946,plain,
% 1.74/2.00 (((~![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(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5947,plain,
% 1.74/2.00 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(5948,plain,
% 1.74/2.00 (((~![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))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[5947])).
% 1.74/2.00 tff(5949,plain,
% 1.74/2.00 (((~![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))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[5948, 5946])).
% 1.74/2.00 tff(5950,plain,
% 1.74/2.00 ((~![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))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(5951,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5950, 5949])).
% 1.74/2.00 tff(5952,plain,
% 1.74/2.00 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5951, 31, 5945, 5943, 5851])).
% 1.74/2.00 tff(5953,plain,
% 1.74/2.00 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[5952, 5920])).
% 1.74/2.00 tff(5954,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1243, 5953, 5918, 5895])).
% 1.74/2.00 tff(5955,plain,(r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5956,plain,
% 1.74/2.00 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5955, 248])).
% 1.74/2.00 tff(5957,plain,
% 1.74/2.00 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5521, 112, 803, 101, 18, 4])).
% 1.74/2.00 tff(5958,plain,
% 1.74/2.00 (r(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[356, 5957])).
% 1.74/2.00 tff(5959,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4307, 5958, 276, 271, 18])).
% 1.74/2.00 tff(5960,plain,
% 1.74/2.00 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5765, 112, 803, 101, 5959, 4])).
% 1.74/2.00 tff(5961,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[398, 5960])).
% 1.74/2.00 tff(5962,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4074, 5961, 276])).
% 1.74/2.00 tff(5963,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[494, 5962])).
% 1.74/2.00 tff(5964,plain,
% 1.74/2.00 (~b(s(z), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1867, 18, 101, 803])).
% 1.74/2.00 tff(5965,plain,
% 1.74/2.00 (r(s(z), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[99, 5964])).
% 1.74/2.00 tff(5966,plain,
% 1.74/2.00 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[783, 5958, 276])).
% 1.74/2.00 tff(5967,plain,
% 1.74/2.00 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[322, 5966])).
% 1.74/2.00 tff(5968,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4074, 568, 276])).
% 1.74/2.00 tff(5969,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[494, 5968])).
% 1.74/2.00 tff(5970,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5751, 464, 85])).
% 1.74/2.00 tff(5971,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[386, 5970])).
% 1.74/2.00 tff(5972,plain,
% 1.74/2.00 (~b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4042, 5971, 5969, 803])).
% 1.74/2.00 tff(5973,plain,
% 1.74/2.00 (r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[527, 5972])).
% 1.74/2.00 tff(5974,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[477, 4288])).
% 1.74/2.00 tff(5975,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4251, 5974, 101, 19])).
% 1.74/2.00 tff(5976,plain,
% 1.74/2.00 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[160, 5975])).
% 1.74/2.00 tff(5977,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[693, 5976, 5973, 568])).
% 1.74/2.00 tff(5978,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5979,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5978, 5961, 101, 5959, 803, 276, 5965])).
% 1.74/2.00 tff(5980,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[462, 5979])).
% 1.74/2.00 tff(5981,plain,
% 1.74/2.00 (~b(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[759, 5980, 5967, 18])).
% 1.74/2.00 tff(5982,plain,
% 1.74/2.00 (r(s(z), s(s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[749, 5981])).
% 1.74/2.00 tff(5983,plain,
% 1.74/2.00 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2676, 5982, 5965])).
% 1.74/2.00 tff(5984,plain,
% 1.74/2.00 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[386, 5983])).
% 1.74/2.00 tff(5985,plain,
% 1.74/2.00 (~b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4042, 5984, 5963, 803])).
% 1.74/2.00 tff(5986,plain,
% 1.74/2.00 (r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[527, 5985])).
% 1.74/2.00 tff(5987,plain,
% 1.74/2.00 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4599, 5982, 276])).
% 1.74/2.00 tff(5988,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[477, 5987])).
% 1.74/2.00 tff(5989,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4251, 5988, 101, 5959])).
% 1.74/2.00 tff(5990,plain,
% 1.74/2.00 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[160, 5989])).
% 1.74/2.00 tff(5991,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[693, 5990, 5986, 5961])).
% 1.74/2.00 tff(5992,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(5993,plain,
% 1.74/2.00 (~b(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5992, 803, 101, 276, 4, 271])).
% 1.74/2.00 tff(5994,plain,
% 1.74/2.00 (r(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[182, 5993])).
% 1.74/2.00 tff(5995,plain,
% 1.74/2.00 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4367, 112, 803, 4, 196])).
% 1.74/2.00 tff(5996,plain,
% 1.74/2.00 (r(z, s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[356, 5995])).
% 1.74/2.00 tff(5997,plain,
% 1.74/2.00 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[589, 5996, 162])).
% 1.74/2.00 tff(5998,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[429, 5997])).
% 1.74/2.00 tff(5999,plain,
% 1.74/2.00 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4259, 5996, 162])).
% 1.74/2.00 tff(6000,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[477, 5999])).
% 1.74/2.00 tff(6001,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4251, 6000, 5998, 101, 196])).
% 1.74/2.00 tff(6002,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(6003,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6002, 5994, 101, 803, 4])).
% 1.74/2.00 tff(6004,plain,
% 1.74/2.00 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[160, 6003])).
% 1.74/2.00 tff(6005,plain,
% 1.74/2.00 (((~![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(s(elem!1))))), 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)))))))) <=> ((~![X0: $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(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(6006,plain,
% 1.74/2.00 (((~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(s(s(elem!1))))), 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)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6007,plain,
% 1.74/2.01 (((~![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(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(s(s(elem!1))))), 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))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6006])).
% 1.74/2.01 tff(6008,plain,
% 1.74/2.01 (((~![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(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(s(s(elem!1))))), 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)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6007, 6005])).
% 1.74/2.01 tff(6009,plain,
% 1.74/2.01 ((~![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(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))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6010,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6009, 6008])).
% 1.74/2.01 tff(6011,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6010, 31, 276, 1, 275])).
% 1.74/2.01 tff(6012,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6013,plain,
% 1.74/2.01 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6012, 6004, 276])).
% 1.74/2.01 tff(6014,plain,
% 1.74/2.01 (b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[386, 6013])).
% 1.74/2.01 tff(6015,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6016,plain,
% 1.74/2.01 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6017,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[6016])).
% 1.74/2.01 tff(6018,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[6017, 6015])).
% 1.74/2.01 tff(6019,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(6020,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[6019, 6018])).
% 1.74/2.01 tff(6021,plain,
% 1.74/2.01 ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6020, 112, 803, 101, 443])).
% 1.74/2.01 tff(6022,plain,
% 1.74/2.01 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6021, 762])).
% 1.74/2.01 tff(6023,plain,
% 1.74/2.01 (r(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[494, 6022])).
% 1.74/2.01 tff(6024,plain,
% 1.74/2.01 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4074, 6023, 276])).
% 1.74/2.01 tff(6025,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[398, 6024])).
% 1.74/2.01 tff(6026,plain,
% 1.74/2.01 (~b(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4333, 6025, 4, 803])).
% 1.74/2.01 tff(6027,plain,
% 1.74/2.01 (r(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[527, 6026])).
% 1.74/2.01 tff(6028,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[720, 31, 6027, 6023])).
% 1.74/2.01 tff(6029,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2752, 6028])).
% 1.74/2.01 tff(6030,plain,
% 1.74/2.01 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3767, 6027, 162])).
% 1.74/2.01 tff(6031,plain,
% 1.74/2.01 (b(z, s(s(s(s(s(elem!1))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[322, 6030])).
% 1.74/2.01 tff(6032,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2531, 112, 803, 6031, 6029, 762])).
% 1.74/2.01 tff(6033,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6034,plain,
% 1.74/2.01 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6033, 6014, 5994, 4, 276, 101, 803])).
% 1.74/2.01 tff(6035,plain,
% 1.74/2.01 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[462, 6034])).
% 1.74/2.01 tff(6036,plain,
% 1.74/2.01 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4291, 6035, 271, 276])).
% 1.74/2.01 tff(6037,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5767, 6035, 101, 4, 5994, 6004])).
% 1.74/2.01 tff(6038,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[429, 6037, 6036])).
% 1.74/2.01 tff(6039,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(6040,plain,
% 1.74/2.01 (~b(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6039, 5278, 4285, 268, 5956])).
% 1.74/2.01 tff(6041,plain,
% 1.74/2.01 (r(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[515, 6040])).
% 1.74/2.01 tff(6042,plain,
% 1.74/2.01 (~b(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6039, 101, 4, 271, 276])).
% 1.74/2.01 tff(6043,plain,
% 1.74/2.01 (r(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[515, 6042])).
% 1.74/2.01 tff(6044,plain,
% 1.74/2.01 (~r(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4697, 1, 20])).
% 1.74/2.01 tff(6045,plain,
% 1.74/2.01 (b(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[356, 6044])).
% 1.74/2.01 tff(6046,plain,
% 1.74/2.01 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3532, 1, 101, 276, 762])).
% 1.74/2.01 tff(6047,plain,
% 1.74/2.01 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[477, 6046])).
% 1.74/2.01 tff(6048,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[547, 6045, 18, 6047])).
% 1.74/2.01 tff(6049,plain,
% 1.74/2.01 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[429, 6048])).
% 1.74/2.01 tff(6050,plain,
% 1.74/2.01 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4291, 6049, 271, 276])).
% 1.74/2.01 tff(6051,plain,
% 1.74/2.01 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[462, 6050])).
% 1.74/2.01 tff(6052,plain,
% 1.74/2.01 (~b(s(z), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4273, 6051, 101, 762])).
% 1.74/2.01 tff(6053,plain,
% 1.74/2.01 (r(s(z), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[99, 6052])).
% 1.74/2.01 tff(6054,plain,
% 1.74/2.01 (~r(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2569, 31, 6053, 20])).
% 1.74/2.01 tff(6055,plain,
% 1.74/2.01 (b(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[608, 6054])).
% 1.74/2.01 tff(6056,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3569, 6055, 6047, 6045])).
% 1.74/2.01 tff(6057,plain,
% 1.74/2.01 (r(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[398, 6056])).
% 1.74/2.01 tff(6058,plain,
% 1.74/2.01 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4074, 6057, 276])).
% 1.74/2.01 tff(6059,plain,
% 1.74/2.01 (b(s(s(s(s(s(elem!1))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[494, 6058])).
% 1.74/2.01 tff(6060,plain,
% 1.74/2.01 (~r(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[693, 6057, 1])).
% 1.74/2.01 tff(6061,plain,
% 1.74/2.01 (b(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[527, 6060])).
% 1.74/2.01 tff(6062,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6063,plain,
% 1.74/2.01 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(6064,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 1.85/2.01 inference(monotonicity,[status(thm)],[6063])).
% 1.85/2.01 tff(6065,plain,
% 1.85/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.85/2.01 inference(transitivity,[status(thm)],[6064, 6062])).
% 1.85/2.01 tff(6066,plain,
% 1.85/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.01 inference(quant_inst,[status(thm)],[])).
% 1.85/2.01 tff(6067,plain,
% 1.85/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 1.85/2.01 inference(modus_ponens,[status(thm)],[6066, 6065])).
% 1.85/2.01 tff(6068,plain,
% 1.85/2.01 ($false),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6067, 112, 859, 101, 18, 2604, 406])).
% 1.85/2.01 tff(6069,plain,((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.01 tff(6070,plain,
% 1.85/2.01 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6069, 6061, 101, 18, 6059])).
% 1.85/2.01 tff(6071,plain,
% 1.85/2.01 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[2752, 6070])).
% 1.85/2.01 tff(6072,plain,
% 1.85/2.01 ($false),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[3250, 31, 276, 1, 6071])).
% 1.85/2.01 tff(6073,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.01 tff(6074,plain,
% 1.85/2.01 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6073, 18, 101, 276, 20, 762, 271])).
% 1.85/2.01 tff(6075,plain,
% 1.85/2.01 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[160, 6074])).
% 1.85/2.01 tff(6076,plain,
% 1.85/2.01 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[4291, 464, 271, 276])).
% 1.85/2.01 tff(6077,plain,
% 1.85/2.01 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[429, 6076])).
% 1.85/2.01 tff(6078,plain,
% 1.85/2.01 ($false),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[4251, 5974, 6077, 101, 196])).
% 1.85/2.01 tff(6079,plain,((~r(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(elem!1)))))) | (~r(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,[]))).
% 1.85/2.01 tff(6080,plain,
% 1.85/2.01 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6079, 6075, 101, 276, 271])).
% 1.85/2.01 tff(6081,plain,
% 1.85/2.01 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[462, 6080])).
% 1.85/2.01 tff(6082,plain,
% 1.85/2.01 (~b(s(z), s(s(s(z))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[4273, 6081, 101, 762])).
% 1.85/2.01 tff(6083,plain,
% 1.85/2.01 (r(s(z), s(s(s(z))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[99, 6082])).
% 1.85/2.01 tff(6084,plain,
% 1.85/2.01 (~r(s(z), z)),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[2569, 31, 6083, 20])).
% 1.85/2.01 tff(6085,plain,
% 1.85/2.01 (b(s(z), z)),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[608, 6084])).
% 1.85/2.01 tff(6086,plain,
% 1.85/2.01 (~r(z, s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[683, 6085, 276, 18, 6081])).
% 1.85/2.01 tff(6087,plain,
% 1.85/2.01 (b(z, s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[356, 6086])).
% 1.85/2.01 tff(6088,plain,
% 1.85/2.01 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[653, 112, 18, 6081, 6085])).
% 1.85/2.01 tff(6089,plain,
% 1.85/2.01 (r(s(s(s(s(s(elem!1))))), z)),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[494, 6088])).
% 1.85/2.01 tff(6090,plain,
% 1.85/2.01 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[4074, 6089, 276])).
% 1.85/2.01 tff(6091,plain,
% 1.85/2.01 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[398, 6090])).
% 1.85/2.01 tff(6092,plain,
% 1.85/2.01 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[3569, 6091, 6085, 6087])).
% 1.85/2.01 tff(6093,plain,
% 1.85/2.01 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[477, 6092])).
% 1.85/2.01 tff(6094,plain,
% 1.85/2.01 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[4599, 6093, 276])).
% 1.85/2.01 tff(6095,plain,
% 1.85/2.01 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[749, 6094])).
% 1.85/2.01 tff(6096,plain,
% 1.85/2.01 (~b(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[759, 6095, 18, 6081])).
% 1.85/2.01 tff(6097,plain,
% 1.85/2.01 (r(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[322, 6096])).
% 1.85/2.01 tff(6098,plain,
% 1.85/2.01 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[5542, 6097, 20])).
% 1.85/2.01 tff(6099,plain,
% 1.85/2.01 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[2752, 6098])).
% 1.85/2.01 tff(6100,plain,
% 1.85/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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))))))))),
% 1.85/2.01 inference(rewrite,[status(thm)],[])).
% 1.85/2.01 tff(6101,plain,
% 1.85/2.01 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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))))))))),
% 1.85/2.01 inference(rewrite,[status(thm)],[])).
% 1.85/2.01 tff(6102,plain,
% 1.85/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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)))))))))),
% 1.85/2.01 inference(monotonicity,[status(thm)],[6101])).
% 1.85/2.01 tff(6103,plain,
% 1.85/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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))))))))),
% 1.85/2.01 inference(transitivity,[status(thm)],[6102, 6100])).
% 1.85/2.01 tff(6104,plain,
% 1.85/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.85/2.01 inference(quant_inst,[status(thm)],[])).
% 1.85/2.01 tff(6105,plain,
% 1.85/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1)))))))),
% 1.85/2.01 inference(modus_ponens,[status(thm)],[6104, 6103])).
% 1.85/2.01 tff(6106,plain,
% 1.85/2.01 ($false),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6105, 112, 101, 18, 6081, 6095, 6085, 6099])).
% 1.85/2.01 tff(6107,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.01 tff(6108,plain,
% 1.85/2.01 (~b(z, s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6107, 762, 6043, 276, 101, 271])).
% 1.85/2.01 tff(6109,plain,
% 1.85/2.01 (r(z, s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[182, 6108])).
% 1.85/2.01 tff(6110,plain,
% 1.85/2.01 (~r(s(z), s(s(s(z))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[170, 6109, 6043])).
% 1.85/2.01 tff(6111,plain,
% 1.85/2.01 (b(s(z), s(s(s(z))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[99, 6110])).
% 1.85/2.01 tff(6112,plain,
% 1.85/2.01 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[4273, 6111, 101, 762])).
% 1.85/2.01 tff(6113,plain,
% 1.85/2.01 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[462, 6112])).
% 1.85/2.01 tff(6114,plain,
% 1.85/2.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[120, 6111, 101, 4])).
% 1.85/2.01 tff(6115,plain,
% 1.85/2.01 (r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[429, 6114])).
% 1.85/2.01 tff(6116,plain,
% 1.85/2.01 ($false),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[4291, 6115, 6113, 271, 276])).
% 1.85/2.01 tff(6117,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.01 tff(6118,plain,
% 1.85/2.01 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6117, 268, 5956, 5278, 4285])).
% 1.85/2.01 tff(6119,plain,
% 1.85/2.01 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[386, 6118])).
% 1.85/2.01 tff(6120,plain,
% 1.85/2.01 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6012, 6119, 5956])).
% 1.85/2.01 tff(6121,plain,
% 1.85/2.01 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[160, 6120])).
% 1.85/2.01 tff(6122,plain,
% 1.85/2.01 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6079, 6121, 5278, 5956, 268])).
% 1.85/2.01 tff(6123,plain,
% 1.85/2.01 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[462, 6122])).
% 1.85/2.01 tff(6124,plain,
% 1.85/2.01 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[310, 6119, 6041])).
% 1.85/2.01 tff(6125,plain,
% 1.85/2.01 (b(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[322, 6124])).
% 1.85/2.01 tff(6126,plain,
% 1.85/2.01 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[6012, 275, 276])).
% 1.85/2.01 tff(6127,plain,
% 1.85/2.01 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[160, 6126])).
% 1.85/2.01 tff(6128,plain,
% 1.85/2.01 (~r(s(z), s(s(s(z))))),
% 1.85/2.01 inference(unit_resolution,[status(thm)],[2676, 731, 275])).
% 1.85/2.02 tff(6129,plain,
% 1.85/2.02 (b(s(z), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[99, 6128])).
% 1.85/2.02 tff(6130,plain,
% 1.85/2.02 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[4599, 731, 276])).
% 1.85/2.02 tff(6131,plain,
% 1.85/2.02 (b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[477, 6130])).
% 1.85/2.02 tff(6132,plain,
% 1.85/2.02 ($false),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[3598, 6131, 6129, 4, 101, 6127])).
% 1.85/2.02 tff(6133,plain,((~r(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~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)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.02 tff(6134,plain,
% 1.85/2.02 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6133, 4285, 5278, 5956, 6119])).
% 1.85/2.02 tff(6135,plain,
% 1.85/2.02 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[749, 6134])).
% 1.85/2.02 tff(6136,plain,
% 1.85/2.02 (~b(z, s(z))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[759, 6135, 6125, 6123])).
% 1.85/2.02 tff(6137,plain,
% 1.85/2.02 (r(z, s(z))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[182, 6136])).
% 1.85/2.02 tff(6138,plain,
% 1.85/2.02 (~r(s(z), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[170, 6137, 6041])).
% 1.85/2.02 tff(6139,plain,
% 1.85/2.02 (b(s(z), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[99, 6138])).
% 1.85/2.02 tff(6140,plain,
% 1.85/2.02 (~r(s(z), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[170, 162, 6041])).
% 1.85/2.02 tff(6141,plain,
% 1.85/2.02 (b(s(z), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[99, 6140])).
% 1.85/2.02 tff(6142,plain,
% 1.85/2.02 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[5880, 6141, 248, 6121])).
% 1.85/2.02 tff(6143,plain,
% 1.85/2.02 (((~![X0: $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(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6144,plain,
% 1.85/2.02 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6145,plain,
% 1.85/2.02 (((~![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(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[6144])).
% 1.85/2.02 tff(6146,plain,
% 1.85/2.02 (((~![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(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.85/2.02 inference(transitivity,[status(thm)],[6145, 6143])).
% 1.85/2.02 tff(6147,plain,
% 1.85/2.02 ((~![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(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(6148,plain,
% 1.85/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[6147, 6146])).
% 1.85/2.02 tff(6149,plain,
% 1.85/2.02 ($false),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6148, 31, 20, 162, 408, 568])).
% 1.85/2.02 tff(6150,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.02 tff(6151,plain,
% 1.85/2.02 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6150, 162, 6041, 408])).
% 1.85/2.02 tff(6152,plain,
% 1.85/2.02 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[398, 6151])).
% 1.85/2.02 tff(6153,plain,
% 1.85/2.02 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[3598, 6141, 4285, 5278, 6121])).
% 1.85/2.02 tff(6154,plain,
% 1.85/2.02 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[477, 6153])).
% 1.85/2.02 tff(6155,plain,
% 1.85/2.02 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[4599, 6154, 5956])).
% 1.85/2.02 tff(6156,plain,
% 1.85/2.02 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[749, 6155])).
% 1.85/2.02 tff(6157,plain,
% 1.85/2.02 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6150, 162, 20, 408])).
% 1.85/2.02 tff(6158,plain,
% 1.85/2.02 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[398, 6157])).
% 1.85/2.02 tff(6159,plain,
% 1.85/2.02 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[1736])).
% 1.85/2.02 tff(6160,plain,
% 1.85/2.02 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.85/2.02 inference(symmetry,[status(thm)],[6159])).
% 1.85/2.02 tff(6161,plain,
% 1.85/2.02 (b(z, s(s(s(s(s(z))))))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[2, 6160])).
% 1.85/2.02 tff(6162,plain,
% 1.85/2.02 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.85/2.02 inference(monotonicity,[status(thm)],[1736])).
% 1.85/2.02 tff(6163,plain,
% 1.85/2.02 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.85/2.02 inference(symmetry,[status(thm)],[6162])).
% 1.85/2.02 tff(6164,plain,
% 1.85/2.02 (b(s(s(s(s(s(z))))), z)),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[1827, 6163])).
% 1.85/2.02 tff(6165,plain,
% 1.85/2.02 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.85/2.02 inference(commutativity,[status(thm)],[])).
% 1.85/2.02 tff(6166,plain,
% 1.85/2.02 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.85/2.02 inference(symmetry,[status(thm)],[6165])).
% 1.85/2.02 tff(6167,plain,
% 1.85/2.02 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[6166])).
% 1.85/2.02 tff(6168,plain,
% 1.85/2.02 (~(z = s(s(s(s(z)))))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[224, 6167])).
% 1.85/2.02 tff(6169,plain,
% 1.85/2.02 (((~![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))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6170,plain,
% 1.85/2.02 (((~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))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6171,plain,
% 1.85/2.02 (((~![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(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)))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[6170])).
% 1.85/2.02 tff(6172,plain,
% 1.85/2.02 (((~![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(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))))),
% 1.85/2.02 inference(transitivity,[status(thm)],[6171, 6169])).
% 1.85/2.02 tff(6173,plain,
% 1.85/2.02 ((~![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(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(6174,plain,
% 1.85/2.02 ((~![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)))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[6173, 6172])).
% 1.85/2.02 tff(6175,plain,
% 1.85/2.02 (~r(z, s(s(s(s(z)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6174, 31, 162, 981])).
% 1.85/2.02 tff(6176,plain,
% 1.85/2.02 (((~![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))))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6177,plain,
% 1.85/2.02 ((~![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))))))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(6178,plain,
% 1.85/2.02 ((~![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)))))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[6177, 6176])).
% 1.85/2.02 tff(6179,plain,
% 1.85/2.02 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6178, 78, 6175])).
% 1.85/2.02 tff(6180,plain,
% 1.85/2.02 (b(z, s(s(s(s(z)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6179, 6168])).
% 1.85/2.02 tff(6181,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6182,plain,
% 1.85/2.02 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6183,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[6182])).
% 1.85/2.02 tff(6184,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.02 inference(transitivity,[status(thm)],[6183, 6181])).
% 1.85/2.02 tff(6185,plain,
% 1.85/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(6186,plain,
% 1.85/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[6185, 6184])).
% 1.85/2.02 tff(6187,plain,
% 1.85/2.02 ($false),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6186, 112, 3898, 6180, 6164, 6161, 2362])).
% 1.85/2.02 tff(6188,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.02 tff(6189,plain,
% 1.85/2.02 (~r(s(s(s(s(z)))), s(z))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6188, 891, 1899, 6158, 265, 4484, 20, 162])).
% 1.85/2.02 tff(6190,plain,
% 1.85/2.02 (b(s(s(s(s(z)))), s(z))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[1733, 6189])).
% 1.85/2.02 tff(6191,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(s(z)))), s(z))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6192,plain,
% 1.85/2.02 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(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(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(s(s(s(z)))), s(z))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6193,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(s(z)))), s(z)))))),
% 1.85/2.02 inference(monotonicity,[status(thm)],[6192])).
% 1.85/2.02 tff(6194,plain,
% 1.85/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(s(s(s(z)))), s(z))))),
% 1.85/2.02 inference(transitivity,[status(thm)],[6193, 6191])).
% 1.85/2.02 tff(6195,plain,
% 1.85/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(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(z))))),
% 1.85/2.02 inference(quant_inst,[status(thm)],[])).
% 1.85/2.02 tff(6196,plain,
% 1.85/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.85/2.02 inference(modus_ponens,[status(thm)],[6195, 6194])).
% 1.85/2.02 tff(6197,plain,
% 1.85/2.02 (~b(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6196, 112, 4129, 101, 443, 751, 6190])).
% 1.85/2.02 tff(6198,plain,
% 1.85/2.02 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[2486, 751, 101, 443, 4129])).
% 1.85/2.02 tff(6199,plain,
% 1.85/2.02 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[2752, 6198])).
% 1.85/2.02 tff(6200,plain,
% 1.85/2.02 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[2440, 6190, 101, 4129])).
% 1.85/2.02 tff(6201,plain,
% 1.85/2.02 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[2954, 6200, 6199])).
% 1.85/2.02 tff(6202,plain,
% 1.85/2.02 (s(s(s(s(z)))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[936, 78, 6201, 6197])).
% 1.85/2.02 tff(6203,plain,
% 1.85/2.02 (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))),
% 1.85/2.02 inference(symmetry,[status(thm)],[6202])).
% 1.85/2.02 tff(6204,plain,
% 1.85/2.02 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.85/2.02 inference(transitivity,[status(thm)],[6203, 893])).
% 1.85/2.02 tff(6205,plain,
% 1.85/2.02 ($false),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[899, 6204])).
% 1.85/2.02 tff(6206,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.02 tff(6207,plain,
% 1.85/2.02 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[6206, 6156, 5278, 6123, 889, 257, 6041, 162, 408])).
% 1.85/2.02 tff(6208,plain,
% 1.85/2.02 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[4411, 31, 276, 21])).
% 1.85/2.02 tff(6209,plain,
% 1.85/2.02 (b(s(z), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[749, 6208])).
% 1.85/2.02 tff(6210,plain,
% 1.85/2.02 (~b(z, s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[4393, 112, 4285, 196, 2])).
% 1.85/2.02 tff(6211,plain,
% 1.85/2.02 (r(z, s(s(s(z))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[515, 6210])).
% 1.85/2.02 tff(6212,plain,
% 1.85/2.02 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[4539, 1392, 4285, 6211, 1827, 196, 2])).
% 1.85/2.02 tff(6213,plain,
% 1.85/2.02 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[872, 6212, 248])).
% 1.85/2.02 tff(6214,plain,
% 1.85/2.02 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[4547, 31, 6213, 276])).
% 1.85/2.02 tff(6215,plain,
% 1.85/2.02 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.85/2.02 inference(unit_resolution,[status(thm)],[1025, 6214, 3141])).
% 1.85/2.02 tff(6216,plain,
% 1.85/2.02 (((~![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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.85/2.02 inference(rewrite,[status(thm)],[])).
% 1.85/2.02 tff(6217,plain,
% 1.85/2.02 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6218,plain,
% 1.85/2.03 (((~![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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~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(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6217])).
% 1.85/2.03 tff(6219,plain,
% 1.85/2.03 (((~![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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~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(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6218, 6216])).
% 1.85/2.03 tff(6220,plain,
% 1.85/2.03 ((~![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(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(6221,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6220, 6219])).
% 1.85/2.03 tff(6222,plain,
% 1.85/2.03 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6221, 31, 6213, 276, 3140])).
% 1.85/2.03 tff(6223,plain,
% 1.85/2.03 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2066, 6222, 3347])).
% 1.85/2.03 tff(6224,plain,
% 1.85/2.03 (~r(s(z), s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[851, 6213, 21])).
% 1.85/2.03 tff(6225,plain,
% 1.85/2.03 (b(s(z), s(s(elem!1)))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[857, 6224])).
% 1.85/2.03 tff(6226,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[3366, 112, 6225, 6223, 6215, 6209])).
% 1.85/2.03 tff(6227,plain,((s(s(elem!1)) = s(s(s(z)))) | (s(s(elem!1)) = s(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(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(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))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(6228,plain,
% 1.85/2.03 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6227, 6207, 5956, 6154, 248, 6152, 6142, 6121, 1899])).
% 1.85/2.03 tff(6229,plain,
% 1.85/2.03 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6228])).
% 1.85/2.03 tff(6230,plain,
% 1.85/2.03 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[145, 6229, 262])).
% 1.85/2.03 tff(6231,plain,
% 1.85/2.03 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6230])).
% 1.85/2.03 tff(6232,plain,
% 1.85/2.03 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.85/2.03 inference(symmetry,[status(thm)],[6231])).
% 1.85/2.03 tff(6233,plain,
% 1.85/2.03 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6228])).
% 1.85/2.03 tff(6234,plain,
% 1.85/2.03 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.85/2.03 inference(symmetry,[status(thm)],[6233])).
% 1.85/2.03 tff(6235,plain,
% 1.85/2.03 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.85/2.03 inference(transitivity,[status(thm)],[6234, 132, 6232, 247])).
% 1.85/2.03 tff(6236,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(elem!1, s(z))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6235])).
% 1.85/2.03 tff(6237,plain,
% 1.85/2.03 (r(elem!1, s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.03 inference(symmetry,[status(thm)],[6236])).
% 1.85/2.03 tff(6238,plain,
% 1.85/2.03 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[1073, 6231, 131, 6233])).
% 1.85/2.03 tff(6239,plain,
% 1.85/2.03 ((elem!1 = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6238])).
% 1.85/2.03 tff(6240,plain,
% 1.85/2.03 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6239, 1113])).
% 1.85/2.03 tff(6241,plain,
% 1.85/2.03 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(z))),
% 1.85/2.03 inference(symmetry,[status(thm)],[6240])).
% 1.85/2.03 tff(6242,plain,
% 1.85/2.03 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(z)))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6241])).
% 1.85/2.03 tff(6243,plain,
% 1.85/2.03 (~(elem!1 = s(z))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[1124, 6242])).
% 1.85/2.03 tff(6244,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6234])).
% 1.85/2.03 tff(6245,plain,
% 1.85/2.03 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.85/2.03 inference(symmetry,[status(thm)],[6244])).
% 1.85/2.03 tff(6246,plain,
% 1.85/2.03 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6233])).
% 1.85/2.03 tff(6247,plain,
% 1.85/2.03 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6246, 775])).
% 1.85/2.03 tff(6248,plain,
% 1.85/2.03 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.85/2.03 inference(symmetry,[status(thm)],[6247])).
% 1.85/2.03 tff(6249,plain,
% 1.85/2.03 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6248])).
% 1.85/2.03 tff(6250,plain,
% 1.85/2.03 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[1041, 6249])).
% 1.85/2.03 tff(6251,plain,
% 1.85/2.03 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[310, 275, 20])).
% 1.85/2.03 tff(6252,plain,
% 1.85/2.03 (b(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[322, 6251])).
% 1.85/2.03 tff(6253,plain,
% 1.85/2.03 (~r(s(s(s(elem!1))), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2464, 1298, 20])).
% 1.85/2.03 tff(6254,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[1298, 3074])).
% 1.85/2.03 tff(6255,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6256,plain,
% 1.85/2.03 (((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6257,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(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(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6256])).
% 1.85/2.03 tff(6258,plain,
% 1.85/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(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(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6257, 6255])).
% 1.85/2.03 tff(6259,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(6260,plain,
% 1.85/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6259, 6258])).
% 1.85/2.03 tff(6261,plain,
% 1.85/2.03 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6260, 31, 276, 275])).
% 1.85/2.03 tff(6262,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6261, 6254])).
% 1.85/2.03 tff(6263,plain,
% 1.85/2.03 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6262, 3092])).
% 1.85/2.03 tff(6264,plain,
% 1.85/2.03 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1225, 6263, 3091])).
% 1.85/2.03 tff(6265,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6264, 4426])).
% 1.85/2.03 tff(6266,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.85/2.03 tff(6267,plain,
% 1.85/2.03 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6266, 4752])).
% 1.85/2.03 tff(6268,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1513, 78, 1510, 6267])).
% 1.85/2.03 tff(6269,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6270,plain,
% 1.85/2.03 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(elem!1)))))), z))) <=> ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6271,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6270])).
% 1.85/2.03 tff(6272,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(elem!1)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6271, 6269])).
% 1.85/2.03 tff(6273,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(s(s(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(s(elem!1)))))), z)))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(6274,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6273, 6272])).
% 1.85/2.03 tff(6275,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6274, 112, 1827, 2, 334, 2604, 6268, 6265])).
% 1.85/2.03 tff(6276,plain,((~(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(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(s(elem!1)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))) | r(s(s(s(elem!1))), z) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(6277,plain,
% 1.85/2.03 ($false),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6276, 6253, 1298, 276, 5884, 275, 2, 6252, 1827, 1068, 2128])).
% 1.85/2.03 tff(6278,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~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))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.03 tff(6279,plain,
% 1.85/2.03 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6278, 1899, 6119, 5956, 6152, 6228, 1193, 6041])).
% 1.85/2.03 tff(6280,plain,
% 1.85/2.03 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1243, 6279, 6250])).
% 1.85/2.03 tff(6281,plain,
% 1.85/2.03 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6280, 6245])).
% 1.85/2.03 tff(6282,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6283,plain,
% 1.85/2.03 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.03 inference(rewrite,[status(thm)],[])).
% 1.85/2.03 tff(6284,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6283])).
% 1.85/2.03 tff(6285,plain,
% 1.85/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.03 inference(transitivity,[status(thm)],[6284, 6282])).
% 1.85/2.03 tff(6286,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.03 inference(quant_inst,[status(thm)],[])).
% 1.85/2.03 tff(6287,plain,
% 1.85/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6286, 6285])).
% 1.85/2.03 tff(6288,plain,
% 1.85/2.03 ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6287, 112, 6141, 5278])).
% 1.85/2.03 tff(6289,plain,
% 1.85/2.03 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[6288, 6281])).
% 1.85/2.03 tff(6290,plain,
% 1.85/2.03 (~b(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[2249, 6289, 6228])).
% 1.85/2.03 tff(6291,plain,
% 1.85/2.03 (r(elem!1, s(z))),
% 1.85/2.03 inference(unit_resolution,[status(thm)],[1139, 6290, 6243])).
% 1.85/2.03 tff(6292,plain,
% 1.85/2.03 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.85/2.03 inference(modus_ponens,[status(thm)],[6291, 6237])).
% 1.85/2.03 tff(6293,plain,
% 1.85/2.03 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.03 inference(monotonicity,[status(thm)],[6233, 6230])).
% 1.85/2.03 tff(6294,plain,
% 1.85/2.03 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6230])).
% 1.85/2.04 tff(6295,plain,
% 1.85/2.04 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6294, 890])).
% 1.85/2.04 tff(6296,plain,
% 1.85/2.04 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6295])).
% 1.85/2.04 tff(6297,plain,
% 1.85/2.04 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6296])).
% 1.85/2.04 tff(6298,plain,
% 1.85/2.04 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[257, 6297])).
% 1.85/2.04 tff(6299,plain,
% 1.85/2.04 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6230])).
% 1.85/2.04 tff(6300,plain,
% 1.85/2.04 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6299])).
% 1.85/2.04 tff(6301,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6234])).
% 1.85/2.04 tff(6302,plain,
% 1.85/2.04 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6301, 6300])).
% 1.85/2.04 tff(6303,plain,
% 1.85/2.04 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6302])).
% 1.85/2.04 tff(6304,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6305,plain,
% 1.85/2.04 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6306,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6305])).
% 1.85/2.04 tff(6307,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6306, 6304])).
% 1.85/2.04 tff(6308,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(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(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6309,plain,
% 1.85/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~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)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6308, 6307])).
% 1.85/2.04 tff(6310,plain,
% 1.85/2.04 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6309, 112, 6141, 5278, 4285, 6121])).
% 1.85/2.04 tff(6311,plain,
% 1.85/2.04 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6310, 6281])).
% 1.85/2.04 tff(6312,plain,
% 1.85/2.04 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6311, 6303])).
% 1.85/2.04 tff(6313,plain,
% 1.85/2.04 (r(s(s(s(elem!1))), s(elem!1))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1166, 6312, 6298])).
% 1.85/2.04 tff(6314,plain,
% 1.85/2.04 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6313, 6293])).
% 1.85/2.04 tff(6315,plain,
% 1.85/2.04 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[4341, 31, 6041, 6119])).
% 1.85/2.04 tff(6316,plain,
% 1.85/2.04 (b(s(s(s(s(s(elem!1))))), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[494, 6315])).
% 1.85/2.04 tff(6317,plain,
% 1.85/2.04 (~b(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[5225, 6156, 6125, 6316])).
% 1.85/2.04 tff(6318,plain,
% 1.85/2.04 (r(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[608, 6317])).
% 1.85/2.04 tff(6319,plain,
% 1.85/2.04 (((~![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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6320,plain,
% 1.85/2.04 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6321,plain,
% 1.85/2.04 (((~![X0: $i, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6320])).
% 1.85/2.04 tff(6322,plain,
% 1.85/2.04 (((~![X0: $i, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6321, 6319])).
% 1.85/2.04 tff(6323,plain,
% 1.85/2.04 ((~![X0: $i, 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(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6324,plain,
% 1.85/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6323, 6322])).
% 1.85/2.04 tff(6325,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6324, 31, 6318, 6314, 6154, 6292])).
% 1.85/2.04 tff(6326,plain,((~r(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6327,plain,
% 1.85/2.04 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6326, 6137, 248])).
% 1.85/2.04 tff(6328,plain,
% 1.85/2.04 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[429, 6327])).
% 1.85/2.04 tff(6329,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[120, 6328, 6139, 5278, 4285])).
% 1.85/2.04 tff(6330,plain,(s(s(elem!1)) = s(s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6331,plain,
% 1.85/2.04 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6330])).
% 1.85/2.04 tff(6332,plain,
% 1.85/2.04 (s(elem!1) = s(s(s(elem!1)))),
% 1.85/2.04 inference(transitivity,[status(thm)],[145, 6331, 131])).
% 1.85/2.04 tff(6333,plain,
% 1.85/2.04 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6332])).
% 1.85/2.04 tff(6334,plain,
% 1.85/2.04 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6333])).
% 1.85/2.04 tff(6335,plain,
% 1.85/2.04 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6330])).
% 1.85/2.04 tff(6336,plain,
% 1.85/2.04 (s(s(s(s(elem!1)))) = elem!1),
% 1.85/2.04 inference(transitivity,[status(thm)],[6335, 253, 6334, 247])).
% 1.85/2.04 tff(6337,plain,
% 1.85/2.04 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6336])).
% 1.85/2.04 tff(6338,plain,
% 1.85/2.04 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6337])).
% 1.85/2.04 tff(6339,plain,
% 1.85/2.04 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[1747, 6338])).
% 1.85/2.04 tff(6340,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.04 tff(6341,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6340, 6339])).
% 1.85/2.04 tff(6342,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6343,plain,
% 1.85/2.04 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6342, 245])).
% 1.85/2.04 tff(6344,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 1.85/2.04 tff(6345,plain,
% 1.85/2.04 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6344, 1073, 6333, 127, 6330])).
% 1.85/2.04 tff(6346,plain,
% 1.85/2.04 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6345])).
% 1.85/2.04 tff(6347,plain,
% 1.85/2.04 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.85/2.04 inference(transitivity,[status(thm)],[221, 6346, 131])).
% 1.85/2.04 tff(6348,plain,
% 1.85/2.04 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[1269, 6330])).
% 1.85/2.04 tff(6349,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6348, 6347])).
% 1.85/2.04 tff(6350,plain,(~(s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6351,plain,
% 1.85/2.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6352,plain,
% 1.85/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6353,plain,
% 1.85/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6352, 6351])).
% 1.85/2.04 tff(6354,plain,
% 1.85/2.04 ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6353, 78])).
% 1.85/2.04 tff(6355,plain,
% 1.85/2.04 (b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6354, 6350])).
% 1.85/2.04 tff(6356,plain,
% 1.85/2.04 (r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6355, 6343])).
% 1.85/2.04 tff(6357,plain,
% 1.85/2.04 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6336])).
% 1.85/2.04 tff(6358,plain,
% 1.85/2.04 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(symmetry,[status(thm)],[6357])).
% 1.85/2.04 tff(6359,plain,
% 1.85/2.04 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[2343, 6358])).
% 1.85/2.04 tff(6360,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.04 tff(6361,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6360, 6359])).
% 1.85/2.04 tff(6362,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6363,plain,
% 1.85/2.04 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6362, 6356])).
% 1.85/2.04 tff(6364,plain,
% 1.85/2.04 (((~![X0: $i, 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(s(z))))), s(z))) | (~r(s(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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6365,plain,
% 1.85/2.04 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(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(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6366,plain,
% 1.85/2.04 (((~![X0: $i, 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(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6365])).
% 1.85/2.04 tff(6367,plain,
% 1.85/2.04 (((~![X0: $i, 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(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.04 inference(transitivity,[status(thm)],[6366, 6364])).
% 1.85/2.04 tff(6368,plain,
% 1.85/2.04 ((~![X0: $i, 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(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6369,plain,
% 1.85/2.04 ((~![X0: $i, 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(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6368, 6367])).
% 1.85/2.04 tff(6370,plain,
% 1.85/2.04 (~r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6369, 31, 85, 21, 6363])).
% 1.85/2.04 tff(6371,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.85/2.04 tff(6372,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.85/2.04 tff(6373,plain,
% 1.85/2.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6374,plain,
% 1.85/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.85/2.04 inference(quant_inst,[status(thm)],[])).
% 1.85/2.04 tff(6375,plain,
% 1.85/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.04 inference(modus_ponens,[status(thm)],[6374, 6373])).
% 1.85/2.04 tff(6376,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6375, 78, 6372, 226, 6371])).
% 1.85/2.04 tff(6377,plain,(b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6378,plain,
% 1.85/2.04 (b(s(s(s(s(s(z))))), s(z))),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6377, 6370])).
% 1.85/2.04 tff(6379,plain,
% 1.85/2.04 ($false),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[2569, 31, 85, 20, 592])).
% 1.85/2.04 tff(6380,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.04 tff(6381,plain,
% 1.85/2.04 (~r(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[6380, 85, 20])).
% 1.85/2.04 tff(6382,plain,
% 1.85/2.04 (b(s(z), z)),
% 1.85/2.04 inference(unit_resolution,[status(thm)],[608, 6381])).
% 1.85/2.04 tff(6383,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6384,plain,
% 1.85/2.04 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.04 inference(rewrite,[status(thm)],[])).
% 1.85/2.04 tff(6385,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.85/2.04 inference(monotonicity,[status(thm)],[6384])).
% 1.85/2.04 tff(6386,plain,
% 1.85/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6385, 6383])).
% 1.85/2.05 tff(6387,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6388,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6387, 6386])).
% 1.85/2.05 tff(6389,plain,
% 1.85/2.05 (~b(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6388, 112, 183, 6382, 6378])).
% 1.85/2.05 tff(6390,plain,
% 1.85/2.05 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[5014, 183, 19, 4, 20])).
% 1.85/2.05 tff(6391,plain,
% 1.85/2.05 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[398, 6390])).
% 1.85/2.05 tff(6392,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.05 tff(6393,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6394,plain,
% 1.85/2.05 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6395,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6394])).
% 1.85/2.05 tff(6396,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6395, 6393])).
% 1.85/2.05 tff(6397,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6398,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6397, 6396])).
% 1.85/2.05 tff(6399,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6398, 31, 568, 1792, 6392])).
% 1.85/2.05 tff(6400,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6401,plain,
% 1.85/2.05 (~r(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6400, 6363, 6391])).
% 1.85/2.05 tff(6402,plain,
% 1.85/2.05 (((~![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))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6403,plain,
% 1.85/2.05 ((~![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))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6404,plain,
% 1.85/2.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6403, 6402])).
% 1.85/2.05 tff(6405,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6404, 78, 15, 6401, 6389])).
% 1.85/2.05 tff(6406,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6407,plain,
% 1.85/2.05 (~r(s(z), s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6406, 21, 4, 20, 19, 2])).
% 1.85/2.05 tff(6408,plain,
% 1.85/2.05 (b(s(z), s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[99, 6407])).
% 1.85/2.05 tff(6409,plain,
% 1.85/2.05 (~b(s(s(s(z))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[120, 6408, 4, 19])).
% 1.85/2.05 tff(6410,plain,
% 1.85/2.05 (r(s(s(s(z))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[83, 6409])).
% 1.85/2.05 tff(6411,plain,
% 1.85/2.05 (~r(z, s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[503, 6410, 20])).
% 1.85/2.05 tff(6412,plain,
% 1.85/2.05 (b(z, s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[182, 6411])).
% 1.85/2.05 tff(6413,plain,
% 1.85/2.05 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[244, 6412, 4, 161, 20, 19, 2])).
% 1.85/2.05 tff(6414,plain,
% 1.85/2.05 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6342, 6413])).
% 1.85/2.05 tff(6415,plain,
% 1.85/2.05 (r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6355, 6414])).
% 1.85/2.05 tff(6416,plain,
% 1.85/2.05 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6362, 6415])).
% 1.85/2.05 tff(6417,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(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(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6418,plain,
% 1.85/2.05 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6419,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6418])).
% 1.85/2.05 tff(6420,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6419, 6417])).
% 1.85/2.05 tff(6421,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6422,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6421, 6420])).
% 1.85/2.05 tff(6423,plain,
% 1.85/2.05 (~r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6422, 31, 21, 6416])).
% 1.85/2.05 tff(6424,plain,
% 1.85/2.05 (b(s(s(s(s(s(z))))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6377, 6423])).
% 1.85/2.05 tff(6425,plain,
% 1.85/2.05 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[5014, 6412, 19, 4, 20])).
% 1.85/2.05 tff(6426,plain,
% 1.85/2.05 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[398, 6425])).
% 1.85/2.05 tff(6427,plain,
% 1.85/2.05 (~r(s(z), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2510, 6426, 21])).
% 1.85/2.05 tff(6428,plain,
% 1.85/2.05 (b(s(z), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[608, 6427])).
% 1.85/2.05 tff(6429,plain,
% 1.85/2.05 (~b(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6388, 112, 6412, 6428, 6424])).
% 1.85/2.05 tff(6430,plain,
% 1.85/2.05 (~r(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6400, 6416, 6426])).
% 1.85/2.05 tff(6431,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6404, 78, 15, 6430, 6429])).
% 1.85/2.05 tff(6432,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6433,plain,
% 1.85/2.05 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6432, 20, 4, 19, 2])).
% 1.85/2.05 tff(6434,plain,
% 1.85/2.05 (b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[477, 6433])).
% 1.85/2.05 tff(6435,plain,
% 1.85/2.05 (~b(z, s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[547, 6434, 2, 19])).
% 1.85/2.05 tff(6436,plain,
% 1.85/2.05 (r(z, s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[182, 6435])).
% 1.85/2.05 tff(6437,plain,
% 1.85/2.05 (~r(s(s(s(z))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[503, 6436, 20])).
% 1.85/2.05 tff(6438,plain,
% 1.85/2.05 (b(s(s(s(z))), s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[83, 6437])).
% 1.85/2.05 tff(6439,plain,
% 1.85/2.05 (~r(s(z), s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[170, 6436, 20])).
% 1.85/2.05 tff(6440,plain,
% 1.85/2.05 (b(s(z), s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[99, 6439])).
% 1.85/2.05 tff(6441,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[120, 6440, 6438, 4, 19])).
% 1.85/2.05 tff(6442,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6443,plain,
% 1.85/2.05 (~r(z, s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6442, 19, 4, 2])).
% 1.85/2.05 tff(6444,plain,
% 1.85/2.05 (b(z, s(s(s(z))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[515, 6443])).
% 1.85/2.05 tff(6445,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[4393, 112, 803, 4, 196, 2])).
% 1.85/2.05 tff(6446,plain,((~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)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6447,plain,
% 1.85/2.05 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6446, 6444, 2, 4])).
% 1.85/2.05 tff(6448,plain,
% 1.85/2.05 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[160, 6447])).
% 1.85/2.05 tff(6449,plain,
% 1.85/2.05 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[122, 6448, 19, 4])).
% 1.85/2.05 tff(6450,plain,
% 1.85/2.05 (b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[477, 6449])).
% 1.85/2.05 tff(6451,plain,
% 1.85/2.05 (~b(z, s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[547, 6450, 2, 19])).
% 1.85/2.05 tff(6452,plain,
% 1.85/2.05 (r(z, s(z))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[182, 6451])).
% 1.85/2.05 tff(6453,plain,
% 1.85/2.05 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.05 inference(commutativity,[status(thm)],[])).
% 1.85/2.05 tff(6454,plain,
% 1.85/2.05 ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6336])).
% 1.85/2.05 tff(6455,plain,
% 1.85/2.05 ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.85/2.05 inference(transitivity,[status(thm)],[6454, 6453])).
% 1.85/2.05 tff(6456,plain,
% 1.85/2.05 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6455])).
% 1.85/2.05 tff(6457,plain,
% 1.85/2.05 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6456])).
% 1.85/2.05 tff(6458,plain,
% 1.85/2.05 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6350, 6457])).
% 1.85/2.05 tff(6459,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6460,plain,
% 1.85/2.05 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(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(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6461,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6460])).
% 1.85/2.05 tff(6462,plain,
% 1.85/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6461, 6459])).
% 1.85/2.05 tff(6463,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6464,plain,
% 1.85/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6463, 6462])).
% 1.85/2.05 tff(6465,plain,
% 1.85/2.05 (~b(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6464, 112, 1827, 2, 184])).
% 1.85/2.05 tff(6466,plain,
% 1.85/2.05 (r(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6404, 78, 15, 6465])).
% 1.85/2.05 tff(6467,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.85/2.05 tff(6468,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), 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(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6469,plain,
% 1.85/2.05 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.05 inference(rewrite,[status(thm)],[])).
% 1.85/2.05 tff(6470,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, 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(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6469])).
% 1.85/2.05 tff(6471,plain,
% 1.85/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, 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(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.05 inference(transitivity,[status(thm)],[6470, 6468])).
% 1.85/2.05 tff(6472,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.85/2.05 inference(quant_inst,[status(thm)],[])).
% 1.85/2.05 tff(6473,plain,
% 1.85/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.85/2.05 inference(modus_ponens,[status(thm)],[6472, 6471])).
% 1.85/2.05 tff(6474,plain,
% 1.85/2.05 (~r(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6473, 31, 162, 6467])).
% 1.85/2.05 tff(6475,plain,
% 1.85/2.05 (b(s(s(s(s(s(z))))), z)),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[6404, 78, 15, 6474])).
% 1.85/2.05 tff(6476,plain,
% 1.85/2.05 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[2350, 31, 981, 6467])).
% 1.85/2.05 tff(6477,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.85/2.05 tff(6478,plain,
% 1.85/2.05 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6477])).
% 1.85/2.05 tff(6479,plain,
% 1.85/2.05 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.85/2.05 inference(monotonicity,[status(thm)],[6478])).
% 1.85/2.05 tff(6480,plain,
% 1.85/2.05 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 1.85/2.05 inference(symmetry,[status(thm)],[6479])).
% 1.85/2.05 tff(6481,plain,
% 1.85/2.05 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.85/2.05 inference(transitivity,[status(thm)],[221, 6480, 215])).
% 1.85/2.05 tff(6482,plain,
% 1.85/2.05 ($false),
% 1.85/2.05 inference(unit_resolution,[status(thm)],[969, 6481])).
% 1.85/2.05 tff(6483,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.05 tff(6484,plain,
% 1.85/2.05 (((~![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))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6485,plain,
% 1.85/2.06 ((~![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))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6486,plain,
% 1.85/2.06 ((~![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)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6485, 6484])).
% 1.85/2.06 tff(6487,plain,
% 1.85/2.06 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6486, 78, 6483, 6476])).
% 1.85/2.06 tff(6488,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6489,plain,
% 1.85/2.06 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6490,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6489])).
% 1.85/2.06 tff(6491,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6490, 6488])).
% 1.85/2.06 tff(6492,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6493,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 1.85/2.06 tff(6494,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6493, 112, 2, 3460, 184, 6475, 6487])).
% 1.85/2.06 tff(6495,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(6496,plain,
% 1.85/2.06 (~r(s(s(s(s(z)))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6495, 6467, 184, 162, 2])).
% 1.85/2.06 tff(6497,plain,
% 1.85/2.06 (b(s(s(s(s(z)))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[1733, 6496])).
% 1.85/2.06 tff(6498,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6499,plain,
% 1.85/2.06 (((~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))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6500,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6499])).
% 1.85/2.06 tff(6501,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6500, 6498])).
% 1.85/2.06 tff(6502,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6503,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6502, 6501])).
% 1.85/2.06 tff(6504,plain,
% 1.85/2.06 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6503, 31, 3, 6467])).
% 1.85/2.06 tff(6505,plain,
% 1.85/2.06 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[235, 6504])).
% 1.85/2.06 tff(6506,plain,
% 1.85/2.06 (b(s(s(s(s(s(z))))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6404, 78, 15, 1786])).
% 1.85/2.06 tff(6507,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.85/2.06 tff(6508,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6509,plain,
% 1.85/2.06 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6510,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6509])).
% 1.85/2.06 tff(6511,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6510, 6508])).
% 1.85/2.06 tff(6512,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6513,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6512, 6511])).
% 1.85/2.06 tff(6514,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6513, 112, 859, 803, 6507, 6506])).
% 1.85/2.06 tff(6515,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | r(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(6516,plain,
% 1.85/2.06 ($false),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6515, 6505, 6474, 803, 3286])).
% 1.85/2.06 tff(6517,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.06 tff(6518,plain,
% 1.85/2.06 (~r(s(s(s(z))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6517, 6467, 162, 803])).
% 1.85/2.06 tff(6519,plain,
% 1.85/2.06 (b(s(s(s(z))), s(z))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[83, 6518])).
% 1.85/2.06 tff(6520,plain,
% 1.85/2.06 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6002, 4, 803, 162, 6519])).
% 1.85/2.06 tff(6521,plain,
% 1.85/2.06 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[160, 6520])).
% 1.85/2.06 tff(6522,plain,
% 1.85/2.06 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[5089, 408, 162])).
% 1.85/2.06 tff(6523,plain,
% 1.85/2.06 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[398, 6522])).
% 1.85/2.06 tff(6524,plain,
% 1.85/2.06 (~b(s(s(s(s(s(z))))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6464, 112, 6523, 2, 184])).
% 1.85/2.06 tff(6525,plain,
% 1.85/2.06 (r(s(s(s(s(s(z))))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6404, 78, 15, 6524])).
% 1.85/2.06 tff(6526,plain,
% 1.85/2.06 (~b(s(s(s(z))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[4333, 6523, 4, 803])).
% 1.85/2.06 tff(6527,plain,
% 1.85/2.06 (r(s(s(s(z))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[527, 6526])).
% 1.85/2.06 tff(6528,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6529,plain,
% 1.85/2.06 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6530,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6529])).
% 1.85/2.06 tff(6531,plain,
% 1.85/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6530, 6528])).
% 1.85/2.06 tff(6532,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6533,plain,
% 1.85/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6532, 6531])).
% 1.85/2.06 tff(6534,plain,
% 1.85/2.06 (~b(s(s(s(s(z)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6533, 112, 1827, 2, 1273])).
% 1.85/2.06 tff(6535,plain,
% 1.85/2.06 (r(s(s(s(s(z)))), z)),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[917, 78, 224, 6534])).
% 1.85/2.06 tff(6536,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6537,plain,
% 1.85/2.06 (((~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)))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6538,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6537])).
% 1.85/2.06 tff(6539,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6538, 6536])).
% 1.85/2.06 tff(6540,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6541,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6540, 6539])).
% 1.85/2.06 tff(6542,plain,
% 1.85/2.06 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6541, 31, 612, 6535])).
% 1.85/2.06 tff(6543,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6544,plain,
% 1.85/2.06 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(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))))))),
% 1.85/2.06 inference(rewrite,[status(thm)],[])).
% 1.85/2.06 tff(6545,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.85/2.06 inference(monotonicity,[status(thm)],[6544])).
% 1.85/2.06 tff(6546,plain,
% 1.85/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.06 inference(transitivity,[status(thm)],[6545, 6543])).
% 1.85/2.06 tff(6547,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.06 inference(quant_inst,[status(thm)],[])).
% 1.85/2.06 tff(6548,plain,
% 1.85/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.85/2.06 inference(modus_ponens,[status(thm)],[6547, 6546])).
% 1.85/2.06 tff(6549,plain,
% 1.85/2.06 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.06 inference(unit_resolution,[status(thm)],[6548, 31, 612, 6466])).
% 1.85/2.07 tff(6550,plain,
% 1.85/2.07 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[235, 6549])).
% 1.85/2.07 tff(6551,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.85/2.07 tff(6552,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6553,plain,
% 1.85/2.07 (((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6554,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6553])).
% 1.85/2.07 tff(6555,plain,
% 1.85/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6554, 6552])).
% 1.85/2.07 tff(6556,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6557,plain,
% 1.85/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6556, 6555])).
% 1.85/2.07 tff(6558,plain,
% 1.85/2.07 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6557, 112, 1273, 6507, 6551])).
% 1.85/2.07 tff(6559,plain,
% 1.85/2.07 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6558, 184])).
% 1.85/2.07 tff(6560,plain,
% 1.85/2.07 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6486, 78, 6483, 6559])).
% 1.85/2.07 tff(6561,plain,
% 1.85/2.07 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6464, 112, 1827, 2])).
% 1.85/2.07 tff(6562,plain,
% 1.85/2.07 (~b(s(s(s(s(s(z))))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6561, 184])).
% 1.85/2.07 tff(6563,plain,
% 1.85/2.07 (r(s(s(s(s(s(z))))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6404, 78, 15, 6562])).
% 1.85/2.07 tff(6564,plain,
% 1.85/2.07 (((~![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(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6565,plain,
% 1.85/2.07 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), 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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6566,plain,
% 1.85/2.07 (((~![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(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))), s(s(s(s(z))))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6565])).
% 1.85/2.07 tff(6567,plain,
% 1.85/2.07 (((~![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(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6566, 6564])).
% 1.85/2.07 tff(6568,plain,
% 1.85/2.07 ((~![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(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6569,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6568, 6567])).
% 1.85/2.07 tff(6570,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6569, 31, 6563, 6535, 6560])).
% 1.85/2.07 tff(6571,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6572,plain,
% 1.85/2.07 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6571, 1273, 2, 184, 1827, 6550])).
% 1.85/2.07 tff(6573,plain,
% 1.85/2.07 ((s(s(s(z))) = s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[4506, 78, 6572])).
% 1.85/2.07 tff(6574,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6573, 6542, 4496])).
% 1.85/2.07 tff(6575,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6576,plain,
% 1.85/2.07 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6575, 6527, 6523, 2, 184])).
% 1.85/2.07 tff(6577,plain,
% 1.85/2.07 (elem!1 = s(s(s(s(elem!1))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[1073, 6333, 127, 6330])).
% 1.85/2.07 tff(6578,plain,
% 1.85/2.07 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6577])).
% 1.85/2.07 tff(6579,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.85/2.07 tff(6580,plain,
% 1.85/2.07 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6579, 6578])).
% 1.85/2.07 tff(6581,assumption,(~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.85/2.07 tff(6582,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6581, 6580])).
% 1.85/2.07 tff(6583,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6584,plain,
% 1.85/2.07 (~b(s(s(s(s(z)))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6583, 6576])).
% 1.85/2.07 tff(6585,plain,
% 1.85/2.07 (~(s(s(s(s(z)))) = elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1330, 6330])).
% 1.85/2.07 tff(6586,plain,
% 1.85/2.07 (b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1335, 6585])).
% 1.85/2.07 tff(6587,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), elem!1)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6586, 6584])).
% 1.85/2.07 tff(6588,plain,
% 1.85/2.07 ((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1343, 6330])).
% 1.85/2.07 tff(6589,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6588, 6587])).
% 1.85/2.07 tff(6590,plain,
% 1.85/2.07 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[5302, 6523, 162, 4, 2, 803])).
% 1.85/2.07 tff(6591,plain,
% 1.85/2.07 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6039, 271, 803, 101, 4])).
% 1.85/2.07 tff(6592,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[404, 6591, 2474, 402])).
% 1.85/2.07 tff(6593,plain,((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(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6594,plain,
% 1.85/2.07 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6593, 6590, 803, 6519, 4])).
% 1.85/2.07 tff(6595,plain,
% 1.85/2.07 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.85/2.07 inference(symmetry,[status(thm)],[4798])).
% 1.85/2.07 tff(6596,plain,
% 1.85/2.07 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6330])).
% 1.85/2.07 tff(6597,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6596])).
% 1.85/2.07 tff(6598,plain,
% 1.85/2.07 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6577, 6597])).
% 1.85/2.07 tff(6599,plain,
% 1.85/2.07 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6598])).
% 1.85/2.07 tff(6600,plain,
% 1.85/2.07 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6596])).
% 1.85/2.07 tff(6601,plain,
% 1.85/2.07 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6600])).
% 1.85/2.07 tff(6602,plain,
% 1.85/2.07 ((s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.85/2.07 inference(transitivity,[status(thm)],[6601, 6599, 6595])).
% 1.85/2.07 tff(6603,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[258, 6602])).
% 1.85/2.07 tff(6604,assumption,(~(s(s(s(s(s(elem!1))))) = elem!1)), introduced(assumption)).
% 1.85/2.07 tff(6605,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6604, 6603])).
% 1.85/2.07 tff(6606,plain,((s(s(s(s(s(elem!1))))) = elem!1) | (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6607,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6606, 258])).
% 1.85/2.07 tff(6608,assumption,(s(s(s(s(s(elem!1))))) = elem!1), introduced(assumption)).
% 1.85/2.07 tff(6609,plain,
% 1.85/2.07 (elem!1 = s(s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6608])).
% 1.85/2.07 tff(6610,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[5261, 6609])).
% 1.85/2.07 tff(6611,plain,((~(s(s(s(s(s(elem!1))))) = elem!1)) | (elem!1 = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6612,plain,
% 1.85/2.07 (elem!1 = s(s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6611, 6607])).
% 1.85/2.07 tff(6613,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = elem!1),
% 1.85/2.07 inference(symmetry,[status(thm)],[6612])).
% 1.85/2.07 tff(6614,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6613, 1073, 6333, 127, 6330])).
% 1.85/2.07 tff(6615,plain,
% 1.85/2.07 (r(s(s(s(z))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6614])).
% 1.85/2.07 tff(6616,plain,
% 1.85/2.07 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6615])).
% 1.85/2.07 tff(6617,plain,
% 1.85/2.07 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[1, 6616])).
% 1.85/2.07 tff(6618,plain,
% 1.85/2.07 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[267, 258])).
% 1.85/2.07 tff(6619,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6335])).
% 1.85/2.07 tff(6620,plain,
% 1.85/2.07 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6619, 251])).
% 1.85/2.07 tff(6621,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6620])).
% 1.85/2.07 tff(6622,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(symmetry,[status(thm)],[6621])).
% 1.85/2.07 tff(6623,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[982, 6622])).
% 1.85/2.07 tff(6624,plain,
% 1.85/2.07 (~r(s(s(s(s(z)))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[990, 982, 408])).
% 1.85/2.07 tff(6625,plain,
% 1.85/2.07 (b(s(s(s(s(z)))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[1733, 6624])).
% 1.85/2.07 tff(6626,plain,
% 1.85/2.07 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2440, 6625, 101, 102])).
% 1.85/2.07 tff(6627,plain,
% 1.85/2.07 (~r(s(s(s(s(z)))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[2954, 6626, 730])).
% 1.85/2.07 tff(6628,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6627, 6623])).
% 1.85/2.07 tff(6629,plain,((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6630,plain,
% 1.85/2.07 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6629, 6618, 982, 101, 102, 408])).
% 1.85/2.07 tff(6631,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6630, 6617])).
% 1.85/2.07 tff(6632,plain,((~(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(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6633,plain,
% 1.85/2.07 (~b(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6632, 6594, 6589, 6519, 6521, 408])).
% 1.85/2.07 tff(6634,plain,
% 1.85/2.07 (r(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[99, 6633])).
% 1.85/2.07 tff(6635,plain,
% 1.85/2.07 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[93, 6634, 6521])).
% 1.85/2.07 tff(6636,plain,
% 1.85/2.07 (b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[477, 6635])).
% 1.85/2.07 tff(6637,plain,
% 1.85/2.07 (~b(s(z), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[3569, 6636, 6523, 2])).
% 1.85/2.07 tff(6638,plain,
% 1.85/2.07 (r(s(z), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[608, 6637])).
% 1.85/2.07 tff(6639,plain,
% 1.85/2.07 (((~![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(z))))), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6640,plain,
% 1.85/2.07 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6641,plain,
% 1.85/2.07 (((~![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(z))))), z)) | (~r(s(z), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.85/2.07 inference(monotonicity,[status(thm)],[6640])).
% 1.85/2.07 tff(6642,plain,
% 1.85/2.07 (((~![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(z))))), z)) | (~r(s(z), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.07 inference(transitivity,[status(thm)],[6641, 6639])).
% 1.85/2.07 tff(6643,plain,
% 1.85/2.07 ((~![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(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.07 inference(quant_inst,[status(thm)],[])).
% 1.85/2.07 tff(6644,plain,
% 1.85/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.85/2.07 inference(modus_ponens,[status(thm)],[6643, 6642])).
% 1.85/2.07 tff(6645,plain,
% 1.85/2.07 ($false),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6644, 31, 6638, 6525, 6467])).
% 1.85/2.07 tff(6646,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.07 tff(6647,plain,
% 1.85/2.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[6646, 4, 2, 803, 6467, 184, 162])).
% 1.85/2.07 tff(6648,plain,
% 1.85/2.07 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[429, 6647])).
% 1.85/2.07 tff(6649,plain,
% 1.85/2.07 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[5765, 112, 803, 6519, 6648, 4])).
% 1.85/2.07 tff(6650,plain,
% 1.85/2.07 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[398, 6649])).
% 1.85/2.07 tff(6651,plain,
% 1.85/2.07 (~b(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[120, 6648, 6519, 4])).
% 1.85/2.07 tff(6652,plain,
% 1.85/2.07 (r(s(z), s(s(s(z))))),
% 1.85/2.07 inference(unit_resolution,[status(thm)],[99, 6651])).
% 1.85/2.07 tff(6653,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.85/2.07 tff(6654,plain,
% 1.85/2.07 (((~![X0: $i, 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(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(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6655,plain,
% 1.85/2.07 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.07 inference(rewrite,[status(thm)],[])).
% 1.85/2.07 tff(6656,plain,
% 1.85/2.07 (((~![X0: $i, 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(s(z))))), s(s(s(z))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6655])).
% 1.85/2.08 tff(6657,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), 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(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6656, 6654])).
% 1.85/2.08 tff(6658,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6659,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6658, 6657])).
% 1.85/2.08 tff(6660,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6659, 31, 85, 6653, 6467])).
% 1.85/2.08 tff(6661,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6662,plain,
% 1.85/2.08 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6661, 6652, 6467])).
% 1.85/2.08 tff(6663,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[235, 6662])).
% 1.85/2.08 tff(6664,plain,
% 1.85/2.08 (~b(s(s(s(z))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6515, 6474, 803, 6663])).
% 1.85/2.08 tff(6665,plain,
% 1.85/2.08 (r(s(s(s(z))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[527, 6664])).
% 1.85/2.08 tff(6666,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[693, 6665, 6650, 6521])).
% 1.85/2.08 tff(6667,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6668,plain,
% 1.85/2.08 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6667, 6467, 162, 803, 2, 184])).
% 1.85/2.08 tff(6669,plain,
% 1.85/2.08 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[646, 6668])).
% 1.85/2.08 tff(6670,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6671,plain,
% 1.85/2.08 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6672,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6671])).
% 1.85/2.08 tff(6673,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6672, 6670])).
% 1.85/2.08 tff(6674,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6675,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6674, 6673])).
% 1.85/2.08 tff(6676,plain,
% 1.85/2.08 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6675, 112, 803, 196, 184, 6475])).
% 1.85/2.08 tff(6677,plain,
% 1.85/2.08 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[235, 6676])).
% 1.85/2.08 tff(6678,plain,
% 1.85/2.08 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[620, 612, 249])).
% 1.85/2.08 tff(6679,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.85/2.08 tff(6680,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6681,plain,
% 1.85/2.08 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(s(z))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6682,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(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(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6681])).
% 1.85/2.08 tff(6683,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(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(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6682, 6680])).
% 1.85/2.08 tff(6684,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(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(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6685,plain,
% 1.85/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6684, 6683])).
% 1.85/2.08 tff(6686,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6685, 31, 249, 6392, 6653])).
% 1.85/2.08 tff(6687,plain,((~r(s(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(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6688,plain,
% 1.85/2.08 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6687, 6653, 249])).
% 1.85/2.08 tff(6689,plain,
% 1.85/2.08 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6362, 6688])).
% 1.85/2.08 tff(6690,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6354, 6689, 6679])).
% 1.85/2.08 tff(6691,plain,
% 1.85/2.08 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6690, 6338])).
% 1.85/2.08 tff(6692,plain,
% 1.85/2.08 (~b(s(s(s(s(s(z))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6561, 6691])).
% 1.85/2.08 tff(6693,plain,
% 1.85/2.08 (r(s(s(s(s(s(z))))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6404, 78, 15, 6692])).
% 1.85/2.08 tff(6694,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6548, 31, 612, 6693, 6653])).
% 1.85/2.08 tff(6695,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6696,plain,
% 1.85/2.08 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6695, 6350])).
% 1.85/2.08 tff(6697,plain,
% 1.85/2.08 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6696, 612, 2, 249, 6653])).
% 1.85/2.08 tff(6698,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[398, 6697, 6678])).
% 1.85/2.08 tff(6699,plain,((~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6700,plain,
% 1.85/2.08 (~r(s(s(s(z))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6699, 6677, 6669, 2])).
% 1.85/2.08 tff(6701,plain,
% 1.85/2.08 (b(s(s(s(z))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[527, 6700])).
% 1.85/2.08 tff(6702,plain,
% 1.85/2.08 (~r(s(z), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6661, 6677, 6467])).
% 1.85/2.08 tff(6703,plain,
% 1.85/2.08 (b(s(z), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[99, 6702])).
% 1.85/2.08 tff(6704,plain,
% 1.85/2.08 (~b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2981, 112, 6703, 6701, 803, 6519])).
% 1.85/2.08 tff(6705,plain,
% 1.85/2.08 (r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[608, 6704])).
% 1.85/2.08 tff(6706,plain,
% 1.85/2.08 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[5089, 568, 162])).
% 1.85/2.08 tff(6707,plain,
% 1.85/2.08 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[429, 6706])).
% 1.85/2.08 tff(6708,plain,
% 1.85/2.08 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2510, 568, 592])).
% 1.85/2.08 tff(6709,plain,
% 1.85/2.08 (b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[477, 6708])).
% 1.85/2.08 tff(6710,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[4251, 6709, 6707, 101, 196])).
% 1.85/2.08 tff(6711,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6712,plain,
% 1.85/2.08 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6711, 196, 6519, 6705, 162])).
% 1.85/2.08 tff(6713,plain,
% 1.85/2.08 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[398, 6712])).
% 1.85/2.08 tff(6714,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[3957, 112, 6701, 6713, 196, 2])).
% 1.85/2.08 tff(6715,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6716,plain,
% 1.85/2.08 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6715, 6467, 162, 803, 2, 184])).
% 1.85/2.08 tff(6717,plain,
% 1.85/2.08 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[160, 6716])).
% 1.85/2.08 tff(6718,plain,
% 1.85/2.08 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6515, 1371, 803, 6474])).
% 1.85/2.08 tff(6719,plain,
% 1.85/2.08 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[235, 6718])).
% 1.85/2.08 tff(6720,plain,
% 1.85/2.08 (~r(s(z), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6661, 6719, 6467])).
% 1.85/2.08 tff(6721,plain,
% 1.85/2.08 (b(s(z), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[99, 6720])).
% 1.85/2.08 tff(6722,plain,
% 1.85/2.08 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2944, 6721, 6519, 1371, 162, 803])).
% 1.85/2.08 tff(6723,plain,
% 1.85/2.08 (~b(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2981, 112, 6721, 1371, 803, 6519])).
% 1.85/2.08 tff(6724,plain,
% 1.85/2.08 (r(s(z), z)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[608, 6723])).
% 1.85/2.08 tff(6725,plain,
% 1.85/2.08 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[2510, 6724, 568])).
% 1.85/2.08 tff(6726,plain,
% 1.85/2.08 (b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[477, 6725])).
% 1.85/2.08 tff(6727,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6728,plain,
% 1.85/2.08 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6729,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6728])).
% 1.85/2.08 tff(6730,plain,
% 1.85/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.85/2.08 inference(transitivity,[status(thm)],[6729, 6727])).
% 1.85/2.08 tff(6731,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.85/2.08 inference(quant_inst,[status(thm)],[])).
% 1.85/2.08 tff(6732,plain,
% 1.85/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.85/2.08 inference(modus_ponens,[status(thm)],[6731, 6730])).
% 1.85/2.08 tff(6733,plain,
% 1.85/2.08 ($false),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6732, 112, 19, 539, 906, 1273])).
% 1.85/2.08 tff(6734,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.08 tff(6735,plain,
% 1.85/2.08 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6734, 6726, 906, 6707])).
% 1.85/2.08 tff(6736,plain,
% 1.85/2.08 (~b(s(s(s(s(z)))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6583, 6735])).
% 1.85/2.08 tff(6737,plain,
% 1.85/2.08 (r(s(s(s(s(z)))), elem!1)),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6586, 6736])).
% 1.85/2.08 tff(6738,plain,
% 1.85/2.08 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.08 inference(unit_resolution,[status(thm)],[6588, 6737])).
% 1.85/2.08 tff(6739,plain,
% 1.85/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6740,plain,
% 1.85/2.08 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.08 inference(rewrite,[status(thm)],[])).
% 1.85/2.08 tff(6741,plain,
% 1.85/2.08 (((~![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(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.85/2.08 inference(monotonicity,[status(thm)],[6740])).
% 1.85/2.08 tff(6742,plain,
% 1.85/2.08 (((~![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(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6741, 6739])).
% 1.85/2.09 tff(6743,plain,
% 1.85/2.09 ((~![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(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6744,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6743, 6742])).
% 1.85/2.09 tff(6745,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6744, 31, 1, 6738, 6722])).
% 1.85/2.09 tff(6746,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6747,plain,
% 1.85/2.09 (~r(s(s(s(s(elem!1)))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6746, 6717, 6497, 803, 162, 6467])).
% 1.85/2.09 tff(6748,plain,
% 1.85/2.09 (b(s(s(s(s(elem!1)))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[398, 6747])).
% 1.85/2.09 tff(6749,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6464, 112, 6748, 2, 184, 6475])).
% 1.85/2.09 tff(6750,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6751,plain,
% 1.85/2.09 (~r(s(s(s(s(s(z))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6750, 184, 2, 803, 162])).
% 1.85/2.09 tff(6752,plain,
% 1.85/2.09 (b(s(s(s(s(s(z))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6377, 6751])).
% 1.85/2.09 tff(6753,plain,
% 1.85/2.09 (~r(s(s(s(z))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3275, 3, 162])).
% 1.85/2.09 tff(6754,plain,
% 1.85/2.09 (b(s(s(s(z))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[527, 6753])).
% 1.85/2.09 tff(6755,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4333, 1827, 859, 803])).
% 1.85/2.09 tff(6756,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[646, 6755])).
% 1.85/2.09 tff(6757,plain,
% 1.85/2.09 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3970, 6756, 3])).
% 1.85/2.09 tff(6758,plain,
% 1.85/2.09 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[429, 6757])).
% 1.85/2.09 tff(6759,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6760,plain,
% 1.85/2.09 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6761,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6760])).
% 1.85/2.09 tff(6762,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6761, 6759])).
% 1.85/2.09 tff(6763,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6764,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6763, 6762])).
% 1.85/2.09 tff(6765,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6764, 112, 19, 539, 4909, 184])).
% 1.85/2.09 tff(6766,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6767,plain,
% 1.85/2.09 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6766, 6758, 4909, 184])).
% 1.85/2.09 tff(6768,plain,
% 1.85/2.09 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[477, 6767])).
% 1.85/2.09 tff(6769,plain,
% 1.85/2.09 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[39, 6768, 3])).
% 1.85/2.09 tff(6770,plain,
% 1.85/2.09 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[160, 6769])).
% 1.85/2.09 tff(6771,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3957, 112, 859, 1827, 6770, 2])).
% 1.85/2.09 tff(6772,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(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(elem!1)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6773,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6772, 6754, 2, 3, 6752, 184, 803])).
% 1.85/2.09 tff(6774,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[398, 6773])).
% 1.85/2.09 tff(6775,plain,
% 1.85/2.09 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5089, 6774, 162])).
% 1.85/2.09 tff(6776,plain,
% 1.85/2.09 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[429, 6775])).
% 1.85/2.09 tff(6777,plain,
% 1.85/2.09 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6766, 6776, 6752, 184])).
% 1.85/2.09 tff(6778,plain,
% 1.85/2.09 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[477, 6777])).
% 1.85/2.09 tff(6779,plain,
% 1.85/2.09 (~r(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2510, 6778, 6774])).
% 1.85/2.09 tff(6780,plain,
% 1.85/2.09 (b(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[608, 6779])).
% 1.85/2.09 tff(6781,plain,
% 1.85/2.09 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[39, 6778, 3])).
% 1.85/2.09 tff(6782,plain,
% 1.85/2.09 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[160, 6781])).
% 1.85/2.09 tff(6783,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6446, 6782, 803, 2])).
% 1.85/2.09 tff(6784,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[646, 6783])).
% 1.85/2.09 tff(6785,plain,
% 1.85/2.09 (~r(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4155, 6784, 6778])).
% 1.85/2.09 tff(6786,plain,
% 1.85/2.09 (b(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[99, 6785])).
% 1.85/2.09 tff(6787,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2519, 112, 6786, 6754, 803, 6780])).
% 1.85/2.09 tff(6788,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6789,plain,
% 1.85/2.09 (~r(s(s(s(z))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6788, 184, 2, 803, 162])).
% 1.85/2.09 tff(6790,plain,
% 1.85/2.09 (b(s(s(s(z))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[83, 6789])).
% 1.85/2.09 tff(6791,plain,
% 1.85/2.09 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6575, 612, 1827, 2, 184])).
% 1.85/2.09 tff(6792,plain,
% 1.85/2.09 (~b(s(s(s(s(z)))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6583, 6791])).
% 1.85/2.09 tff(6793,plain,
% 1.85/2.09 (r(s(s(s(s(z)))), elem!1)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6586, 6792])).
% 1.85/2.09 tff(6794,plain,
% 1.85/2.09 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6588, 6793])).
% 1.85/2.09 tff(6795,plain,
% 1.85/2.09 (~r(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3767, 612, 162])).
% 1.85/2.09 tff(6796,plain,
% 1.85/2.09 (b(z, s(s(s(s(s(elem!1))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[322, 6795])).
% 1.85/2.09 tff(6797,plain,
% 1.85/2.09 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6632, 3559, 408, 101, 1, 982])).
% 1.85/2.09 tff(6798,plain,
% 1.85/2.09 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[3645, 6797, 408, 101, 249])).
% 1.85/2.09 tff(6799,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[342, 6798, 334, 2, 6797])).
% 1.85/2.09 tff(6800,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(s(s(s(s(elem!1))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[299, 6799, 6797])).
% 1.85/2.09 tff(6801,plain,
% 1.85/2.09 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1911, 6797, 162, 408])).
% 1.85/2.09 tff(6802,plain,
% 1.85/2.09 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[462, 6801])).
% 1.85/2.09 tff(6803,plain,
% 1.85/2.09 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4273, 6802, 101, 3559])).
% 1.85/2.09 tff(6804,plain,
% 1.85/2.09 (r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[386, 6803])).
% 1.85/2.09 tff(6805,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2471, 6804, 6800, 249])).
% 1.85/2.09 tff(6806,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6807,plain,
% 1.85/2.09 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6806, 6796, 6790, 2, 408, 162, 1, 6794])).
% 1.85/2.09 tff(6808,plain,
% 1.85/2.09 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[646, 6807])).
% 1.85/2.09 tff(6809,plain,
% 1.85/2.09 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[5302, 6808, 162, 1827, 2, 803])).
% 1.85/2.09 tff(6810,plain,
% 1.85/2.09 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6593, 6809, 803, 6790, 6808])).
% 1.85/2.09 tff(6811,plain,
% 1.85/2.09 (~b(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6632, 6810, 408, 6790, 1, 6794])).
% 1.85/2.09 tff(6812,plain,
% 1.85/2.09 (r(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[99, 6811])).
% 1.85/2.09 tff(6813,plain,
% 1.85/2.09 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[93, 6812, 1])).
% 1.85/2.09 tff(6814,plain,
% 1.85/2.09 (b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[477, 6813])).
% 1.85/2.09 tff(6815,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6816,plain,
% 1.85/2.09 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6817,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6816])).
% 1.85/2.09 tff(6818,plain,
% 1.85/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6817, 6815])).
% 1.85/2.09 tff(6819,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6820,plain,
% 1.85/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6819, 6818])).
% 1.85/2.09 tff(6821,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6820, 112, 6790, 6814, 6550, 6752, 184])).
% 1.85/2.09 tff(6822,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6823,plain,
% 1.85/2.09 (~r(s(s(s(z))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6822, 408, 1, 184, 803, 162, 1827, 2])).
% 1.85/2.09 tff(6824,plain,
% 1.85/2.09 (b(s(s(s(z))), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[527, 6823])).
% 1.85/2.09 tff(6825,plain,
% 1.85/2.09 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[4333, 6824, 1827, 803])).
% 1.85/2.09 tff(6826,plain,
% 1.85/2.09 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[646, 6825])).
% 1.85/2.09 tff(6827,plain,
% 1.85/2.09 (~r(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[1855, 6826, 408])).
% 1.85/2.09 tff(6828,plain,
% 1.85/2.09 (b(s(z), s(s(s(z))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[99, 6827])).
% 1.85/2.09 tff(6829,plain,
% 1.85/2.09 (~b(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[2981, 112, 6828, 6824, 803, 6790])).
% 1.85/2.09 tff(6830,plain,
% 1.85/2.09 (r(s(z), z)),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[608, 6829])).
% 1.85/2.09 tff(6831,plain,
% 1.85/2.09 (((~![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(z))))), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6832,plain,
% 1.85/2.09 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6833,plain,
% 1.85/2.09 (((~![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(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.85/2.09 inference(monotonicity,[status(thm)],[6832])).
% 1.85/2.09 tff(6834,plain,
% 1.85/2.09 (((~![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(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), 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), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(transitivity,[status(thm)],[6833, 6831])).
% 1.85/2.09 tff(6835,plain,
% 1.85/2.09 ((~![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(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.85/2.09 inference(quant_inst,[status(thm)],[])).
% 1.85/2.09 tff(6836,plain,
% 1.85/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.85/2.09 inference(modus_ponens,[status(thm)],[6835, 6834])).
% 1.85/2.09 tff(6837,plain,
% 1.85/2.09 (~r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[6836, 31, 6830, 6466])).
% 1.85/2.09 tff(6838,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.85/2.09 tff(6839,plain,
% 1.85/2.09 (s(s(s(s(s(z))))) = s(z)),
% 1.85/2.09 inference(symmetry,[status(thm)],[6838])).
% 1.85/2.09 tff(6840,plain,
% 1.85/2.09 ($false),
% 1.85/2.09 inference(unit_resolution,[status(thm)],[226, 6839])).
% 1.85/2.09 tff(6841,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.09 tff(6842,plain,
% 1.85/2.09 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.85/2.09 inference(rewrite,[status(thm)],[])).
% 1.85/2.09 tff(6843,plain,
% 1.85/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6844,plain,
% 1.85/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6843, 6842])).
% 1.85/2.10 tff(6845,plain,
% 1.85/2.10 (b(s(z), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6844, 78, 6841, 6837])).
% 1.85/2.10 tff(6846,plain,
% 1.85/2.10 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2944, 6828, 6790, 6824, 162, 803])).
% 1.85/2.10 tff(6847,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6848,plain,
% 1.85/2.10 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6849,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6848])).
% 1.85/2.10 tff(6850,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6849, 6847])).
% 1.85/2.10 tff(6851,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6852,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6851, 6850])).
% 1.85/2.10 tff(6853,plain,
% 1.85/2.10 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6852, 112, 6828, 6790, 6752, 6845])).
% 1.85/2.10 tff(6854,plain,
% 1.85/2.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(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(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6855,plain,
% 1.85/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6856,plain,
% 1.85/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6855, 6854])).
% 1.85/2.10 tff(6857,plain,
% 1.85/2.10 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6856, 78, 228, 6853])).
% 1.85/2.10 tff(6858,plain,
% 1.85/2.10 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[3221, 6857, 6846])).
% 1.85/2.10 tff(6859,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.85/2.10 tff(6860,plain,
% 1.85/2.10 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.85/2.10 inference(symmetry,[status(thm)],[6859])).
% 1.85/2.10 tff(6861,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6483, 6860])).
% 1.85/2.10 tff(6862,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(6863,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.85/2.10 tff(6864,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1778, 78, 1775, 6863, 6862])).
% 1.85/2.10 tff(6865,plain,(b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(6866,plain,
% 1.85/2.10 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6865, 6858])).
% 1.85/2.10 tff(6867,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6868,plain,
% 1.85/2.10 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(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(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6869,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(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(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6868])).
% 1.85/2.10 tff(6870,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(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(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6869, 6867])).
% 1.85/2.10 tff(6871,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(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(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6872,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6871, 6870])).
% 1.85/2.10 tff(6873,plain,
% 1.85/2.10 (~b(s(s(s(s(z)))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6872, 112, 6866, 6752, 6845])).
% 1.85/2.10 tff(6874,plain,
% 1.85/2.10 (r(s(s(s(s(z)))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[1733, 6873])).
% 1.85/2.10 tff(6875,plain,
% 1.85/2.10 (~r(s(s(s(s(z)))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2940, 31, 162, 6874])).
% 1.85/2.10 tff(6876,plain,
% 1.85/2.10 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[990, 6874, 408])).
% 1.85/2.10 tff(6877,plain,
% 1.85/2.10 (~r(s(s(s(s(z)))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6588, 6876])).
% 1.85/2.10 tff(6878,plain,
% 1.85/2.10 (b(s(s(s(s(z)))), elem!1)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6586, 6877])).
% 1.85/2.10 tff(6879,plain,
% 1.85/2.10 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6583, 6878])).
% 1.85/2.10 tff(6880,plain,
% 1.85/2.10 (~b(s(s(s(s(z)))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6533, 112, 1827, 2, 6879])).
% 1.85/2.10 tff(6881,plain,
% 1.85/2.10 ($false),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[917, 78, 224, 6880, 6875])).
% 1.85/2.10 tff(6882,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.10 tff(6883,plain,
% 1.85/2.10 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6882, 1827, 162, 2, 803, 1, 184])).
% 1.85/2.10 tff(6884,plain,
% 1.85/2.10 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[429, 6883])).
% 1.85/2.10 tff(6885,plain,
% 1.85/2.10 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6766, 6884, 6752, 184])).
% 1.85/2.10 tff(6886,plain,
% 1.85/2.10 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[477, 6885])).
% 1.85/2.10 tff(6887,plain,
% 1.85/2.10 (~r(s(z), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[93, 6886, 1])).
% 1.85/2.10 tff(6888,plain,
% 1.85/2.10 (b(s(z), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[99, 6887])).
% 1.85/2.10 tff(6889,plain,
% 1.85/2.10 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[120, 6888, 6790, 6884])).
% 1.85/2.10 tff(6890,plain,
% 1.85/2.10 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[646, 6889])).
% 1.85/2.10 tff(6891,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6892,plain,
% 1.85/2.10 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6893,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6892])).
% 1.85/2.10 tff(6894,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6893, 6891])).
% 1.85/2.10 tff(6895,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6896,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6895, 6894])).
% 1.85/2.10 tff(6897,plain,
% 1.85/2.10 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6896, 112, 6888, 6790, 6752])).
% 1.85/2.10 tff(6898,plain,
% 1.85/2.10 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[235, 6897])).
% 1.85/2.10 tff(6899,plain,
% 1.85/2.10 (~r(s(s(s(z))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6699, 6898, 6890, 2])).
% 1.85/2.10 tff(6900,plain,
% 1.85/2.10 (b(s(s(s(z))), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[527, 6899])).
% 1.85/2.10 tff(6901,plain,
% 1.85/2.10 (~b(s(z), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[2981, 112, 6888, 6900, 803, 6790])).
% 1.85/2.10 tff(6902,plain,
% 1.85/2.10 (r(s(z), z)),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[608, 6901])).
% 1.85/2.10 tff(6903,plain,
% 1.85/2.10 (~r(s(z), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6836, 31, 6902, 6466])).
% 1.85/2.10 tff(6904,plain,
% 1.85/2.10 (b(s(z), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6844, 78, 6841, 6903])).
% 1.85/2.10 tff(6905,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6906,plain,
% 1.85/2.10 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6907,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 1.85/2.10 inference(monotonicity,[status(thm)],[6906])).
% 1.85/2.10 tff(6908,plain,
% 1.85/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.85/2.10 inference(transitivity,[status(thm)],[6907, 6905])).
% 1.85/2.10 tff(6909,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6910,plain,
% 1.85/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6909, 6908])).
% 1.85/2.10 tff(6911,plain,
% 1.85/2.10 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(unit_resolution,[status(thm)],[6910, 112, 6888, 6790, 6884, 6752, 6904])).
% 1.85/2.10 tff(6912,plain,
% 1.85/2.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(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(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(rewrite,[status(thm)],[])).
% 1.85/2.10 tff(6913,plain,
% 1.85/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 1.85/2.10 inference(quant_inst,[status(thm)],[])).
% 1.85/2.10 tff(6914,plain,
% 1.85/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.85/2.10 inference(modus_ponens,[status(thm)],[6913, 6912])).
% 1.85/2.11 tff(6915,plain,
% 1.85/2.11 ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6914, 78, 6911])).
% 1.85/2.11 tff(6916,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6915, 6458])).
% 1.85/2.11 tff(6917,plain,
% 1.85/2.11 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6852, 112, 6888, 6790, 6752, 6904])).
% 1.85/2.11 tff(6918,plain,
% 1.85/2.11 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6856, 78, 228, 6917])).
% 1.85/2.11 tff(6919,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, 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(z))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6920,plain,
% 1.85/2.11 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(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(s(z))))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6921,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(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(s(elem!1)))), s(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(s(z)))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6920])).
% 1.85/2.11 tff(6922,plain,
% 1.85/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(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(s(elem!1)))), s(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(s(z))))))))),
% 1.85/2.11 inference(transitivity,[status(thm)],[6921, 6919])).
% 1.85/2.11 tff(6923,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(quant_inst,[status(thm)],[])).
% 1.85/2.11 tff(6924,plain,
% 1.85/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.85/2.11 inference(modus_ponens,[status(thm)],[6923, 6922])).
% 1.85/2.11 tff(6925,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6924, 31, 1, 6918, 6916])).
% 1.85/2.11 tff(6926,plain,((~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(6927,plain,
% 1.85/2.11 (~b(s(s(s(s(elem!1)))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6926, 1, 803, 2, 184, 162])).
% 1.85/2.11 tff(6928,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[398, 6927])).
% 1.85/2.11 tff(6929,plain,
% 1.85/2.11 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[5089, 6928, 162])).
% 1.85/2.11 tff(6930,plain,
% 1.85/2.11 (b(s(s(s(s(elem!1)))), s(z))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[429, 6929])).
% 1.85/2.11 tff(6931,plain,
% 1.85/2.11 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6766, 6930, 6752, 184])).
% 1.85/2.11 tff(6932,plain,
% 1.85/2.11 (r(s(z), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[477, 6931])).
% 1.85/2.11 tff(6933,plain,
% 1.85/2.11 (~r(s(z), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2510, 6932, 6928])).
% 1.85/2.11 tff(6934,plain,
% 1.85/2.11 (b(s(z), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[608, 6933])).
% 1.85/2.11 tff(6935,plain,
% 1.85/2.11 (~r(s(s(s(z))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[693, 6928, 1])).
% 1.85/2.11 tff(6936,plain,
% 1.85/2.11 (b(s(s(s(z))), z)),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[527, 6935])).
% 1.85/2.11 tff(6937,plain,
% 1.85/2.11 (~r(s(z), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[93, 6932, 1])).
% 1.85/2.11 tff(6938,plain,
% 1.85/2.11 (b(s(z), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[99, 6937])).
% 1.85/2.11 tff(6939,plain,
% 1.85/2.11 ($false),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[2981, 112, 6938, 6936, 803, 6790, 6934])).
% 1.85/2.11 tff(6940,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.85/2.11 tff(6941,plain,
% 1.85/2.11 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6940, 184, 803, 162, 2])).
% 1.85/2.11 tff(6942,plain,
% 1.85/2.11 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[160, 6941])).
% 1.85/2.11 tff(6943,plain,
% 1.85/2.11 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[6446, 6942, 803, 2])).
% 1.85/2.11 tff(6944,plain,
% 1.85/2.11 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.85/2.11 inference(unit_resolution,[status(thm)],[646, 6943])).
% 1.85/2.11 tff(6945,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6946,plain,
% 1.85/2.11 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(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(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(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)))))))),
% 1.85/2.11 inference(rewrite,[status(thm)],[])).
% 1.85/2.11 tff(6947,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.85/2.11 inference(monotonicity,[status(thm)],[6946])).
% 1.85/2.11 tff(6948,plain,
% 1.85/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(transitivity,[status(thm)],[6947, 6945])).
% 1.95/2.11 tff(6949,plain,
% 1.95/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(6950,plain,
% 1.95/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[6949, 6948])).
% 1.95/2.11 tff(6951,plain,
% 1.95/2.11 (~b(s(s(s(z))), z)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6950, 112, 101, 19, 196, 2])).
% 1.95/2.11 tff(6952,plain,
% 1.95/2.11 (r(s(s(s(z))), z)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[527, 6951])).
% 1.95/2.11 tff(6953,plain,
% 1.95/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(6954,plain,
% 1.95/2.11 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(6955,plain,
% 1.95/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[6954])).
% 1.95/2.11 tff(6956,plain,
% 1.95/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(transitivity,[status(thm)],[6955, 6953])).
% 1.95/2.11 tff(6957,plain,
% 1.95/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(6958,plain,
% 1.95/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[6957, 6956])).
% 1.95/2.11 tff(6959,plain,
% 1.95/2.11 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6958, 112, 19, 196, 4909, 184])).
% 1.95/2.11 tff(6960,plain,
% 1.95/2.11 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[235, 6959])).
% 1.95/2.11 tff(6961,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6699, 6960, 6952, 249, 2])).
% 1.95/2.11 tff(6962,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(6963,plain,
% 1.95/2.11 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6962, 6944, 2, 6942, 6752, 184, 6790])).
% 1.95/2.11 tff(6964,plain,
% 1.95/2.11 (r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[429, 6963])).
% 1.95/2.11 tff(6965,plain,
% 1.95/2.11 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[5089, 6964, 162])).
% 1.95/2.11 tff(6966,plain,
% 1.95/2.11 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[398, 6965])).
% 1.95/2.11 tff(6967,plain,
% 1.95/2.11 (~b(s(s(s(z))), z)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[3957, 112, 6966, 6942, 2])).
% 1.95/2.11 tff(6968,plain,
% 1.95/2.11 (r(s(s(s(z))), z)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[527, 6967])).
% 1.95/2.11 tff(6969,plain,
% 1.95/2.11 (~r(s(z), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1855, 6964, 6944])).
% 1.95/2.11 tff(6970,plain,
% 1.95/2.11 (b(s(z), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[99, 6969])).
% 1.95/2.11 tff(6971,plain,
% 1.95/2.11 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6896, 112, 6970, 6790, 6752])).
% 1.95/2.11 tff(6972,plain,
% 1.95/2.11 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[235, 6971])).
% 1.95/2.11 tff(6973,plain,
% 1.95/2.11 ($false),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6699, 6972, 6968, 6944, 2])).
% 1.95/2.11 tff(6974,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.11 tff(6975,plain,
% 1.95/2.11 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6974, 6452, 6444, 2])).
% 1.95/2.11 tff(6976,plain,
% 1.95/2.11 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6342, 6975])).
% 1.95/2.11 tff(6977,plain,
% 1.95/2.11 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6355, 6976])).
% 1.95/2.11 tff(6978,plain,
% 1.95/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6362, 6977])).
% 1.95/2.11 tff(6979,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(6980,plain,
% 1.95/2.11 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(6981,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.11 inference(monotonicity,[status(thm)],[6980])).
% 1.95/2.11 tff(6982,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(transitivity,[status(thm)],[6981, 6979])).
% 1.95/2.11 tff(6983,plain,
% 1.95/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.95/2.11 inference(quant_inst,[status(thm)],[])).
% 1.95/2.11 tff(6984,plain,
% 1.95/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.11 inference(modus_ponens,[status(thm)],[6983, 6982])).
% 1.95/2.11 tff(6985,plain,
% 1.95/2.11 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6984, 31, 6448, 6978])).
% 1.95/2.11 tff(6986,plain,
% 1.95/2.11 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[235, 6985])).
% 1.95/2.11 tff(6987,plain,
% 1.95/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[3469, 6754, 3, 162, 803])).
% 1.95/2.11 tff(6988,plain,
% 1.95/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[1733, 6987])).
% 1.95/2.11 tff(6989,plain,
% 1.95/2.11 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6734, 6988, 19, 539])).
% 1.95/2.11 tff(6990,plain,
% 1.95/2.11 (~b(s(s(s(s(z)))), elem!1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6583, 6989])).
% 1.95/2.11 tff(6991,plain,
% 1.95/2.11 (r(s(s(s(s(z)))), elem!1)),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6586, 6990])).
% 1.95/2.11 tff(6992,plain,
% 1.95/2.11 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.11 inference(unit_resolution,[status(thm)],[6588, 6991])).
% 1.95/2.11 tff(6993,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(6994,plain,
% 1.95/2.11 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.11 inference(rewrite,[status(thm)],[])).
% 1.95/2.11 tff(6995,plain,
% 1.95/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[6994])).
% 1.95/2.12 tff(6996,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(transitivity,[status(thm)],[6995, 6993])).
% 1.95/2.12 tff(6997,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(6998,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[6997, 6996])).
% 1.95/2.12 tff(6999,plain,
% 1.95/2.12 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6998, 31, 6992, 6392])).
% 1.95/2.12 tff(7000,plain,
% 1.95/2.12 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6865, 6999])).
% 1.95/2.12 tff(7001,plain,
% 1.95/2.12 (((~![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(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7002,plain,
% 1.95/2.12 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(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(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7003,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7002])).
% 1.95/2.12 tff(7004,plain,
% 1.95/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(transitivity,[status(thm)],[7003, 7001])).
% 1.95/2.12 tff(7005,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(7006,plain,
% 1.95/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7005, 7004])).
% 1.95/2.12 tff(7007,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7006, 31, 1, 3213, 6392])).
% 1.95/2.12 tff(7008,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(7009,plain,
% 1.95/2.12 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7008, 6392, 1])).
% 1.95/2.12 tff(7010,assumption,(~b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.95/2.12 tff(7011,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6856, 78, 3207, 228, 7010])).
% 1.95/2.12 tff(7012,plain,(b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(7013,plain,
% 1.95/2.12 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7012, 7009])).
% 1.95/2.12 tff(7014,plain,
% 1.95/2.12 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6517, 3, 162, 803])).
% 1.95/2.12 tff(7015,plain,
% 1.95/2.12 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6377, 7014])).
% 1.95/2.12 tff(7016,plain,
% 1.95/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7017,plain,
% 1.95/2.12 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7018,plain,
% 1.95/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7017])).
% 1.95/2.12 tff(7019,plain,
% 1.95/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.12 inference(transitivity,[status(thm)],[7018, 7016])).
% 1.95/2.12 tff(7020,plain,
% 1.95/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(7021,plain,
% 1.95/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7020, 7019])).
% 1.95/2.12 tff(7022,plain,
% 1.95/2.12 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7021, 112, 6988, 7015, 7013])).
% 1.95/2.12 tff(7023,plain,
% 1.95/2.12 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7022, 7000])).
% 1.95/2.12 tff(7024,plain,
% 1.95/2.12 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1718, 7023])).
% 1.95/2.12 tff(7025,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6744, 31, 1, 6992, 7024])).
% 1.95/2.12 tff(7026,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(7027,plain,
% 1.95/2.12 (~r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7026, 6448, 6978, 19, 6450, 6452, 6444])).
% 1.95/2.12 tff(7028,plain,
% 1.95/2.12 (b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[83, 7027])).
% 1.95/2.12 tff(7029,plain,
% 1.95/2.12 (~b(s(s(s(s(elem!1)))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[5765, 112, 6444, 7028, 19, 4])).
% 1.95/2.12 tff(7030,plain,
% 1.95/2.12 (r(s(s(s(s(elem!1)))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[398, 7029])).
% 1.95/2.12 tff(7031,plain,
% 1.95/2.12 (~r(s(s(s(s(s(z))))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6400, 7030, 6978])).
% 1.95/2.12 tff(7032,plain,
% 1.95/2.12 (~r(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[693, 7030, 6448])).
% 1.95/2.12 tff(7033,plain,
% 1.95/2.12 (b(s(s(s(z))), z)),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[527, 7032])).
% 1.95/2.12 tff(7034,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6515, 7033, 7031, 6986, 6444])).
% 1.95/2.12 tff(7035,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(7036,plain,
% 1.95/2.12 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7035, 4, 2])).
% 1.95/2.12 tff(7037,plain,
% 1.95/2.12 (r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[429, 7036])).
% 1.95/2.12 tff(7038,plain,
% 1.95/2.12 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[6446, 803, 2, 4])).
% 1.95/2.12 tff(7039,plain,
% 1.95/2.12 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[160, 7038])).
% 1.95/2.12 tff(7040,plain,
% 1.95/2.12 (~r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[416, 7039, 7037])).
% 1.95/2.12 tff(7041,plain,
% 1.95/2.12 (b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[83, 7040])).
% 1.95/2.12 tff(7042,plain,
% 1.95/2.12 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1337])).
% 1.95/2.12 tff(7043,plain,
% 1.95/2.12 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.95/2.12 inference(commutativity,[status(thm)],[])).
% 1.95/2.12 tff(7044,plain,
% 1.95/2.12 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.95/2.12 inference(symmetry,[status(thm)],[1311])).
% 1.95/2.12 tff(7045,plain,
% 1.95/2.12 (s(s(s(s(elem!1)))) = elem!1),
% 1.95/2.12 inference(transitivity,[status(thm)],[1323, 253, 7044, 247])).
% 1.95/2.12 tff(7046,plain,
% 1.95/2.12 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7045])).
% 1.95/2.12 tff(7047,plain,
% 1.95/2.12 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(z))))),
% 1.95/2.12 inference(transitivity,[status(thm)],[7046, 7043])).
% 1.95/2.12 tff(7048,plain,
% 1.95/2.12 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7047])).
% 1.95/2.12 tff(7049,assumption,(s(s(s(z))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.95/2.12 tff(7050,plain,
% 1.95/2.12 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7049])).
% 1.95/2.12 tff(7051,plain,
% 1.95/2.12 (s(s(z)) = s(s(s(elem!1)))),
% 1.95/2.12 inference(transitivity,[status(thm)],[56, 7050, 131])).
% 1.95/2.12 tff(7052,plain,
% 1.95/2.12 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7051])).
% 1.95/2.12 tff(7053,plain,
% 1.95/2.12 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.95/2.12 inference(symmetry,[status(thm)],[7052])).
% 1.95/2.12 tff(7054,plain,
% 1.95/2.12 (s(s(s(s(elem!1)))) = s(z)),
% 1.95/2.12 inference(transitivity,[status(thm)],[1323, 253, 7053, 137])).
% 1.95/2.12 tff(7055,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[424, 7054])).
% 1.95/2.12 tff(7056,plain,((~(s(s(s(z))) = s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(7057,plain,
% 1.95/2.12 (~(s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7056, 1264])).
% 1.95/2.12 tff(7058,plain,
% 1.95/2.12 (~(elem!1 = s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7057, 7048])).
% 1.95/2.12 tff(7059,plain,
% 1.95/2.12 (r(elem!1, s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[1337])).
% 1.95/2.12 tff(7060,plain,
% 1.95/2.12 (r(s(s(s(s(elem!1)))), s(z)) <=> r(elem!1, s(z))),
% 1.95/2.12 inference(symmetry,[status(thm)],[7059])).
% 1.95/2.12 tff(7061,plain,
% 1.95/2.12 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[547, 539, 2, 18])).
% 1.95/2.12 tff(7062,plain,
% 1.95/2.12 (r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[429, 7061])).
% 1.95/2.12 tff(7063,plain,
% 1.95/2.12 (r(elem!1, s(z))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7062, 7060])).
% 1.95/2.12 tff(7064,plain,
% 1.95/2.12 (~b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[2543, 803, 18, 2, 539])).
% 1.95/2.12 tff(7065,plain,
% 1.95/2.12 (r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[83, 7064])).
% 1.95/2.12 tff(7066,plain,
% 1.95/2.12 (~r(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1568, 7065, 7063])).
% 1.95/2.12 tff(7067,plain,
% 1.95/2.12 (b(elem!1, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1498, 7066, 7058])).
% 1.95/2.12 tff(7068,plain,
% 1.95/2.12 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7067, 7042])).
% 1.95/2.12 tff(7069,plain,
% 1.95/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7070,plain,
% 1.95/2.12 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7071,plain,
% 1.95/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.95/2.12 inference(monotonicity,[status(thm)],[7070])).
% 1.95/2.12 tff(7072,plain,
% 1.95/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(transitivity,[status(thm)],[7071, 7069])).
% 1.95/2.12 tff(7073,plain,
% 1.95/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))))),
% 1.95/2.12 inference(quant_inst,[status(thm)],[])).
% 1.95/2.12 tff(7074,plain,
% 1.95/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.95/2.12 inference(modus_ponens,[status(thm)],[7073, 7072])).
% 1.95/2.12 tff(7075,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7074, 112, 803, 18, 7068, 2, 539])).
% 1.95/2.12 tff(7076,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(7077,plain,
% 1.95/2.12 ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7076, 6330])).
% 1.95/2.12 tff(7078,plain,
% 1.95/2.12 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7077, 803, 2, 18])).
% 1.95/2.12 tff(7079,plain,
% 1.95/2.12 (r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[477, 7078])).
% 1.95/2.12 tff(7080,plain,
% 1.95/2.12 (~r(s(z), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[93, 7079, 7039])).
% 1.95/2.12 tff(7081,plain,
% 1.95/2.12 (b(s(z), s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[99, 7080])).
% 1.95/2.12 tff(7082,plain,
% 1.95/2.12 ($false),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[1867, 7081, 7041, 18, 803])).
% 1.95/2.12 tff(7083,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.12 tff(7084,plain,
% 1.95/2.12 (~b(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[7083, 18, 2, 4])).
% 1.95/2.12 tff(7085,plain,
% 1.95/2.12 (r(z, s(s(s(z))))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[515, 7084])).
% 1.95/2.12 tff(7086,plain,
% 1.95/2.12 (~r(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[416, 1, 7037])).
% 1.95/2.12 tff(7087,plain,
% 1.95/2.12 (b(s(s(s(z))), s(z))),
% 1.95/2.12 inference(unit_resolution,[status(thm)],[83, 7086])).
% 1.95/2.12 tff(7088,plain,
% 1.95/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, 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(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, 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(z, s(s(s(s(elem!1)))))))),
% 1.95/2.12 inference(rewrite,[status(thm)],[])).
% 1.95/2.12 tff(7089,plain,
% 1.95/2.12 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, 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(z, s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7090,plain,
% 1.95/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, 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(z, s(s(s(s(elem!1))))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7089])).
% 1.95/2.13 tff(7091,plain,
% 1.95/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, 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(z, s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7090, 7088])).
% 1.95/2.13 tff(7092,plain,
% 1.95/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7093,plain,
% 1.95/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, 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(z, s(s(s(s(elem!1))))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7092, 7091])).
% 1.95/2.13 tff(7094,plain,
% 1.95/2.13 (~b(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7093, 112, 102, 18, 4, 2, 539])).
% 1.95/2.13 tff(7095,plain,
% 1.95/2.13 (r(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[608, 7094])).
% 1.95/2.13 tff(7096,plain,
% 1.95/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7097,plain,
% 1.95/2.13 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7098,plain,
% 1.95/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7097])).
% 1.95/2.13 tff(7099,plain,
% 1.95/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7098, 7096])).
% 1.95/2.13 tff(7100,plain,
% 1.95/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7101,plain,
% 1.95/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7100, 7099])).
% 1.95/2.13 tff(7102,plain,
% 1.95/2.13 (~b(s(z), s(s(s(s(z)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7101, 112, 102, 4, 539, 1273])).
% 1.95/2.13 tff(7103,plain,
% 1.95/2.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7104,plain,
% 1.95/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7105,plain,
% 1.95/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7104, 7103])).
% 1.95/2.13 tff(7106,plain,
% 1.95/2.13 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7105, 78, 948])).
% 1.95/2.13 tff(7107,plain,
% 1.95/2.13 (r(s(z), s(s(s(s(z)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7106, 7102])).
% 1.95/2.13 tff(7108,plain,
% 1.95/2.13 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[600, 592, 7037])).
% 1.95/2.13 tff(7109,plain,
% 1.95/2.13 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[398, 7108])).
% 1.95/2.13 tff(7110,plain,
% 1.95/2.13 (~b(s(s(s(s(z)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6533, 112, 7109, 2, 1273])).
% 1.95/2.13 tff(7111,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.95/2.13 tff(7112,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.95/2.13 tff(7113,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[917, 78, 224, 7112, 7111])).
% 1.95/2.13 tff(7114,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7115,plain,
% 1.95/2.13 (r(s(s(s(s(z)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7114, 7110])).
% 1.95/2.13 tff(7116,plain,
% 1.95/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(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(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7117,plain,
% 1.95/2.13 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7118,plain,
% 1.95/2.13 (((~![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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7117])).
% 1.95/2.13 tff(7119,plain,
% 1.95/2.13 (((~![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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7118, 7116])).
% 1.95/2.13 tff(7120,plain,
% 1.95/2.13 ((~![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(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7121,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7120, 7119])).
% 1.95/2.13 tff(7122,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7121, 31, 592, 7115, 7107])).
% 1.95/2.13 tff(7123,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~b(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(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7124,plain,
% 1.95/2.13 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7123, 7095, 2, 102, 4, 539])).
% 1.95/2.13 tff(7125,plain,
% 1.95/2.13 (~b(s(s(s(s(z)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6583, 7124])).
% 1.95/2.13 tff(7126,plain,
% 1.95/2.13 (r(s(s(s(s(z)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6586, 7125])).
% 1.95/2.13 tff(7127,plain,
% 1.95/2.13 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6588, 7126])).
% 1.95/2.13 tff(7128,plain,
% 1.95/2.13 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6632, 7127, 7037, 1, 7087, 102])).
% 1.95/2.13 tff(7129,plain,
% 1.95/2.13 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3642, 7128, 7037, 539])).
% 1.95/2.13 tff(7130,plain,
% 1.95/2.13 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[462, 7129])).
% 1.95/2.13 tff(7131,plain,
% 1.95/2.13 (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[4273, 7130, 7087, 102])).
% 1.95/2.13 tff(7132,plain,
% 1.95/2.13 (r(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2030, 7130, 18, 7087, 7128, 2, 102, 7037])).
% 1.95/2.13 tff(7133,plain,
% 1.95/2.13 (~r(s(s(s(s(s(elem!1))))), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6012, 7132, 1])).
% 1.95/2.13 tff(7134,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[386, 7133, 7131])).
% 1.95/2.13 tff(7135,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7136,plain,
% 1.95/2.13 (~b(s(z), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7135, 539, 18, 2, 1, 4])).
% 1.95/2.13 tff(7137,plain,
% 1.95/2.13 (r(s(z), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[99, 7136])).
% 1.95/2.13 tff(7138,plain,
% 1.95/2.13 (~r(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6380, 7137, 7085])).
% 1.95/2.13 tff(7139,plain,
% 1.95/2.13 (b(s(z), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[608, 7138])).
% 1.95/2.13 tff(7140,plain,
% 1.95/2.13 (~b(s(s(s(s(elem!1)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[3569, 7139, 2, 539])).
% 1.95/2.13 tff(7141,plain,
% 1.95/2.13 (r(s(s(s(s(elem!1)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[398, 7140])).
% 1.95/2.13 tff(7142,plain,
% 1.95/2.13 (~r(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[693, 7141, 1])).
% 1.95/2.13 tff(7143,plain,
% 1.95/2.13 (b(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[527, 7142])).
% 1.95/2.13 tff(7144,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2685, 112, 7143, 7087, 18, 7139])).
% 1.95/2.13 tff(7145,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(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)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7146,plain,
% 1.95/2.13 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7145, 1, 18, 2, 4])).
% 1.95/2.13 tff(7147,plain,
% 1.95/2.13 (r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[477, 7146])).
% 1.95/2.13 tff(7148,plain,
% 1.95/2.13 (~r(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[416, 1, 408])).
% 1.95/2.13 tff(7149,plain,
% 1.95/2.13 (b(s(s(s(z))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[83, 7148])).
% 1.95/2.13 tff(7150,plain,
% 1.95/2.13 (~b(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[5462, 112, 3530, 7149, 18, 673])).
% 1.95/2.13 tff(7151,plain,
% 1.95/2.13 (r(s(s(s(z))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[527, 7150])).
% 1.95/2.13 tff(7152,plain,
% 1.95/2.13 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[693, 7151, 1])).
% 1.95/2.13 tff(7153,plain,
% 1.95/2.13 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[398, 7152])).
% 1.95/2.13 tff(7154,plain,
% 1.95/2.13 (~b(s(s(s(s(z)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2428, 112, 102, 101, 18, 673, 906])).
% 1.95/2.13 tff(7155,plain,
% 1.95/2.13 (r(s(s(s(s(z)))), z)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[917, 78, 224, 7154])).
% 1.95/2.13 tff(7156,plain,
% 1.95/2.13 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[2440, 906, 101, 102])).
% 1.95/2.13 tff(7157,plain,
% 1.95/2.13 (((~![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))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7158,plain,
% 1.95/2.13 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7159,plain,
% 1.95/2.13 (((~![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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7158])).
% 1.95/2.13 tff(7160,plain,
% 1.95/2.13 (((~![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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7159, 7157])).
% 1.95/2.13 tff(7161,plain,
% 1.95/2.13 ((~![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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.95/2.13 inference(quant_inst,[status(thm)],[])).
% 1.95/2.13 tff(7162,plain,
% 1.95/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.95/2.13 inference(modus_ponens,[status(thm)],[7161, 7160])).
% 1.95/2.13 tff(7163,plain,
% 1.95/2.13 ($false),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7162, 31, 612, 7156, 7155])).
% 1.95/2.13 tff(7164,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.13 tff(7165,plain,
% 1.95/2.13 (~b(s(s(s(s(z)))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7164, 7151, 18, 7149, 3530, 673])).
% 1.95/2.13 tff(7166,plain,
% 1.95/2.13 (r(s(s(s(s(z)))), s(z))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[1733, 7165])).
% 1.95/2.13 tff(7167,plain,
% 1.95/2.13 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[990, 7166, 408])).
% 1.95/2.13 tff(7168,plain,
% 1.95/2.13 (~r(s(s(s(s(z)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6588, 7167])).
% 1.95/2.13 tff(7169,plain,
% 1.95/2.13 (b(s(s(s(s(z)))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6586, 7168])).
% 1.95/2.13 tff(7170,plain,
% 1.95/2.13 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6583, 7169])).
% 1.95/2.13 tff(7171,plain,
% 1.95/2.13 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6575, 7170, 2, 7151, 7153])).
% 1.95/2.13 tff(7172,plain,
% 1.95/2.13 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6342, 7171])).
% 1.95/2.13 tff(7173,plain,
% 1.95/2.13 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6355, 7172])).
% 1.95/2.13 tff(7174,plain,
% 1.95/2.13 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[6362, 7173])).
% 1.95/2.13 tff(7175,plain,
% 1.95/2.13 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7008, 7174, 1])).
% 1.95/2.13 tff(7176,plain,
% 1.95/2.13 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.13 inference(unit_resolution,[status(thm)],[7012, 7175])).
% 1.95/2.13 tff(7177,plain,
% 1.95/2.13 (((~![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(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7178,plain,
% 1.95/2.13 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(rewrite,[status(thm)],[])).
% 1.95/2.13 tff(7179,plain,
% 1.95/2.13 (((~![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(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.13 inference(monotonicity,[status(thm)],[7178])).
% 1.95/2.13 tff(7180,plain,
% 1.95/2.13 (((~![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(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.13 inference(transitivity,[status(thm)],[7179, 7177])).
% 1.95/2.14 tff(7181,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7182,plain,
% 1.95/2.14 ((~![X0: $i, 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(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7181, 7180])).
% 1.95/2.14 tff(7183,plain,
% 1.95/2.14 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7182, 31, 21, 7174])).
% 1.95/2.14 tff(7184,plain,
% 1.95/2.14 (b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6844, 78, 6841])).
% 1.95/2.14 tff(7185,plain,
% 1.95/2.14 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7184, 7183])).
% 1.95/2.14 tff(7186,plain,
% 1.95/2.14 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6422, 31, 21, 7174])).
% 1.95/2.14 tff(7187,plain,
% 1.95/2.14 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6377, 7186])).
% 1.95/2.14 tff(7188,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7189,plain,
% 1.95/2.14 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7190,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(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))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7189])).
% 1.95/2.14 tff(7191,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(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))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7190, 7188])).
% 1.95/2.14 tff(7192,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7193,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7192, 7191])).
% 1.95/2.14 tff(7194,plain,
% 1.95/2.14 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7193, 31, 7151, 1, 7174])).
% 1.95/2.14 tff(7195,plain,
% 1.95/2.14 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[235, 7194])).
% 1.95/2.14 tff(7196,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7197,plain,
% 1.95/2.14 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7198,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7197])).
% 1.95/2.14 tff(7199,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7198, 7196])).
% 1.95/2.14 tff(7200,plain,
% 1.95/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7201,plain,
% 1.95/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7200, 7199])).
% 1.95/2.14 tff(7202,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7201, 112, 3530, 7195, 7187, 7185, 7176])).
% 1.95/2.14 tff(7203,plain,((~b(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7204,plain,
% 1.95/2.14 (~b(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7203, 7147, 1, 2, 7037, 18])).
% 1.95/2.14 tff(7205,plain,
% 1.95/2.14 (r(s(z), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[608, 7204])).
% 1.95/2.14 tff(7206,plain,
% 1.95/2.14 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[600, 7205, 7037])).
% 1.95/2.14 tff(7207,plain,
% 1.95/2.14 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[398, 7206])).
% 1.95/2.14 tff(7208,plain,
% 1.95/2.14 (~r(s(z), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[93, 7147, 1])).
% 1.95/2.14 tff(7209,plain,
% 1.95/2.14 (b(s(z), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[99, 7208])).
% 1.95/2.14 tff(7210,plain,
% 1.95/2.14 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6836, 31, 592, 6466])).
% 1.95/2.14 tff(7211,plain,
% 1.95/2.14 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7184, 7210])).
% 1.95/2.14 tff(7212,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7213,plain,
% 1.95/2.14 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7214,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7213])).
% 1.95/2.14 tff(7215,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7214, 7212])).
% 1.95/2.14 tff(7216,plain,
% 1.95/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7217,plain,
% 1.95/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7216, 7215])).
% 1.95/2.14 tff(7218,plain,
% 1.95/2.14 (~b(z, s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7217, 112, 18, 2, 7211, 184])).
% 1.95/2.14 tff(7219,plain,
% 1.95/2.14 (r(z, s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[194, 78, 7218, 17])).
% 1.95/2.14 tff(7220,plain,
% 1.95/2.14 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6644, 31, 592, 6466])).
% 1.95/2.14 tff(7221,plain,
% 1.95/2.14 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6377, 7220])).
% 1.95/2.14 tff(7222,plain,
% 1.95/2.14 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6896, 112, 102, 101, 7221])).
% 1.95/2.14 tff(7223,plain,
% 1.95/2.14 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[235, 7222])).
% 1.95/2.14 tff(7224,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[242, 31, 20, 7223, 7219])).
% 1.95/2.14 tff(7225,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(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(s(elem!1)))))) | (~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7226,plain,
% 1.95/2.14 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7225, 7209, 7085, 7087, 18, 2, 7205, 7207])).
% 1.95/2.14 tff(7227,plain,
% 1.95/2.14 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6342, 7226])).
% 1.95/2.14 tff(7228,plain,
% 1.95/2.14 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6355, 7227])).
% 1.95/2.14 tff(7229,plain,
% 1.95/2.14 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6362, 7228])).
% 1.95/2.14 tff(7230,plain,
% 1.95/2.14 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7008, 7229, 1])).
% 1.95/2.14 tff(7231,plain,
% 1.95/2.14 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7012, 7230])).
% 1.95/2.14 tff(7232,plain,
% 1.95/2.14 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7182, 31, 7147, 7229])).
% 1.95/2.14 tff(7233,plain,
% 1.95/2.14 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7184, 7232])).
% 1.95/2.14 tff(7234,plain,
% 1.95/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(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(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7235,plain,
% 1.95/2.14 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7236,plain,
% 1.95/2.14 (((~![X0: $i, 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(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), 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), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7235])).
% 1.95/2.14 tff(7237,plain,
% 1.95/2.14 (((~![X0: $i, 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(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), 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), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7236, 7234])).
% 1.95/2.14 tff(7238,plain,
% 1.95/2.14 ((~![X0: $i, 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(z))))), s(s(s(s(elem!1)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.14 inference(quant_inst,[status(thm)],[])).
% 1.95/2.14 tff(7239,plain,
% 1.95/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.14 inference(modus_ponens,[status(thm)],[7238, 7237])).
% 1.95/2.14 tff(7240,plain,
% 1.95/2.14 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7239, 31, 7205, 7147, 7229])).
% 1.95/2.14 tff(7241,plain,
% 1.95/2.14 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6377, 7240])).
% 1.95/2.14 tff(7242,plain,
% 1.95/2.14 ($false),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6852, 112, 7209, 7087, 7241, 7233, 7231])).
% 1.95/2.14 tff(7243,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.14 tff(7244,plain,
% 1.95/2.14 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[7243, 18, 2, 4])).
% 1.95/2.14 tff(7245,plain,
% 1.95/2.14 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[160, 7244])).
% 1.95/2.14 tff(7246,plain,
% 1.95/2.14 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6661, 236, 85])).
% 1.95/2.14 tff(7247,plain,
% 1.95/2.14 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.14 inference(unit_resolution,[status(thm)],[6377, 7246])).
% 1.95/2.14 tff(7248,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7249,plain,
% 1.95/2.14 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(rewrite,[status(thm)],[])).
% 1.95/2.14 tff(7250,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.14 inference(monotonicity,[status(thm)],[7249])).
% 1.95/2.14 tff(7251,plain,
% 1.95/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.14 inference(transitivity,[status(thm)],[7250, 7248])).
% 1.95/2.15 tff(7252,plain,
% 1.95/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7253,plain,
% 1.95/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7252, 7251])).
% 1.95/2.15 tff(7254,plain,
% 1.95/2.15 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7253, 112, 2, 6382, 184])).
% 1.95/2.15 tff(7255,plain,
% 1.95/2.15 (~b(s(s(s(s(s(z))))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7254, 7247])).
% 1.95/2.15 tff(7256,plain,
% 1.95/2.15 (r(s(s(s(s(s(z))))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6404, 78, 15, 7255])).
% 1.95/2.15 tff(7257,plain,
% 1.95/2.15 (((~![X0: $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))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7258,plain,
% 1.95/2.15 (((~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))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7259,plain,
% 1.95/2.15 (((~![X0: $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)))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7258])).
% 1.95/2.15 tff(7260,plain,
% 1.95/2.15 (((~![X0: $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))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7259, 7257])).
% 1.95/2.15 tff(7261,plain,
% 1.95/2.15 ((~![X0: $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)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7262,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7261, 7260])).
% 1.95/2.15 tff(7263,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7262, 31, 20, 7256, 236])).
% 1.95/2.15 tff(7264,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(z), 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))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7265,plain,
% 1.95/2.15 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7264, 85, 2, 7085, 4, 7245])).
% 1.95/2.15 tff(7266,plain,
% 1.95/2.15 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6342, 7265])).
% 1.95/2.15 tff(7267,plain,
% 1.95/2.15 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6355, 7266])).
% 1.95/2.15 tff(7268,plain,
% 1.95/2.15 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6362, 7267])).
% 1.95/2.15 tff(7269,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(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(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7270,plain,
% 1.95/2.15 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(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(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7271,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(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(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7270])).
% 1.95/2.15 tff(7272,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(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(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7271, 7269])).
% 1.95/2.15 tff(7273,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7274,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7273, 7272])).
% 1.95/2.15 tff(7275,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7274, 31, 408, 6392, 6467])).
% 1.95/2.15 tff(7276,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7277,plain,
% 1.95/2.15 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7276, 7268, 7037])).
% 1.95/2.15 tff(7278,plain,
% 1.95/2.15 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6377, 7277])).
% 1.95/2.15 tff(7279,plain,
% 1.95/2.15 (~r(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6380, 85, 7085])).
% 1.95/2.15 tff(7280,plain,
% 1.95/2.15 (b(s(z), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[608, 7279])).
% 1.95/2.15 tff(7281,plain,
% 1.95/2.15 (~b(s(s(s(s(s(z))))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6388, 112, 18, 7280, 7278])).
% 1.95/2.15 tff(7282,plain,
% 1.95/2.15 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7182, 31, 21, 6392])).
% 1.95/2.15 tff(7283,plain,
% 1.95/2.15 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7184, 7282])).
% 1.95/2.15 tff(7284,plain,
% 1.95/2.15 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6422, 31, 21, 6392])).
% 1.95/2.15 tff(7285,plain,
% 1.95/2.15 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6377, 7284])).
% 1.95/2.15 tff(7286,plain,
% 1.95/2.15 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6998, 31, 982, 6392])).
% 1.95/2.15 tff(7287,plain,
% 1.95/2.15 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[4915, 112, 18, 673, 6625, 4909, 4908])).
% 1.95/2.15 tff(7288,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6865, 7287, 7286])).
% 1.95/2.15 tff(7289,plain,((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7290,plain,
% 1.95/2.15 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7289, 7285, 673, 18, 7283, 6392, 7037])).
% 1.95/2.15 tff(7291,plain,
% 1.95/2.15 (~r(s(s(s(s(z)))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6588, 7290])).
% 1.95/2.15 tff(7292,plain,
% 1.95/2.15 (b(s(s(s(s(z)))), elem!1)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6586, 7291])).
% 1.95/2.15 tff(7293,plain,
% 1.95/2.15 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6583, 7292])).
% 1.95/2.15 tff(7294,plain,
% 1.95/2.15 (~b(s(s(s(s(s(z))))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6388, 112, 18, 673, 7285])).
% 1.95/2.15 tff(7295,plain,
% 1.95/2.15 (r(s(s(s(s(s(z))))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6404, 78, 15, 7294])).
% 1.95/2.15 tff(7296,plain,
% 1.95/2.15 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6400, 7295, 6392])).
% 1.95/2.15 tff(7297,plain,
% 1.95/2.15 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[398, 7296])).
% 1.95/2.15 tff(7298,plain,
% 1.95/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7299,plain,
% 1.95/2.15 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(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(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7300,plain,
% 1.95/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7299])).
% 1.95/2.15 tff(7301,plain,
% 1.95/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7300, 7298])).
% 1.95/2.15 tff(7302,plain,
% 1.95/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7303,plain,
% 1.95/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), z))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7302, 7301])).
% 1.95/2.15 tff(7304,plain,
% 1.95/2.15 (~b(s(s(s(s(z)))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7303, 112, 4, 7297, 7245, 2, 7293])).
% 1.95/2.15 tff(7305,plain,
% 1.95/2.15 (r(s(s(s(s(z)))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7114, 7304])).
% 1.95/2.15 tff(7306,plain,
% 1.95/2.15 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1294, 112, 4, 7245, 7293])).
% 1.95/2.15 tff(7307,plain,
% 1.95/2.15 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[1718, 7306])).
% 1.95/2.15 tff(7308,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7309,plain,
% 1.95/2.15 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7310,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.95/2.15 inference(monotonicity,[status(thm)],[7309])).
% 1.95/2.15 tff(7311,plain,
% 1.95/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.95/2.15 inference(transitivity,[status(thm)],[7310, 7308])).
% 1.95/2.15 tff(7312,plain,
% 1.95/2.15 ((~![X0: $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)))),
% 1.95/2.15 inference(quant_inst,[status(thm)],[])).
% 1.95/2.15 tff(7313,plain,
% 1.95/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.95/2.15 inference(modus_ponens,[status(thm)],[7312, 7311])).
% 1.95/2.15 tff(7314,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7313, 31, 7085, 7307, 7305])).
% 1.95/2.15 tff(7315,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7316,plain,
% 1.95/2.15 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7315, 7280, 2, 4, 18, 7268])).
% 1.95/2.15 tff(7317,plain,
% 1.95/2.15 (b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[477, 7316])).
% 1.95/2.15 tff(7318,plain,
% 1.95/2.15 (~b(s(s(s(s(elem!1)))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[3569, 7317, 2, 7280])).
% 1.95/2.15 tff(7319,plain,
% 1.95/2.15 (r(s(s(s(s(elem!1)))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[398, 7318])).
% 1.95/2.15 tff(7320,plain,
% 1.95/2.15 (~r(s(s(s(s(s(z))))), z)),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6400, 7319, 7268])).
% 1.95/2.15 tff(7321,plain,
% 1.95/2.15 ($false),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[6404, 78, 15, 7320, 7281])).
% 1.95/2.15 tff(7322,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.15 tff(7323,plain,
% 1.95/2.15 (~r(s(z), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[7322, 18, 2, 4])).
% 1.95/2.15 tff(7324,plain,
% 1.95/2.15 (b(s(z), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[99, 7323])).
% 1.95/2.15 tff(7325,plain,
% 1.95/2.15 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[4595, 112, 7324, 4, 7245])).
% 1.95/2.15 tff(7326,plain,
% 1.95/2.15 (r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[477, 7325])).
% 1.95/2.15 tff(7327,plain,
% 1.95/2.15 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[202, 112, 4, 7245, 184])).
% 1.95/2.15 tff(7328,plain,
% 1.95/2.15 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[235, 7327])).
% 1.95/2.15 tff(7329,plain,
% 1.95/2.15 (~r(z, s(s(s(s(s(z))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[242, 31, 7085, 7328])).
% 1.95/2.15 tff(7330,plain,
% 1.95/2.15 (b(z, s(s(s(s(s(z))))))),
% 1.95/2.15 inference(unit_resolution,[status(thm)],[194, 78, 17, 7329])).
% 1.95/2.15 tff(7331,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.95/2.15 tff(7332,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.95/2.15 tff(7333,plain,
% 1.95/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7334,plain,
% 1.95/2.15 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(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(s(s(elem!1)))), s(s(s(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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.95/2.15 inference(rewrite,[status(thm)],[])).
% 1.95/2.15 tff(7335,plain,
% 1.95/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7334])).
% 1.95/2.16 tff(7336,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7335, 7333])).
% 1.95/2.16 tff(7337,plain,
% 1.95/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7338,plain,
% 1.95/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7337, 7336])).
% 1.95/2.16 tff(7339,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7338, 112, 4, 196, 2, 184, 7332, 7331])).
% 1.95/2.16 tff(7340,plain,((~b(s(s(s(s(elem!1)))), s(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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7341,plain,
% 1.95/2.16 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7340, 184, 7245, 2, 4, 7330])).
% 1.95/2.16 tff(7342,plain,
% 1.95/2.16 ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6914, 78])).
% 1.95/2.16 tff(7343,plain,
% 1.95/2.16 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7342, 7341, 6458])).
% 1.95/2.16 tff(7344,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.95/2.16 tff(7345,assumption,(r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.95/2.16 tff(7346,plain,
% 1.95/2.16 (((~![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(z))) | (~r(s(s(s(s(elem!1)))), 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(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7347,plain,
% 1.95/2.16 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~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(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7348,plain,
% 1.95/2.16 (((~![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(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(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(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7347])).
% 1.95/2.16 tff(7349,plain,
% 1.95/2.16 (((~![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(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(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(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7348, 7346])).
% 1.95/2.16 tff(7350,plain,
% 1.95/2.16 ((~![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(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7351,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7350, 7349])).
% 1.95/2.16 tff(7352,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7351, 31, 408, 7345, 7344])).
% 1.95/2.16 tff(7353,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7354,plain,
% 1.95/2.16 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7353, 7343, 7037])).
% 1.95/2.16 tff(7355,plain,
% 1.95/2.16 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7184, 7354])).
% 1.95/2.16 tff(7356,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7357,plain,
% 1.95/2.16 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7358,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7357])).
% 1.95/2.16 tff(7359,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7358, 7356])).
% 1.95/2.16 tff(7360,plain,
% 1.95/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7361,plain,
% 1.95/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7360, 7359])).
% 1.95/2.16 tff(7362,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7361, 112, 7324, 18, 7245, 2, 7355, 184, 7330])).
% 1.95/2.16 tff(7363,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7364,plain,
% 1.95/2.16 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7363, 18, 2, 4])).
% 1.95/2.16 tff(7365,plain,
% 1.95/2.16 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6342, 7364])).
% 1.95/2.16 tff(7366,plain,
% 1.95/2.16 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6355, 7365])).
% 1.95/2.16 tff(7367,plain,
% 1.95/2.16 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6362, 7366])).
% 1.95/2.16 tff(7368,plain,
% 1.95/2.16 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6844, 78, 6841, 7282])).
% 1.95/2.16 tff(7369,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7370,plain,
% 1.95/2.16 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7371,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7370])).
% 1.95/2.16 tff(7372,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7371, 7369])).
% 1.95/2.16 tff(7373,plain,
% 1.95/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7374,plain,
% 1.95/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7373, 7372])).
% 1.95/2.16 tff(7375,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7374, 112, 18, 7285, 7368, 7331])).
% 1.95/2.16 tff(7376,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7377,plain,
% 1.95/2.16 (~b(z, s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7376, 7367, 7326, 18])).
% 1.95/2.16 tff(7378,plain,
% 1.95/2.16 (r(z, s(s(s(s(s(z))))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[194, 78, 7377, 17])).
% 1.95/2.16 tff(7379,plain,
% 1.95/2.16 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7276, 7367, 7037])).
% 1.95/2.16 tff(7380,plain,
% 1.95/2.16 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6377, 7379])).
% 1.95/2.16 tff(7381,plain,
% 1.95/2.16 (~b(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7315, 7367, 2, 4, 18, 7326])).
% 1.95/2.16 tff(7382,plain,
% 1.95/2.16 (r(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[608, 7381])).
% 1.95/2.16 tff(7383,plain,
% 1.95/2.16 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[600, 7382, 7037])).
% 1.95/2.16 tff(7384,plain,
% 1.95/2.16 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[398, 7383])).
% 1.95/2.16 tff(7385,plain,
% 1.95/2.16 (~b(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4419, 112, 4, 7384, 7245, 2])).
% 1.95/2.16 tff(7386,plain,
% 1.95/2.16 (r(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[527, 7385])).
% 1.95/2.16 tff(7387,plain,
% 1.95/2.16 (~r(s(s(s(z))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[5054, 7386, 7382])).
% 1.95/2.16 tff(7388,plain,
% 1.95/2.16 (b(s(s(s(z))), s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[83, 7387])).
% 1.95/2.16 tff(7389,plain,
% 1.95/2.16 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6896, 112, 7324, 7388, 7380])).
% 1.95/2.16 tff(7390,plain,
% 1.95/2.16 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[235, 7389])).
% 1.95/2.16 tff(7391,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[242, 31, 7085, 7390, 7378])).
% 1.95/2.16 tff(7392,plain,((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7393,plain,
% 1.95/2.16 (~b(z, s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7392, 4, 2])).
% 1.95/2.16 tff(7394,plain,
% 1.95/2.16 (r(z, s(z))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[182, 7393])).
% 1.95/2.16 tff(7395,plain,
% 1.95/2.16 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[5089, 7394, 7037])).
% 1.95/2.16 tff(7396,plain,
% 1.95/2.16 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[398, 7395])).
% 1.95/2.16 tff(7397,plain,
% 1.95/2.16 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[5302, 803, 4, 7394, 2, 7396])).
% 1.95/2.16 tff(7398,plain,
% 1.95/2.16 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6593, 7041, 803, 7397, 4])).
% 1.95/2.16 tff(7399,plain,
% 1.95/2.16 (~b(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[4333, 803, 7396, 4])).
% 1.95/2.16 tff(7400,plain,
% 1.95/2.16 (r(s(s(s(z))), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[527, 7399])).
% 1.95/2.16 tff(7401,plain,
% 1.95/2.16 (~b(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[3569, 2525, 2, 1827])).
% 1.95/2.16 tff(7402,plain,
% 1.95/2.16 (r(s(z), z)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[608, 7401])).
% 1.95/2.16 tff(7403,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7404,plain,
% 1.95/2.16 (((~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)))),
% 1.95/2.16 inference(rewrite,[status(thm)],[])).
% 1.95/2.16 tff(7405,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))),
% 1.95/2.16 inference(monotonicity,[status(thm)],[7404])).
% 1.95/2.16 tff(7406,plain,
% 1.95/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))),
% 1.95/2.16 inference(transitivity,[status(thm)],[7405, 7403])).
% 1.95/2.16 tff(7407,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.95/2.16 inference(quant_inst,[status(thm)],[])).
% 1.95/2.16 tff(7408,plain,
% 1.95/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.95/2.16 inference(modus_ponens,[status(thm)],[7407, 7406])).
% 1.95/2.16 tff(7409,plain,
% 1.95/2.16 ($false),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7408, 31, 85, 612, 7402])).
% 1.95/2.16 tff(7410,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.16 tff(7411,plain,
% 1.95/2.16 (~r(s(z), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[7410, 7400, 2, 7396, 7039])).
% 1.95/2.16 tff(7412,plain,
% 1.95/2.16 (b(s(z), s(s(s(z))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[99, 7411])).
% 1.95/2.16 tff(7413,plain,
% 1.95/2.16 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6632, 7412, 7037, 7039, 7041, 7398])).
% 1.95/2.16 tff(7414,plain,
% 1.95/2.16 (~r(s(s(s(s(z)))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6588, 7413])).
% 1.95/2.16 tff(7415,plain,
% 1.95/2.16 (b(s(s(s(s(z)))), elem!1)),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6586, 7414])).
% 1.95/2.16 tff(7416,plain,
% 1.95/2.16 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.16 inference(unit_resolution,[status(thm)],[6583, 7415])).
% 1.95/2.16 tff(7417,plain,
% 1.95/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7418,plain,
% 1.95/2.17 (((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7419,plain,
% 1.95/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7418])).
% 1.95/2.17 tff(7420,plain,
% 1.95/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[7419, 7417])).
% 1.95/2.17 tff(7421,plain,
% 1.95/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7422,plain,
% 1.95/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7421, 7420])).
% 1.95/2.17 tff(7423,plain,
% 1.95/2.17 (~b(z, s(s(s(s(z)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7422, 112, 803, 4, 2, 7416])).
% 1.95/2.17 tff(7424,plain,
% 1.95/2.17 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6178, 78])).
% 1.95/2.17 tff(7425,plain,
% 1.95/2.17 (r(z, s(s(s(s(z)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7424, 7423, 6168])).
% 1.95/2.17 tff(7426,plain,
% 1.95/2.17 (~b(s(s(s(s(z)))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6533, 112, 7396, 2, 7416])).
% 1.95/2.17 tff(7427,plain,
% 1.95/2.17 (r(s(s(s(s(z)))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7114, 7426])).
% 1.95/2.17 tff(7428,plain,
% 1.95/2.17 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7162, 31, 7400, 7427])).
% 1.95/2.17 tff(7429,plain,
% 1.95/2.17 (~b(s(s(s(s(z)))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2440, 7428, 7041, 7412])).
% 1.95/2.17 tff(7430,plain,
% 1.95/2.17 (r(s(s(s(s(z)))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1733, 7429])).
% 1.95/2.17 tff(7431,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6174, 31, 7394, 7430, 7425])).
% 1.95/2.17 tff(7432,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7433,plain,
% 1.95/2.17 (~b(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7432, 4, 2])).
% 1.95/2.17 tff(7434,plain,
% 1.95/2.17 (r(z, s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[515, 7433])).
% 1.95/2.17 tff(7435,plain,
% 1.95/2.17 (((~![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(z))) | (~r(s(s(s(s(s(z))))), 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(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7436,plain,
% 1.95/2.17 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), 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(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7437,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), 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(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7436])).
% 1.95/2.17 tff(7438,plain,
% 1.95/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), 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(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[7437, 7435])).
% 1.95/2.17 tff(7439,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7440,plain,
% 1.95/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7439, 7438])).
% 1.95/2.17 tff(7441,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7440, 31, 20, 162, 1792, 6467])).
% 1.95/2.17 tff(7442,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7443,plain,
% 1.95/2.17 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7442, 1792, 162, 20])).
% 1.95/2.17 tff(7444,plain,
% 1.95/2.17 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6377, 7443])).
% 1.95/2.17 tff(7445,plain,
% 1.95/2.17 (~r(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[503, 20, 162])).
% 1.95/2.17 tff(7446,plain,
% 1.95/2.17 (b(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[83, 7445])).
% 1.95/2.17 tff(7447,plain,
% 1.95/2.17 (~r(s(z), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[170, 20, 162])).
% 1.95/2.17 tff(7448,plain,
% 1.95/2.17 (b(s(z), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[99, 7447])).
% 1.95/2.17 tff(7449,plain,
% 1.95/2.17 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6896, 112, 7448, 7446, 7444])).
% 1.95/2.17 tff(7450,plain,
% 1.95/2.17 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[235, 7449])).
% 1.95/2.17 tff(7451,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7262, 31, 20, 1792, 7450])).
% 1.95/2.17 tff(7452,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7453,plain,
% 1.95/2.17 (~r(s(s(s(s(s(z))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7452, 7434, 7394])).
% 1.95/2.17 tff(7454,plain,
% 1.95/2.17 (b(s(s(s(s(s(z))))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6404, 78, 15, 7453])).
% 1.95/2.17 tff(7455,plain,
% 1.95/2.17 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7456,plain,
% 1.95/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7455])).
% 1.95/2.17 tff(7457,plain,
% 1.95/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[7456, 6459])).
% 1.95/2.17 tff(7458,plain,
% 1.95/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7459,plain,
% 1.95/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7458, 7457])).
% 1.95/2.17 tff(7460,plain,
% 1.95/2.17 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7459, 112, 7396, 2, 7454])).
% 1.95/2.17 tff(7461,plain,
% 1.95/2.17 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6342, 7460])).
% 1.95/2.17 tff(7462,plain,
% 1.95/2.17 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6355, 7461])).
% 1.95/2.17 tff(7463,plain,
% 1.95/2.17 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6362, 7462])).
% 1.95/2.17 tff(7464,plain,
% 1.95/2.17 (~r(s(z), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[170, 7434, 7394])).
% 1.95/2.17 tff(7465,plain,
% 1.95/2.17 (b(s(z), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[99, 7464])).
% 1.95/2.17 tff(7466,plain,
% 1.95/2.17 (~r(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[503, 7434, 7394])).
% 1.95/2.17 tff(7467,plain,
% 1.95/2.17 (b(s(s(s(z))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[83, 7466])).
% 1.95/2.17 tff(7468,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.95/2.17 tff(7469,plain,
% 1.95/2.17 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7459, 112, 7396, 2, 7468])).
% 1.95/2.17 tff(7470,plain,
% 1.95/2.17 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6342, 7469])).
% 1.95/2.17 tff(7471,plain,
% 1.95/2.17 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6355, 7470])).
% 1.95/2.17 tff(7472,plain,
% 1.95/2.17 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6362, 7471])).
% 1.95/2.17 tff(7473,plain,
% 1.95/2.17 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7008, 7472, 1])).
% 1.95/2.17 tff(7474,plain,
% 1.95/2.17 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7012, 7473])).
% 1.95/2.17 tff(7475,plain,
% 1.95/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7476,plain,
% 1.95/2.17 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(z))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(rewrite,[status(thm)],[])).
% 1.95/2.17 tff(7477,plain,
% 1.95/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(s(s(z)))))))))),
% 1.95/2.17 inference(monotonicity,[status(thm)],[7476])).
% 1.95/2.17 tff(7478,plain,
% 1.95/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), s(s(s(s(s(z))))))))),
% 1.95/2.17 inference(transitivity,[status(thm)],[7477, 7475])).
% 1.95/2.17 tff(7479,plain,
% 1.95/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.95/2.17 inference(quant_inst,[status(thm)],[])).
% 1.95/2.17 tff(7480,plain,
% 1.95/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 1.95/2.17 inference(modus_ponens,[status(thm)],[7479, 7478])).
% 1.95/2.17 tff(7481,plain,
% 1.95/2.17 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7480, 112, 4, 7396, 7474, 7468])).
% 1.95/2.17 tff(7482,plain,
% 1.95/2.17 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7342, 7481, 6458])).
% 1.95/2.17 tff(7483,plain,
% 1.95/2.17 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7353, 7482, 7037])).
% 1.95/2.17 tff(7484,plain,
% 1.95/2.17 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7184, 7483])).
% 1.95/2.17 tff(7485,plain,
% 1.95/2.17 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7276, 7472, 7037])).
% 1.95/2.17 tff(7486,plain,
% 1.95/2.17 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6377, 7485])).
% 1.95/2.17 tff(7487,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6852, 112, 7465, 7467, 7486, 7484, 7474])).
% 1.95/2.17 tff(7488,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7489,plain,
% 1.95/2.17 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7488, 7454, 4, 2])).
% 1.95/2.17 tff(7490,plain,
% 1.95/2.17 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[160, 7489])).
% 1.95/2.17 tff(7491,plain,
% 1.95/2.17 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[3598, 7490, 7467, 4, 7465])).
% 1.95/2.17 tff(7492,plain,
% 1.95/2.17 (r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[477, 7491])).
% 1.95/2.17 tff(7493,plain,
% 1.95/2.17 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7182, 31, 7492, 7463])).
% 1.95/2.17 tff(7494,plain,
% 1.95/2.17 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7184, 7493])).
% 1.95/2.17 tff(7495,plain,
% 1.95/2.17 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7276, 7463, 7037])).
% 1.95/2.17 tff(7496,plain,
% 1.95/2.17 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6377, 7495])).
% 1.95/2.17 tff(7497,plain,
% 1.95/2.17 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6852, 112, 7465, 7467, 7496, 7494])).
% 1.95/2.17 tff(7498,plain,
% 1.95/2.17 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7012, 7497])).
% 1.95/2.17 tff(7499,plain,
% 1.95/2.17 (~b(s(s(s(s(z)))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7303, 112, 4, 7396, 7490, 2, 1273])).
% 1.95/2.17 tff(7500,plain,
% 1.95/2.17 (r(s(s(s(s(z)))), z)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7114, 7499])).
% 1.95/2.17 tff(7501,plain,
% 1.95/2.17 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1294, 112, 4, 7490, 1273])).
% 1.95/2.17 tff(7502,plain,
% 1.95/2.17 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1718, 7501])).
% 1.95/2.17 tff(7503,plain,
% 1.95/2.17 ($false),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7313, 31, 7434, 7502, 7500])).
% 1.95/2.17 tff(7504,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.17 tff(7505,plain,
% 1.95/2.17 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[7504, 4, 2])).
% 1.95/2.17 tff(7506,plain,
% 1.95/2.17 (~b(s(s(s(s(z)))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6583, 7505])).
% 1.95/2.17 tff(7507,plain,
% 1.95/2.17 (r(s(s(s(s(z)))), elem!1)),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6586, 7506])).
% 1.95/2.17 tff(7508,plain,
% 1.95/2.17 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6588, 7507])).
% 1.95/2.17 tff(7509,plain,
% 1.95/2.17 (~r(s(s(s(s(z)))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[990, 7508, 7037])).
% 1.95/2.17 tff(7510,plain,
% 1.95/2.17 (b(s(s(s(s(z)))), s(z))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[1733, 7509])).
% 1.95/2.17 tff(7511,plain,
% 1.95/2.17 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[2440, 7510, 7467, 7465])).
% 1.95/2.17 tff(7512,plain,
% 1.95/2.17 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[3221, 7511, 7498])).
% 1.95/2.17 tff(7513,plain,
% 1.95/2.17 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.95/2.17 inference(unit_resolution,[status(thm)],[6865, 7512])).
% 1.95/2.18 tff(7514,plain,
% 1.95/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))), s(z))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7515,plain,
% 1.95/2.18 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7516,plain,
% 1.95/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7515])).
% 1.95/2.18 tff(7517,plain,
% 1.95/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7516, 7514])).
% 1.95/2.18 tff(7518,plain,
% 1.95/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7519,plain,
% 1.95/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7518, 7517])).
% 1.95/2.18 tff(7520,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7519, 112, 7465, 7467, 7510, 7513, 7496, 7494])).
% 1.95/2.18 tff(7521,plain,((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7522,plain,
% 1.95/2.18 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7521, 2])).
% 1.95/2.18 tff(7523,plain,
% 1.95/2.18 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[646, 7522])).
% 1.95/2.18 tff(7524,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1855, 85, 7523])).
% 1.95/2.18 tff(7525,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[429, 7524])).
% 1.95/2.18 tff(7526,plain,
% 1.95/2.18 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[4155, 85, 7523])).
% 1.95/2.18 tff(7527,plain,
% 1.95/2.18 (b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[477, 7526])).
% 1.95/2.18 tff(7528,plain,
% 1.95/2.18 (~b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[547, 7527, 2, 7525])).
% 1.95/2.18 tff(7529,plain,
% 1.95/2.18 (r(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[182, 7528])).
% 1.95/2.18 tff(7530,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6974, 7529, 803, 2])).
% 1.95/2.18 tff(7531,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6342, 7530])).
% 1.95/2.18 tff(7532,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6355, 7531])).
% 1.95/2.18 tff(7533,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6362, 7532])).
% 1.95/2.18 tff(7534,plain,
% 1.95/2.18 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6687, 7533, 7523])).
% 1.95/2.18 tff(7535,plain,
% 1.95/2.18 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[235, 7534])).
% 1.95/2.18 tff(7536,plain,
% 1.95/2.18 (~r(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[620, 568, 249])).
% 1.95/2.18 tff(7537,plain,
% 1.95/2.18 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6687, 6392, 249])).
% 1.95/2.18 tff(7538,plain,
% 1.95/2.18 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[235, 7537])).
% 1.95/2.18 tff(7539,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6515, 7538, 803, 859])).
% 1.95/2.18 tff(7540,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6398, 31, 568, 7539, 6392])).
% 1.95/2.18 tff(7541,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7542,plain,
% 1.95/2.18 (~b(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7541, 568, 249, 6392, 803])).
% 1.95/2.18 tff(7543,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[527, 7542, 7536])).
% 1.95/2.18 tff(7544,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7545,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7544, 7533, 7523, 803])).
% 1.95/2.18 tff(7546,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[398, 7545])).
% 1.95/2.18 tff(7547,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6974, 3774, 803, 2])).
% 1.95/2.18 tff(7548,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6342, 7547])).
% 1.95/2.18 tff(7549,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6355, 7548])).
% 1.95/2.18 tff(7550,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6362, 7549])).
% 1.95/2.18 tff(7551,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7544, 7550, 7523, 803])).
% 1.95/2.18 tff(7552,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[398, 7551])).
% 1.95/2.18 tff(7553,plain,
% 1.95/2.18 (~b(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3569, 7552, 2, 539])).
% 1.95/2.18 tff(7554,plain,
% 1.95/2.18 (r(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[608, 7553])).
% 1.95/2.18 tff(7555,plain,
% 1.95/2.18 (~r(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[5054, 3, 7554])).
% 1.95/2.18 tff(7556,plain,
% 1.95/2.18 (b(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[527, 7555])).
% 1.95/2.18 tff(7557,plain,
% 1.95/2.18 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7026, 3, 7550, 19, 539, 3774, 803])).
% 1.95/2.18 tff(7558,plain,
% 1.95/2.18 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[160, 7557])).
% 1.95/2.18 tff(7559,plain,
% 1.95/2.18 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6446, 196, 803, 2])).
% 1.95/2.18 tff(7560,plain,
% 1.95/2.18 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[646, 7559])).
% 1.95/2.18 tff(7561,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7541, 7560, 6392, 859, 803])).
% 1.95/2.18 tff(7562,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[398, 7561])).
% 1.95/2.18 tff(7563,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3957, 112, 859, 7562, 196, 2])).
% 1.95/2.18 tff(7564,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7565,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7564, 7558, 7556, 2, 803, 7550])).
% 1.95/2.18 tff(7566,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7567,plain,
% 1.95/2.18 (~r(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7566, 7525, 803, 2, 7527])).
% 1.95/2.18 tff(7568,plain,
% 1.95/2.18 (b(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[83, 7567])).
% 1.95/2.18 tff(7569,plain,
% 1.95/2.18 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[4251, 7568, 7525, 7527])).
% 1.95/2.18 tff(7570,plain,
% 1.95/2.18 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[160, 7569])).
% 1.95/2.18 tff(7571,plain,
% 1.95/2.18 (~r(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7410, 7570, 2, 85, 7546])).
% 1.95/2.18 tff(7572,plain,
% 1.95/2.18 (b(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[527, 7571])).
% 1.95/2.18 tff(7573,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6515, 7572, 803, 7535])).
% 1.95/2.18 tff(7574,plain,
% 1.95/2.18 (~b(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3569, 7546, 2, 7527])).
% 1.95/2.18 tff(7575,plain,
% 1.95/2.18 (r(s(z), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[608, 7574])).
% 1.95/2.18 tff(7576,plain,
% 1.95/2.18 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7008, 7570, 7533])).
% 1.95/2.18 tff(7577,plain,
% 1.95/2.18 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7012, 7576])).
% 1.95/2.18 tff(7578,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.95/2.18 tff(7579,plain,
% 1.95/2.18 (~r(s(z), s(s(s(s(s(z))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6836, 31, 592, 1792])).
% 1.95/2.18 tff(7580,plain,
% 1.95/2.18 (b(s(z), s(s(s(s(s(z))))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7184, 7579])).
% 1.95/2.18 tff(7581,plain,
% 1.95/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7582,plain,
% 1.95/2.18 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(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(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7583,plain,
% 1.95/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7582])).
% 1.95/2.18 tff(7584,plain,
% 1.95/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7583, 7581])).
% 1.95/2.18 tff(7585,plain,
% 1.95/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7586,plain,
% 1.95/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7585, 7584])).
% 1.95/2.18 tff(7587,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7586, 112, 101, 19, 539, 4909, 7580, 7578])).
% 1.95/2.18 tff(7588,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(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(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7589,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7588, 7568, 7525, 7527, 7577, 7575, 7573])).
% 1.95/2.18 tff(7590,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6377, 7589])).
% 1.95/2.18 tff(7591,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7592,plain,
% 1.95/2.18 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7593,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), 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(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7592])).
% 1.95/2.18 tff(7594,plain,
% 1.95/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), 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(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7593, 7591])).
% 1.95/2.18 tff(7595,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.95/2.18 inference(quant_inst,[status(thm)],[])).
% 1.95/2.18 tff(7596,plain,
% 1.95/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7595, 7594])).
% 1.95/2.18 tff(7597,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7596, 31, 85, 7575, 7573, 7590])).
% 1.95/2.18 tff(7598,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7599,plain,
% 1.95/2.18 (~r(s(z), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7598, 803, 2])).
% 1.95/2.18 tff(7600,plain,
% 1.95/2.18 (b(s(z), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[99, 7599])).
% 1.95/2.18 tff(7601,plain,
% 1.95/2.18 (b(z, elem!1) <=> b(z, s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[6577])).
% 1.95/2.18 tff(7602,plain,
% 1.95/2.18 (b(z, s(s(s(s(elem!1))))) <=> b(z, elem!1)),
% 1.95/2.18 inference(symmetry,[status(thm)],[7601])).
% 1.95/2.18 tff(7603,plain,
% 1.95/2.18 (b(z, elem!1)),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[2, 7602])).
% 1.95/2.18 tff(7604,plain,
% 1.95/2.18 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[6577])).
% 1.95/2.18 tff(7605,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.95/2.18 inference(symmetry,[status(thm)],[7604])).
% 1.95/2.18 tff(7606,plain,
% 1.95/2.18 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7605])).
% 1.95/2.18 tff(7607,plain,
% 1.95/2.18 (~b(elem!1, s(s(s(z))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[7522, 7606])).
% 1.95/2.18 tff(7608,plain,
% 1.95/2.18 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[6577])).
% 1.95/2.18 tff(7609,plain,
% 1.95/2.18 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(transitivity,[status(thm)],[7608, 124])).
% 1.95/2.18 tff(7610,plain,
% 1.95/2.18 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(z))))),
% 1.95/2.18 inference(symmetry,[status(thm)],[7609])).
% 1.95/2.18 tff(7611,plain,
% 1.95/2.18 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7610])).
% 1.95/2.18 tff(7612,plain,
% 1.95/2.18 (~(elem!1 = s(s(s(z))))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[153, 7611])).
% 1.95/2.18 tff(7613,plain,
% 1.95/2.18 (b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1498, 7612])).
% 1.95/2.18 tff(7614,plain,
% 1.95/2.18 (r(elem!1, s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7613, 7607])).
% 1.95/2.18 tff(7615,plain,
% 1.95/2.18 (~r(elem!1, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1568, 3, 7614])).
% 1.95/2.18 tff(7616,plain,
% 1.95/2.18 ((elem!1 = s(z)) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[6577])).
% 1.95/2.18 tff(7617,plain,
% 1.95/2.18 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(z))),
% 1.95/2.18 inference(symmetry,[status(thm)],[7616])).
% 1.95/2.18 tff(7618,plain,
% 1.95/2.18 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.95/2.18 inference(monotonicity,[status(thm)],[7617])).
% 1.95/2.18 tff(7619,plain,
% 1.95/2.18 (~(elem!1 = s(z))),
% 1.95/2.18 inference(modus_ponens,[status(thm)],[424, 7618])).
% 1.95/2.18 tff(7620,plain,
% 1.95/2.18 (b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1139, 7619])).
% 1.95/2.18 tff(7621,plain,
% 1.95/2.18 (b(elem!1, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7620, 7615])).
% 1.95/2.18 tff(7622,plain,
% 1.95/2.18 (~b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1585, 7621, 7603, 803, 7600])).
% 1.95/2.18 tff(7623,plain,
% 1.95/2.18 (r(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[182, 7622])).
% 1.95/2.18 tff(7624,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6974, 7623, 803, 2])).
% 1.95/2.18 tff(7625,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6342, 7624])).
% 1.95/2.18 tff(7626,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6355, 7625])).
% 1.95/2.18 tff(7627,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3970, 3, 7523])).
% 1.95/2.18 tff(7628,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[429, 7627])).
% 1.95/2.18 tff(7629,plain,
% 1.95/2.18 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7566, 7628, 803, 2, 3])).
% 1.95/2.18 tff(7630,plain,
% 1.95/2.18 (r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[477, 7629])).
% 1.95/2.18 tff(7631,plain,
% 1.95/2.18 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[39, 7630, 3])).
% 1.95/2.18 tff(7632,plain,
% 1.95/2.18 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[160, 7631])).
% 1.95/2.18 tff(7633,plain,
% 1.95/2.18 (~r(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[3275, 7623, 3])).
% 1.95/2.18 tff(7634,plain,
% 1.95/2.18 (b(s(s(s(z))), z)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[527, 7633])).
% 1.95/2.18 tff(7635,plain,
% 1.95/2.18 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7564, 7634, 2, 803, 7632])).
% 1.95/2.18 tff(7636,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6362, 7635, 7626])).
% 1.95/2.18 tff(7637,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7638,plain,
% 1.95/2.18 (~r(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7637, 803, 2])).
% 1.95/2.18 tff(7639,plain,
% 1.95/2.18 (b(s(s(s(z))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[83, 7638])).
% 1.95/2.18 tff(7640,plain,
% 1.95/2.18 (~b(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[1867, 7639, 803, 7600])).
% 1.95/2.18 tff(7641,plain,
% 1.95/2.18 (r(z, s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[182, 7640])).
% 1.95/2.18 tff(7642,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6974, 7641, 803, 2])).
% 1.95/2.18 tff(7643,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6342, 7642])).
% 1.95/2.18 tff(7644,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6355, 7643])).
% 1.95/2.18 tff(7645,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6362, 7644])).
% 1.95/2.18 tff(7646,plain,
% 1.95/2.18 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6687, 7645, 7523])).
% 1.95/2.18 tff(7647,plain,
% 1.95/2.18 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[235, 7646])).
% 1.95/2.18 tff(7648,plain,
% 1.95/2.18 ($false),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6896, 112, 102, 101, 6507, 4909])).
% 1.95/2.18 tff(7649,plain,((~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(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.18 tff(7650,plain,
% 1.95/2.18 (~b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7649, 7600, 7639, 7647])).
% 1.95/2.18 tff(7651,plain,
% 1.95/2.18 (r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[6377, 7650])).
% 1.95/2.18 tff(7652,plain,
% 1.95/2.18 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[7276, 7651, 7645])).
% 1.95/2.18 tff(7653,plain,
% 1.95/2.18 (b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.18 inference(unit_resolution,[status(thm)],[429, 7652])).
% 1.95/2.18 tff(7654,plain,
% 1.95/2.18 (((~![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(z))))), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.95/2.18 inference(rewrite,[status(thm)],[])).
% 1.95/2.18 tff(7655,plain,
% 1.95/2.18 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7656,plain,
% 1.95/2.19 (((~![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(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7655])).
% 1.95/2.19 tff(7657,plain,
% 1.95/2.19 (((~![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(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), 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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7656, 7654])).
% 1.95/2.19 tff(7658,plain,
% 1.95/2.19 ((~![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(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7659,plain,
% 1.95/2.19 ((~![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(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7658, 7657])).
% 1.95/2.19 tff(7660,plain,
% 1.95/2.19 (~r(z, s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7659, 31, 162, 6467])).
% 1.95/2.19 tff(7661,plain,
% 1.95/2.19 (b(z, s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[194, 78, 17, 7660])).
% 1.95/2.19 tff(7662,plain,
% 1.95/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7663,plain,
% 1.95/2.19 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7664,plain,
% 1.95/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7663])).
% 1.95/2.19 tff(7665,plain,
% 1.95/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7664, 7662])).
% 1.95/2.19 tff(7666,plain,
% 1.95/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7667,plain,
% 1.95/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7666, 7665])).
% 1.95/2.19 tff(7668,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7667, 112, 803, 6507, 7661, 7578, 6475])).
% 1.95/2.19 tff(7669,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7670,plain,
% 1.95/2.19 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7669, 7651, 7647, 803, 7641])).
% 1.95/2.19 tff(7671,plain,
% 1.95/2.19 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7012, 7670])).
% 1.95/2.19 tff(7672,plain,
% 1.95/2.19 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7008, 7671, 7645])).
% 1.95/2.19 tff(7673,plain,
% 1.95/2.19 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[160, 7672])).
% 1.95/2.19 tff(7674,plain,
% 1.95/2.19 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4251, 7673, 7639, 7653])).
% 1.95/2.19 tff(7675,plain,
% 1.95/2.19 (r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[477, 7674])).
% 1.95/2.19 tff(7676,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6422, 31, 7675, 7645, 7651])).
% 1.95/2.19 tff(7677,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7678,plain,
% 1.95/2.19 (~b(z, s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7677, 2])).
% 1.95/2.19 tff(7679,plain,
% 1.95/2.19 (r(z, s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[515, 7678])).
% 1.95/2.19 tff(7680,plain,
% 1.95/2.19 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4030, 3, 7523, 7679])).
% 1.95/2.19 tff(7681,plain,
% 1.95/2.19 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[160, 7680])).
% 1.95/2.19 tff(7682,plain,
% 1.95/2.19 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[39, 7681, 3])).
% 1.95/2.19 tff(7683,plain,
% 1.95/2.19 (~r(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[503, 3, 7679])).
% 1.95/2.19 tff(7684,plain,
% 1.95/2.19 (b(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[182, 7683])).
% 1.95/2.19 tff(7685,plain,
% 1.95/2.19 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[547, 7684, 2, 7628])).
% 1.95/2.19 tff(7686,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[477, 7685, 7682])).
% 1.95/2.19 tff(7687,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7688,plain,
% 1.95/2.19 (~r(s(s(s(z))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7687, 2])).
% 1.95/2.19 tff(7689,plain,
% 1.95/2.19 (b(s(s(s(z))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[83, 7688])).
% 1.95/2.19 tff(7690,plain,
% 1.95/2.19 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[6330])).
% 1.95/2.19 tff(7691,plain,
% 1.95/2.19 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[7690])).
% 1.95/2.19 tff(7692,plain,
% 1.95/2.19 ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7691])).
% 1.95/2.19 tff(7693,plain,
% 1.95/2.19 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7522, 7692])).
% 1.95/2.19 tff(7694,plain,
% 1.95/2.19 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[6330])).
% 1.95/2.19 tff(7695,plain,
% 1.95/2.19 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7694, 124])).
% 1.95/2.19 tff(7696,plain,
% 1.95/2.19 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[7695])).
% 1.95/2.19 tff(7697,plain,
% 1.95/2.19 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7696])).
% 1.95/2.19 tff(7698,plain,
% 1.95/2.19 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[153, 7697])).
% 1.95/2.19 tff(7699,plain,
% 1.95/2.19 (b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4880, 7698])).
% 1.95/2.19 tff(7700,plain,
% 1.95/2.19 (r(s(s(elem!1)), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7699, 7693])).
% 1.95/2.19 tff(7701,plain,
% 1.95/2.19 (~r(s(z), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[4876, 7679, 7700])).
% 1.95/2.19 tff(7702,plain,
% 1.95/2.19 (b(s(z), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[99, 7701])).
% 1.95/2.19 tff(7703,plain,
% 1.95/2.19 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7045])).
% 1.95/2.19 tff(7704,plain,
% 1.95/2.19 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.19 inference(symmetry,[status(thm)],[7703])).
% 1.95/2.19 tff(7705,plain,
% 1.95/2.19 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[1560, 7704])).
% 1.95/2.19 tff(7706,plain,
% 1.95/2.19 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[393, 31, 20, 568])).
% 1.95/2.19 tff(7707,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7706, 7705])).
% 1.95/2.19 tff(7708,plain,((~r(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7709,plain,
% 1.95/2.19 ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7708, 6330])).
% 1.95/2.19 tff(7710,plain,
% 1.95/2.19 (~r(s(s(s(s(elem!1)))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7709, 7679, 7614])).
% 1.95/2.19 tff(7711,plain,
% 1.95/2.19 (b(s(s(s(s(elem!1)))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[398, 7710])).
% 1.95/2.19 tff(7712,plain,
% 1.95/2.19 (~r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6644, 31, 592, 1792])).
% 1.95/2.19 tff(7713,plain,
% 1.95/2.19 (b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6377, 7712])).
% 1.95/2.19 tff(7714,plain,
% 1.95/2.19 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6896, 112, 102, 101, 7713])).
% 1.95/2.19 tff(7715,plain,
% 1.95/2.19 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[235, 7714])).
% 1.95/2.19 tff(7716,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7262, 31, 20, 1792, 7715])).
% 1.95/2.19 tff(7717,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7718,plain,
% 1.95/2.19 (~r(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7717, 1792, 7679, 7702, 7689])).
% 1.95/2.19 tff(7719,plain,
% 1.95/2.19 (b(s(z), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[608, 7718])).
% 1.95/2.19 tff(7720,plain,
% 1.95/2.19 (~r(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7452, 1792, 7679])).
% 1.95/2.19 tff(7721,plain,
% 1.95/2.19 (b(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[182, 7720])).
% 1.95/2.19 tff(7722,plain,
% 1.95/2.19 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[3569, 7719, 2, 7711])).
% 1.95/2.19 tff(7723,plain,
% 1.95/2.19 (r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[477, 7722])).
% 1.95/2.19 tff(7724,plain,
% 1.95/2.19 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[1835, 7721, 7719, 7711])).
% 1.95/2.19 tff(7725,plain,
% 1.95/2.19 (r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[429, 7724])).
% 1.95/2.19 tff(7726,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7203, 7725, 7723, 1, 2, 7721, 7719])).
% 1.95/2.19 tff(7727,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7728,plain,
% 1.95/2.19 (~r(s(s(s(s(s(z))))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7727, 1, 2])).
% 1.95/2.19 tff(7729,plain,
% 1.95/2.19 (b(s(s(s(s(s(z))))), z)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6404, 78, 15, 7728])).
% 1.95/2.19 tff(7730,plain,
% 1.95/2.19 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7459, 112, 7711, 2, 7729])).
% 1.95/2.19 tff(7731,plain,
% 1.95/2.19 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6342, 7730])).
% 1.95/2.19 tff(7732,plain,
% 1.95/2.19 (r(s(s(s(s(s(z))))), elem!1)),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6355, 7731])).
% 1.95/2.19 tff(7733,plain,
% 1.95/2.19 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6362, 7732])).
% 1.95/2.19 tff(7734,plain,
% 1.95/2.19 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7008, 7733, 1])).
% 1.95/2.19 tff(7735,plain,
% 1.95/2.19 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7012, 7734])).
% 1.95/2.19 tff(7736,plain,
% 1.95/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7737,plain,
% 1.95/2.19 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(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(z))), s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7738,plain,
% 1.95/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7737])).
% 1.95/2.19 tff(7739,plain,
% 1.95/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7738, 7736])).
% 1.95/2.19 tff(7740,plain,
% 1.95/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7741,plain,
% 1.95/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.95/2.19 inference(modus_ponens,[status(thm)],[7740, 7739])).
% 1.95/2.19 tff(7742,plain,
% 1.95/2.19 ($false),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7741, 112, 101, 7285, 7283, 7578])).
% 1.95/2.19 tff(7743,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.95/2.19 tff(7744,plain,
% 1.95/2.19 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7743, 7735, 7689, 7733])).
% 1.95/2.19 tff(7745,plain,
% 1.95/2.19 (b(s(z), s(s(s(s(elem!1)))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[477, 7744])).
% 1.95/2.19 tff(7746,plain,
% 1.95/2.19 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6687, 7733, 7523])).
% 1.95/2.19 tff(7747,plain,
% 1.95/2.19 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[235, 7746])).
% 1.95/2.19 tff(7748,plain,
% 1.95/2.19 (~b(s(s(s(s(s(z))))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7649, 7747, 7702, 7689])).
% 1.95/2.19 tff(7749,plain,
% 1.95/2.19 (r(s(s(s(s(s(z))))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[6377, 7748])).
% 1.95/2.19 tff(7750,plain,
% 1.95/2.19 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[7276, 7749, 7733])).
% 1.95/2.19 tff(7751,plain,
% 1.95/2.19 (b(s(s(s(s(elem!1)))), s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[429, 7750])).
% 1.95/2.19 tff(7752,plain,
% 1.95/2.19 (~b(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[547, 7751, 2, 7745])).
% 1.95/2.19 tff(7753,plain,
% 1.95/2.19 (r(z, s(z))),
% 1.95/2.19 inference(unit_resolution,[status(thm)],[182, 7752])).
% 1.95/2.19 tff(7754,plain,
% 1.95/2.19 (((~![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(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(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(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7755,plain,
% 1.95/2.19 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(rewrite,[status(thm)],[])).
% 1.95/2.19 tff(7756,plain,
% 1.95/2.19 (((~![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(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 1.95/2.19 inference(monotonicity,[status(thm)],[7755])).
% 1.95/2.19 tff(7757,plain,
% 1.95/2.19 (((~![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(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.95/2.19 inference(transitivity,[status(thm)],[7756, 7754])).
% 1.95/2.19 tff(7758,plain,
% 1.95/2.19 ((~![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(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.95/2.19 inference(quant_inst,[status(thm)],[])).
% 1.95/2.19 tff(7759,plain,
% 1.95/2.19 ((~![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(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7758, 7757])).
% 2.04/2.20 tff(7760,plain,
% 2.04/2.20 (~r(z, s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7759, 31, 7753, 7733, 7749])).
% 2.04/2.20 tff(7761,plain,
% 2.04/2.20 (b(z, s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[194, 78, 17, 7760])).
% 2.04/2.20 tff(7762,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7763,plain,
% 2.04/2.20 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(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(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7764,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(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(z))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7763])).
% 2.04/2.20 tff(7765,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(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(z))), z)) | (~b(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7764, 7762])).
% 2.04/2.20 tff(7766,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(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(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7767,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 2.04/2.20 tff(7768,plain,
% 2.04/2.20 (~b(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7767, 112, 7761, 7735, 7729])).
% 2.04/2.20 tff(7769,plain,
% 2.04/2.20 (r(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[527, 7768])).
% 2.04/2.20 tff(7770,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7771,plain,
% 2.04/2.20 (((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7772,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7771])).
% 2.04/2.20 tff(7773,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7772, 7770])).
% 2.04/2.20 tff(7774,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7775,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7774, 7773])).
% 2.04/2.20 tff(7776,plain,
% 2.04/2.20 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7775, 31, 982, 6392])).
% 2.04/2.20 tff(7777,plain,
% 2.04/2.20 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6486, 78, 6483, 7776])).
% 2.04/2.20 tff(7778,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7779,plain,
% 2.04/2.20 (((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(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)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7780,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7779])).
% 2.04/2.20 tff(7781,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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)))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7780, 7778])).
% 2.04/2.20 tff(7782,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7783,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7782, 7781])).
% 2.04/2.20 tff(7784,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7783, 31, 1, 982])).
% 2.04/2.20 tff(7785,plain,
% 2.04/2.20 ((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)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4506, 78])).
% 2.04/2.20 tff(7786,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7785, 7784, 4496])).
% 2.04/2.20 tff(7787,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7788,plain,
% 2.04/2.20 (((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(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(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7789,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7788])).
% 2.04/2.20 tff(7790,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7789, 7787])).
% 2.04/2.20 tff(7791,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7792,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7791, 7790])).
% 2.04/2.20 tff(7793,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7792, 31, 612, 1, 982])).
% 2.04/2.20 tff(7794,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1718, 7793])).
% 2.04/2.20 tff(7795,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7796,plain,
% 2.04/2.20 (((~b(s(s(s(s(z)))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), 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))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(7797,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[7796])).
% 2.04/2.20 tff(7798,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[7797, 7795])).
% 2.04/2.20 tff(7799,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(7800,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[7799, 7798])).
% 2.04/2.20 tff(7801,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7800, 112, 102, 101, 7794, 6507, 7786, 7777])).
% 2.04/2.20 tff(7802,plain,((~r(s(s(s(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(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7803,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7802, 7747, 7689, 7702, 7769, 1, 7733])).
% 2.04/2.20 tff(7804,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6588, 7803])).
% 2.04/2.20 tff(7805,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6586, 7804])).
% 2.04/2.20 tff(7806,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6583, 7805])).
% 2.04/2.20 tff(7807,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6734, 7806, 7751, 7745])).
% 2.04/2.20 tff(7808,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1733, 7807])).
% 2.04/2.20 tff(7809,plain,
% 2.04/2.20 (~r(s(s(s(s(z)))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3896, 31, 7679, 7753, 7808])).
% 2.04/2.20 tff(7810,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6533, 112, 7711, 2, 7806])).
% 2.04/2.20 tff(7811,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7114, 7810, 7809])).
% 2.04/2.20 tff(7812,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(7813,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7812, 2])).
% 2.04/2.20 tff(7814,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[160, 7813])).
% 2.04/2.20 tff(7815,plain,
% 2.04/2.20 (~b(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3957, 112, 7711, 7814, 2])).
% 2.04/2.20 tff(7816,plain,
% 2.04/2.20 (r(s(s(s(z))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[527, 7815])).
% 2.04/2.20 tff(7817,plain,
% 2.04/2.20 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6696, 7816, 2, 7523, 7711])).
% 2.04/2.20 tff(7818,plain,
% 2.04/2.20 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[235, 7817])).
% 2.04/2.20 tff(7819,plain,
% 2.04/2.20 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7649, 7818, 7702, 7689])).
% 2.04/2.20 tff(7820,plain,
% 2.04/2.20 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6377, 7819])).
% 2.04/2.20 tff(7821,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6575, 184, 2, 7816, 7711])).
% 2.04/2.20 tff(7822,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6583, 7821])).
% 2.04/2.20 tff(7823,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6586, 7822])).
% 2.04/2.20 tff(7824,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6588, 7823])).
% 2.04/2.20 tff(7825,plain,
% 2.04/2.20 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6464, 112, 7711, 2, 184])).
% 2.04/2.20 tff(7826,plain,
% 2.04/2.20 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[6404, 78, 15, 7825])).
% 2.04/2.20 tff(7827,plain,
% 2.04/2.20 (~r(s(z), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7717, 7826, 7679, 7702, 7689])).
% 2.04/2.20 tff(7828,plain,
% 2.04/2.20 (b(s(z), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[608, 7827])).
% 2.04/2.20 tff(7829,plain,
% 2.04/2.20 (~r(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7452, 7826, 7679])).
% 2.04/2.20 tff(7830,plain,
% 2.04/2.20 (b(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[182, 7829])).
% 2.04/2.20 tff(7831,plain,
% 2.04/2.20 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1835, 7830, 7828, 7711])).
% 2.04/2.20 tff(7832,plain,
% 2.04/2.20 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[429, 7831])).
% 2.04/2.20 tff(7833,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7164, 7830, 7816, 7828, 7702, 7689])).
% 2.04/2.20 tff(7834,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1733, 7833])).
% 2.04/2.21 tff(7835,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[990, 7834, 7832, 7824])).
% 2.04/2.21 tff(7836,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7837,plain,
% 2.04/2.21 (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7836, 2])).
% 2.04/2.21 tff(7838,plain,
% 2.04/2.21 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6342, 7837])).
% 2.04/2.21 tff(7839,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6355, 7838])).
% 2.04/2.21 tff(7840,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6362, 7839])).
% 2.04/2.21 tff(7841,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7276, 7840, 7820])).
% 2.04/2.21 tff(7842,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[429, 7841])).
% 2.04/2.21 tff(7843,plain,
% 2.04/2.21 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4251, 7842, 7689, 7814])).
% 2.04/2.21 tff(7844,plain,
% 2.04/2.21 (r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[477, 7843])).
% 2.04/2.21 tff(7845,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6422, 31, 7844, 7840, 7820])).
% 2.04/2.21 tff(7846,plain,(~b(z, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7847,plain,
% 2.04/2.21 (r(z, s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[356, 7846])).
% 2.04/2.21 tff(7848,plain,
% 2.04/2.21 (~r(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[563, 31, 7847, 1])).
% 2.04/2.21 tff(7849,plain,
% 2.04/2.21 (b(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[527, 7848])).
% 2.04/2.21 tff(7850,plain,
% 2.04/2.21 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4697, 7847])).
% 2.04/2.21 tff(7851,plain,
% 2.04/2.21 (~r(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7850, 1])).
% 2.04/2.21 tff(7852,plain,
% 2.04/2.21 (b(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[515, 7851])).
% 2.04/2.21 tff(7853,plain,
% 2.04/2.21 (~r(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4697, 1, 569])).
% 2.04/2.21 tff(7854,plain,
% 2.04/2.21 (b(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[515, 7853])).
% 2.04/2.21 tff(7855,plain,
% 2.04/2.21 (~r(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4259, 21, 569])).
% 2.04/2.21 tff(7856,plain,
% 2.04/2.21 (b(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[182, 7855])).
% 2.04/2.21 tff(7857,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1867, 3530, 7856, 101, 803])).
% 2.04/2.21 tff(7858,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7859,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7858, 84, 7854, 569, 1, 21])).
% 2.04/2.21 tff(7860,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7861,plain,
% 2.04/2.21 ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7860, 7847])).
% 2.04/2.21 tff(7862,plain,
% 2.04/2.21 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7861, 1])).
% 2.04/2.21 tff(7863,plain,
% 2.04/2.21 (b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[477, 7862])).
% 2.04/2.21 tff(7864,plain,
% 2.04/2.21 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[589, 7847])).
% 2.04/2.21 tff(7865,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7864, 162])).
% 2.04/2.21 tff(7866,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[429, 7865])).
% 2.04/2.21 tff(7867,plain,
% 2.04/2.21 (b(z, s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[1576, 7601])).
% 2.04/2.21 tff(7868,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[351, 7867])).
% 2.04/2.21 tff(7869,plain,((~b(z, elem!1)) | b(z, s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7870,plain,
% 2.04/2.21 (~b(z, elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7869, 7846])).
% 2.04/2.21 tff(7871,plain,
% 2.04/2.21 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 2.04/2.21 inference(commutativity,[status(thm)],[])).
% 2.04/2.21 tff(7872,plain,
% 2.04/2.21 ((z = elem!1) <=> (z = s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[6577])).
% 2.04/2.21 tff(7873,plain,
% 2.04/2.21 ((z = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 2.04/2.21 inference(transitivity,[status(thm)],[7872, 7871])).
% 2.04/2.21 tff(7874,plain,
% 2.04/2.21 ((s(s(s(s(elem!1)))) = z) <=> (z = elem!1)),
% 2.04/2.21 inference(symmetry,[status(thm)],[7873])).
% 2.04/2.21 tff(7875,plain,
% 2.04/2.21 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7874])).
% 2.04/2.21 tff(7876,plain,
% 2.04/2.21 (~(z = elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[347, 7875])).
% 2.04/2.21 tff(7877,plain,
% 2.04/2.21 (b(z, elem!1) | r(z, elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1109, 7876])).
% 2.04/2.21 tff(7878,plain,
% 2.04/2.21 (r(z, elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7877, 7870])).
% 2.04/2.21 tff(7879,plain,
% 2.04/2.21 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.21 inference(commutativity,[status(thm)],[])).
% 2.04/2.21 tff(7880,plain,
% 2.04/2.21 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[6336])).
% 2.04/2.21 tff(7881,plain,
% 2.04/2.21 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.21 inference(transitivity,[status(thm)],[7880, 7879])).
% 2.04/2.21 tff(7882,plain,
% 2.04/2.21 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[7881])).
% 2.04/2.21 tff(7883,plain,
% 2.04/2.21 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7882])).
% 2.04/2.21 tff(7884,plain,
% 2.04/2.21 (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[6585, 7883])).
% 2.04/2.21 tff(7885,plain,
% 2.04/2.21 (((~![X0: $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(s(z))))), z)) | (~r(s(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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7886,plain,
% 2.04/2.21 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7887,plain,
% 2.04/2.21 (((~![X0: $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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7886])).
% 2.04/2.21 tff(7888,plain,
% 2.04/2.21 (((~![X0: $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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~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(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7887, 7885])).
% 2.04/2.21 tff(7889,plain,
% 2.04/2.21 ((~![X0: $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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7890,plain,
% 2.04/2.21 ((~![X0: $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(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7889, 7888])).
% 2.04/2.21 tff(7891,plain,
% 2.04/2.21 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7890, 31, 569, 6392])).
% 2.04/2.21 tff(7892,plain,
% 2.04/2.21 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6404, 78, 15, 7891])).
% 2.04/2.21 tff(7893,plain,
% 2.04/2.21 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.04/2.21 inference(commutativity,[status(thm)],[])).
% 2.04/2.21 tff(7894,plain,
% 2.04/2.21 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[7893])).
% 2.04/2.21 tff(7895,plain,
% 2.04/2.21 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7894])).
% 2.04/2.21 tff(7896,plain,
% 2.04/2.21 (~(z = s(s(s(s(s(z))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[15, 7895])).
% 2.04/2.21 tff(7897,plain,
% 2.04/2.21 (((~![X0: $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(s(s(z))))))) | (~r(s(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(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7898,plain,
% 2.04/2.21 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7899,plain,
% 2.04/2.21 (((~![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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7898])).
% 2.04/2.21 tff(7900,plain,
% 2.04/2.21 (((~![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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7899, 7897])).
% 2.04/2.21 tff(7901,plain,
% 2.04/2.21 ((~![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(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7902,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7901, 7900])).
% 2.04/2.21 tff(7903,plain,
% 2.04/2.21 (~r(z, s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7902, 31, 569, 6392])).
% 2.04/2.21 tff(7904,plain,
% 2.04/2.21 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[194, 78, 7903])).
% 2.04/2.21 tff(7905,plain,
% 2.04/2.21 (b(z, s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7904, 7896])).
% 2.04/2.21 tff(7906,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4697, 20, 569])).
% 2.04/2.21 tff(7907,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[160, 7906])).
% 2.04/2.21 tff(7908,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[503, 162, 20])).
% 2.04/2.21 tff(7909,plain,
% 2.04/2.21 (b(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[83, 7908])).
% 2.04/2.21 tff(7910,plain,
% 2.04/2.21 (b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[477, 5797])).
% 2.04/2.21 tff(7911,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4251, 5799, 7910, 7909, 7907])).
% 2.04/2.21 tff(7912,plain,((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7913,plain,
% 2.04/2.21 (~r(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7912, 20, 569])).
% 2.04/2.21 tff(7914,plain,
% 2.04/2.21 (b(z, s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[182, 7913])).
% 2.04/2.21 tff(7915,plain,
% 2.04/2.21 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7376, 7914, 7905, 6392])).
% 2.04/2.21 tff(7916,plain,
% 2.04/2.21 (b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[477, 7915])).
% 2.04/2.21 tff(7917,plain,
% 2.04/2.21 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7376, 18, 7905, 6392])).
% 2.04/2.21 tff(7918,plain,
% 2.04/2.21 (b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[477, 7917])).
% 2.04/2.21 tff(7919,plain,
% 2.04/2.21 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[6577])).
% 2.04/2.21 tff(7920,plain,
% 2.04/2.21 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), elem!1)),
% 2.04/2.21 inference(symmetry,[status(thm)],[7919])).
% 2.04/2.21 tff(7921,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4030, 249, 20, 7907])).
% 2.04/2.21 tff(7922,plain,
% 2.04/2.21 (b(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[83, 7921])).
% 2.04/2.21 tff(7923,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1877, 7922, 569, 249])).
% 2.04/2.21 tff(7924,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[429, 7923])).
% 2.04/2.21 tff(7925,plain,
% 2.04/2.21 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4251, 7924, 7922, 7907])).
% 2.04/2.21 tff(7926,plain,
% 2.04/2.21 (r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[477, 7925])).
% 2.04/2.21 tff(7927,plain,
% 2.04/2.21 (r(s(z), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7926, 7920])).
% 2.04/2.21 tff(7928,plain,
% 2.04/2.21 (~b(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1835, 7924, 1827, 18])).
% 2.04/2.21 tff(7929,plain,
% 2.04/2.21 (r(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[608, 7928])).
% 2.04/2.21 tff(7930,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 2.04/2.21 tff(7931,plain,
% 2.04/2.21 (((~![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(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7932,plain,
% 2.04/2.21 (((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7933,plain,
% 2.04/2.21 (((~![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(z), elem!1)) | (~r(z, 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(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7932])).
% 2.04/2.21 tff(7934,plain,
% 2.04/2.21 (((~![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(z), elem!1)) | (~r(z, 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(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7933, 7931])).
% 2.04/2.21 tff(7935,plain,
% 2.04/2.21 ((~![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(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7936,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[7935, 7934])).
% 2.04/2.21 tff(7937,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7936, 31, 1622, 592, 7930])).
% 2.04/2.21 tff(7938,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7939,plain,
% 2.04/2.21 (~r(s(z), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7938, 7929, 1622])).
% 2.04/2.21 tff(7940,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7939, 7927])).
% 2.04/2.21 tff(7941,plain,((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(z, elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(7942,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7941, 18, 1827, 1622, 569, 20])).
% 2.04/2.21 tff(7943,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[646, 7942])).
% 2.04/2.21 tff(7944,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7945,plain,
% 2.04/2.21 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(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(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(7946,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[7945])).
% 2.04/2.21 tff(7947,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[7946, 7944])).
% 2.04/2.21 tff(7948,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(7949,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7948, 7947])).
% 2.04/2.22 tff(7950,plain,
% 2.04/2.22 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7949, 112, 1827, 7905, 7892])).
% 2.04/2.22 tff(7951,plain,
% 2.04/2.22 ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6914, 78, 7950])).
% 2.04/2.22 tff(7952,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7951, 6458])).
% 2.04/2.22 tff(7953,plain,
% 2.04/2.22 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5014, 7943, 20, 1827, 18])).
% 2.04/2.22 tff(7954,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[429, 7953])).
% 2.04/2.22 tff(7955,plain,
% 2.04/2.22 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7353, 7954, 7952])).
% 2.04/2.22 tff(7956,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6844, 78, 6841, 7955])).
% 2.04/2.22 tff(7957,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7958,plain,
% 2.04/2.22 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), 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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7959,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7958])).
% 2.04/2.22 tff(7960,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7959, 7957])).
% 2.04/2.22 tff(7961,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7962,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7961, 7960])).
% 2.04/2.22 tff(7963,plain,
% 2.04/2.22 (~b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7962, 112, 1827, 7918, 7956, 7905])).
% 2.04/2.22 tff(7964,plain,
% 2.04/2.22 (r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[608, 7963])).
% 2.04/2.22 tff(7965,plain,
% 2.04/2.22 (~r(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6380, 7964, 20])).
% 2.04/2.22 tff(7966,plain,
% 2.04/2.22 (b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[99, 7965])).
% 2.04/2.22 tff(7967,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4595, 112, 7966, 7943, 7907, 7918])).
% 2.04/2.22 tff(7968,plain,((~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(7969,plain,
% 2.04/2.22 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7968, 7914, 20, 6392, 1622, 569])).
% 2.04/2.22 tff(7970,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[398, 7969])).
% 2.04/2.22 tff(7971,plain,
% 2.04/2.22 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[577, 7970, 20, 569])).
% 2.04/2.22 tff(7972,plain,
% 2.04/2.22 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[646, 7971])).
% 2.04/2.22 tff(7973,plain,
% 2.04/2.22 (~b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4954, 112, 7972, 7907, 7916])).
% 2.04/2.22 tff(7974,plain,
% 2.04/2.22 (r(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[99, 7973])).
% 2.04/2.22 tff(7975,plain,
% 2.04/2.22 (~r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6380, 7974, 20])).
% 2.04/2.22 tff(7976,plain,
% 2.04/2.22 (b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[608, 7975])).
% 2.04/2.22 tff(7977,plain,
% 2.04/2.22 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7978,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7977])).
% 2.04/2.22 tff(7979,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7978, 6383])).
% 2.04/2.22 tff(7980,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7981,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7980, 7979])).
% 2.04/2.22 tff(7982,plain,
% 2.04/2.22 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7981, 112, 7914, 7976, 7892])).
% 2.04/2.22 tff(7983,plain,
% 2.04/2.22 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6377, 7982])).
% 2.04/2.22 tff(7984,plain,
% 2.04/2.22 (((~![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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7985,plain,
% 2.04/2.22 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7986,plain,
% 2.04/2.22 (((~![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(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7985])).
% 2.04/2.22 tff(7987,plain,
% 2.04/2.22 (((~![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(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7986, 7984])).
% 2.04/2.22 tff(7988,plain,
% 2.04/2.22 ((~![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(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7989,plain,
% 2.04/2.22 ((~![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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7988, 7987])).
% 2.04/2.22 tff(7990,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7989, 31, 20, 569, 982])).
% 2.04/2.22 tff(7991,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[917, 78, 224, 7990])).
% 2.04/2.22 tff(7992,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6865, 7286])).
% 2.04/2.22 tff(7993,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7994,plain,
% 2.04/2.22 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(7995,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[7994])).
% 2.04/2.22 tff(7996,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[7995, 7993])).
% 2.04/2.22 tff(7997,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(7998,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[7997, 7996])).
% 2.04/2.22 tff(7999,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7998, 112, 7914, 673, 7992, 7991, 7905, 7892])).
% 2.04/2.22 tff(8000,plain,((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8001,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8000, 7976, 6392, 20, 569])).
% 2.04/2.22 tff(8002,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6588, 8001])).
% 2.04/2.22 tff(8003,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6586, 8002])).
% 2.04/2.22 tff(8004,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6583, 8003])).
% 2.04/2.22 tff(8005,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6734, 1273, 539, 19])).
% 2.04/2.22 tff(8006,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1733, 8005])).
% 2.04/2.22 tff(8007,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1728, 8006, 85])).
% 2.04/2.22 tff(8008,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1718, 8007])).
% 2.04/2.22 tff(8009,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1294, 112, 4, 196, 1273, 8008])).
% 2.04/2.22 tff(8010,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8011,plain,
% 2.04/2.22 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8010, 8004, 7907, 7916, 7972, 7974])).
% 2.04/2.22 tff(8012,plain,
% 2.04/2.22 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[429, 8011])).
% 2.04/2.22 tff(8013,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7274, 31, 8012, 6392, 7983])).
% 2.04/2.22 tff(8014,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8015,plain,
% 2.04/2.22 (~r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8014, 6392, 569, 1622])).
% 2.04/2.22 tff(8016,plain,
% 2.04/2.22 (b(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[515, 8015])).
% 2.04/2.22 tff(8017,plain,
% 2.04/2.22 (~b(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7376, 21, 7905, 6392])).
% 2.04/2.22 tff(8018,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[182, 8017, 7855])).
% 2.04/2.22 tff(8019,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8020,plain,
% 2.04/2.22 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8019, 6392, 569])).
% 2.04/2.22 tff(8021,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[477, 8020])).
% 2.04/2.22 tff(8022,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7008, 1, 6392])).
% 2.04/2.22 tff(8023,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7012, 8022])).
% 2.04/2.22 tff(8024,plain,
% 2.04/2.22 (~b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7767, 112, 7905, 7892, 8023])).
% 2.04/2.22 tff(8025,plain,
% 2.04/2.22 (r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[527, 8024])).
% 2.04/2.22 tff(8026,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[563, 31, 8025, 569, 1])).
% 2.04/2.22 tff(8027,plain,((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8028,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8027, 6392, 569])).
% 2.04/2.22 tff(8029,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[160, 8028])).
% 2.04/2.22 tff(8030,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4251, 539, 8029, 19])).
% 2.04/2.22 tff(8031,plain,
% 2.04/2.22 (r(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[83, 8030])).
% 2.04/2.22 tff(8032,plain,
% 2.04/2.22 (~r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5054, 592, 8031])).
% 2.04/2.22 tff(8033,plain,
% 2.04/2.22 (b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[527, 8032])).
% 2.04/2.22 tff(8034,plain,
% 2.04/2.22 (~r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5054, 592, 3])).
% 2.04/2.22 tff(8035,plain,
% 2.04/2.22 (b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[527, 8034])).
% 2.04/2.22 tff(8036,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1718, 3461])).
% 2.04/2.22 tff(8037,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1692, 8036, 803, 8035])).
% 2.04/2.22 tff(8038,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[917, 78, 224, 8037])).
% 2.04/2.22 tff(8039,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8040,plain,
% 2.04/2.22 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(8041,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[8040])).
% 2.04/2.22 tff(8042,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[8041, 8039])).
% 2.04/2.22 tff(8043,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(8044,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[8043, 8042])).
% 2.04/2.22 tff(8045,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8044, 31, 592, 981, 8038])).
% 2.04/2.22 tff(8046,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(8047,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8046, 592, 803, 8031])).
% 2.04/2.22 tff(8048,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1733, 8047])).
% 2.04/2.22 tff(8049,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6734, 8048, 19, 539])).
% 2.04/2.22 tff(8050,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6583, 8049])).
% 2.04/2.22 tff(8051,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6586, 8050])).
% 2.04/2.22 tff(8052,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6588, 8051])).
% 2.04/2.22 tff(8053,plain,
% 2.04/2.22 (((~![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(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8054,plain,
% 2.04/2.23 (((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8055,plain,
% 2.04/2.23 (((~![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)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8054])).
% 2.04/2.23 tff(8056,plain,
% 2.04/2.23 (((~![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)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8055, 8053])).
% 2.04/2.23 tff(8057,plain,
% 2.04/2.23 ((~![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)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8058,plain,
% 2.04/2.23 ((~![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)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(z))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8057, 8056])).
% 2.04/2.23 tff(8059,plain,
% 2.04/2.23 (~r(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8058, 31, 569, 982])).
% 2.04/2.23 tff(8060,plain,
% 2.04/2.23 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6178, 78, 8059])).
% 2.04/2.23 tff(8061,plain,
% 2.04/2.23 (b(z, s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8060, 6168])).
% 2.04/2.23 tff(8062,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[917, 78, 224, 7111])).
% 2.04/2.23 tff(8063,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8064,plain,
% 2.04/2.23 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), 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(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8065,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8064])).
% 2.04/2.23 tff(8066,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8065, 8063])).
% 2.04/2.23 tff(8067,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8068,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8067, 8066])).
% 2.04/2.23 tff(8069,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8068, 112, 859, 803, 8062, 7777, 7892, 8061])).
% 2.04/2.23 tff(8070,plain,(r(s(s(s(s(z)))), z) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8071,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8070, 8052, 569, 803, 8033, 6392])).
% 2.04/2.23 tff(8072,plain,
% 2.04/2.23 (((~![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)))), s(s(s(s(elem!1)))))) | (~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(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8073,plain,
% 2.04/2.23 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8074,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8073])).
% 2.04/2.23 tff(8075,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8074, 8072])).
% 2.04/2.23 tff(8076,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8077,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8076, 8075])).
% 2.04/2.23 tff(8078,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8077, 31, 569, 8052, 8071])).
% 2.04/2.23 tff(8079,plain,((~r(s(z), z)) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8080,plain,
% 2.04/2.23 (~r(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8079, 539, 803, 6392, 19, 569])).
% 2.04/2.23 tff(8081,plain,
% 2.04/2.23 (b(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[608, 8080])).
% 2.04/2.23 tff(8082,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8083,plain,
% 2.04/2.23 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8084,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8083])).
% 2.04/2.23 tff(8085,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8084, 8082])).
% 2.04/2.23 tff(8086,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8087,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8086, 8085])).
% 2.04/2.23 tff(8088,plain,
% 2.04/2.23 ((~b(s(z), s(s(s(z))))) | (~b(s(z), z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8087, 112, 803, 8029, 539])).
% 2.04/2.23 tff(8089,plain,
% 2.04/2.23 (~b(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8088, 8081])).
% 2.04/2.23 tff(8090,plain,
% 2.04/2.23 (r(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[99, 8089])).
% 2.04/2.23 tff(8091,plain,
% 2.04/2.23 (~r(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3275, 612, 8031])).
% 2.04/2.23 tff(8092,plain,
% 2.04/2.23 (b(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[182, 8091])).
% 2.04/2.23 tff(8093,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1835, 8092, 19, 673])).
% 2.04/2.23 tff(8094,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[398, 8093])).
% 2.04/2.23 tff(8095,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[620, 8094, 612])).
% 2.04/2.23 tff(8096,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[646, 8095])).
% 2.04/2.23 tff(8097,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8010, 8096, 8029, 19, 539, 85])).
% 2.04/2.23 tff(8098,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6583, 8097])).
% 2.04/2.23 tff(8099,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6586, 8098])).
% 2.04/2.23 tff(8100,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6588, 8099])).
% 2.04/2.23 tff(8101,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8077, 31, 569, 8100])).
% 2.04/2.23 tff(8102,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[917, 78, 224, 8101])).
% 2.04/2.23 tff(8103,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6998, 31, 8100, 6392])).
% 2.04/2.23 tff(8104,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6865, 8103])).
% 2.04/2.23 tff(8105,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[7998, 112, 8092, 673, 8104, 8102, 7905, 7892])).
% 2.04/2.23 tff(8106,plain,((~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(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)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8107,plain,
% 2.04/2.23 (~r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8106, 8081, 6392, 569, 19, 539, 8090])).
% 2.04/2.23 tff(8108,plain,
% 2.04/2.23 (b(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[527, 8107])).
% 2.04/2.23 tff(8109,plain,
% 2.04/2.23 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6515, 8108, 7891, 803])).
% 2.04/2.23 tff(8110,plain,
% 2.04/2.23 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[235, 8109])).
% 2.04/2.23 tff(8111,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6687, 8110, 6392])).
% 2.04/2.23 tff(8112,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[646, 8111])).
% 2.04/2.23 tff(8113,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8010, 8112, 8029, 19, 539, 8090])).
% 2.04/2.23 tff(8114,plain,
% 2.04/2.23 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6583, 8113])).
% 2.04/2.23 tff(8115,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6586, 8114])).
% 2.04/2.23 tff(8116,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[6588, 8115])).
% 2.04/2.23 tff(8117,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8070, 8116, 569, 803, 8108, 6392])).
% 2.04/2.23 tff(8118,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8077, 31, 569, 8116, 8117])).
% 2.04/2.23 tff(8119,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8120,plain,
% 2.04/2.23 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8119, 8021, 8016, 6392, 569])).
% 2.04/2.23 tff(8121,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[429, 8120])).
% 2.04/2.23 tff(8122,plain,
% 2.04/2.23 (~r(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[589, 8121, 569])).
% 2.04/2.23 tff(8123,plain,
% 2.04/2.23 (b(z, s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[182, 8122])).
% 2.04/2.23 tff(8124,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1867, 102, 803, 18])).
% 2.04/2.23 tff(8125,plain,
% 2.04/2.23 (r(s(s(s(z))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[83, 8124])).
% 2.04/2.23 tff(8126,plain,
% 2.04/2.23 ((~b(s(z), s(s(s(z))))) | (~b(s(z), z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8087, 112, 803, 196, 539])).
% 2.04/2.23 tff(8127,plain,
% 2.04/2.23 (~b(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8126, 102])).
% 2.04/2.23 tff(8128,plain,
% 2.04/2.23 (r(s(z), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[608, 8127])).
% 2.04/2.23 tff(8129,plain,
% 2.04/2.23 (~r(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[5054, 8128, 8125])).
% 2.04/2.23 tff(8130,plain,
% 2.04/2.23 (b(s(s(s(z))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[527, 8129])).
% 2.04/2.23 tff(8131,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3970, 8125, 408])).
% 2.04/2.23 tff(8132,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[646, 8131])).
% 2.04/2.23 tff(8133,plain,
% 2.04/2.23 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[600, 8128, 408])).
% 2.04/2.23 tff(8134,plain,
% 2.04/2.23 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[398, 8133])).
% 2.04/2.23 tff(8135,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4333, 8134, 8132, 803, 8130])).
% 2.04/2.23 tff(8136,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(8137,plain,
% 2.04/2.23 (~b(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8136, 8016, 8121, 8029, 8021, 8123])).
% 2.04/2.23 tff(8138,plain,
% 2.04/2.23 (r(s(z), s(s(s(z))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[99, 8137])).
% 2.04/2.23 tff(8139,plain,
% 2.04/2.23 (~r(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8077, 31, 569, 982])).
% 2.04/2.23 tff(8140,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[917, 78, 224, 8139])).
% 2.04/2.23 tff(8141,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8142,plain,
% 2.04/2.23 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(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))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(8143,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(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))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[8142])).
% 2.04/2.23 tff(8144,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(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))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[8143, 8141])).
% 2.04/2.23 tff(8145,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(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))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(8146,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[8145, 8144])).
% 2.04/2.23 tff(8147,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[8146, 112, 7992, 8140, 7905, 7892])).
% 2.04/2.23 tff(8148,plain,((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8149,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8148, 6392, 569])).
% 2.04/2.24 tff(8150,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6588, 8149])).
% 2.04/2.24 tff(8151,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6586, 8150])).
% 2.04/2.24 tff(8152,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[6583, 8151])).
% 2.04/2.24 tff(8153,plain,
% 2.04/2.24 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1855, 8138, 8121])).
% 2.04/2.24 tff(8154,plain,
% 2.04/2.24 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[646, 8153])).
% 2.04/2.24 tff(8155,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1294, 112, 8154, 8029, 8152])).
% 2.04/2.24 tff(8156,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1718, 8155])).
% 2.04/2.24 tff(8157,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1728, 8156, 8138])).
% 2.04/2.24 tff(8158,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1733, 8157])).
% 2.04/2.24 tff(8159,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, 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(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, 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(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8160,plain,
% 2.04/2.24 (((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, 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(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8161,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, 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(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8160])).
% 2.04/2.24 tff(8162,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, 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(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8161, 8159])).
% 2.04/2.24 tff(8163,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8164,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8163, 8162])).
% 2.04/2.24 tff(8165,plain,
% 2.04/2.24 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8164, 112, 8016, 8123, 8029, 8021, 8152])).
% 2.04/2.24 tff(8166,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8165, 8158])).
% 2.04/2.24 tff(8167,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[917, 78, 224, 8166])).
% 2.04/2.24 tff(8168,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1294, 112, 4, 196, 1273])).
% 2.04/2.24 tff(8169,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1718, 8168])).
% 2.04/2.24 tff(8170,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1728, 8169, 85])).
% 2.04/2.24 tff(8171,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1733, 8170])).
% 2.04/2.24 tff(8172,plain,
% 2.04/2.24 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8164, 112, 803, 18, 196, 539, 1273])).
% 2.04/2.24 tff(8173,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8172, 8171])).
% 2.04/2.24 tff(8174,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[917, 78, 224, 8173])).
% 2.04/2.24 tff(8175,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7162, 31, 612, 8169, 8174])).
% 2.04/2.24 tff(8176,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(8177,plain,
% 2.04/2.24 (~r(s(s(s(z))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8176, 8152, 8016, 8123, 8029, 8021, 8138, 8154])).
% 2.04/2.24 tff(8178,plain,
% 2.04/2.24 (b(s(s(s(z))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[527, 8177])).
% 2.04/2.24 tff(8179,plain,
% 2.04/2.24 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4333, 8178, 8016, 8154])).
% 2.04/2.24 tff(8180,plain,
% 2.04/2.24 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[398, 8179])).
% 2.04/2.24 tff(8181,plain,
% 2.04/2.24 (((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8182,plain,
% 2.04/2.24 (((~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(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8183,plain,
% 2.04/2.24 (((~![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(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(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8182])).
% 2.04/2.24 tff(8184,plain,
% 2.04/2.24 (((~![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(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(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8183, 8181])).
% 2.04/2.24 tff(8185,plain,
% 2.04/2.24 ((~![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(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)))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8186,plain,
% 2.04/2.24 ((~![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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8185, 8184])).
% 2.04/2.24 tff(8187,plain,
% 2.04/2.24 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8186, 31, 8180, 8167])).
% 2.04/2.24 tff(8188,plain,
% 2.04/2.24 (((~![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))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8189,plain,
% 2.04/2.24 ((~![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))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8190,plain,
% 2.04/2.24 ((~![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)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8189, 8188])).
% 2.04/2.24 tff(8191,plain,
% 2.04/2.24 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8190, 78, 8187])).
% 2.04/2.24 tff(8192,plain,
% 2.04/2.24 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8191, 7884])).
% 2.04/2.24 tff(8193,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8194,plain,
% 2.04/2.24 (((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8195,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[8194])).
% 2.04/2.24 tff(8196,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[8195, 8193])).
% 2.04/2.24 tff(8197,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(8198,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[8197, 8196])).
% 2.04/2.24 tff(8199,plain,
% 2.04/2.24 (~b(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[8198, 112, 8154, 8029, 8021, 8152, 8192])).
% 2.04/2.24 tff(8200,plain,
% 2.04/2.24 (r(s(z), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[7105, 78, 948, 8199])).
% 2.04/2.24 tff(8201,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8202,plain,
% 2.04/2.24 (((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(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(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(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(8203,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(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(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8202])).
% 2.04/2.25 tff(8204,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(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(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8203, 8201])).
% 2.04/2.25 tff(8205,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(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(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8206,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8205, 8204])).
% 2.04/2.25 tff(8207,plain,
% 2.04/2.25 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8206, 112, 8154, 8029, 8152, 8192])).
% 2.04/2.25 tff(8208,plain,
% 2.04/2.25 ((s(s(s(z))) = s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4506, 78, 8207])).
% 2.04/2.25 tff(8209,plain,
% 2.04/2.25 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8208, 4496])).
% 2.04/2.25 tff(8210,plain,
% 2.04/2.25 (((~![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(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)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8211,plain,
% 2.04/2.25 (((~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)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8212,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8211])).
% 2.04/2.25 tff(8213,plain,
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% 2.04/2.25 tff(8302,plain,
% 2.04/2.25 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[202, 112, 8301, 8267, 8221])).
% 2.04/2.25 tff(8303,plain,
% 2.04/2.25 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[235, 8302])).
% 2.04/2.25 tff(8304,plain,
% 2.04/2.25 (~r(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6661, 6467, 6653])).
% 2.04/2.25 tff(8305,plain,
% 2.04/2.25 (b(s(z), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[99, 8304])).
% 2.04/2.25 tff(8306,plain,
% 2.04/2.25 (~b(s(s(s(s(s(elem!1))))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4042, 859, 803, 762])).
% 2.04/2.25 tff(8307,plain,
% 2.04/2.25 (r(s(s(s(s(s(elem!1))))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[494, 8306])).
% 2.04/2.25 tff(8308,plain,
% 2.04/2.25 (~b(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2519, 112, 102, 859, 803])).
% 2.04/2.25 tff(8309,plain,
% 2.04/2.25 (r(s(z), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[608, 8308])).
% 2.04/2.25 tff(8310,plain,
% 2.04/2.25 (~r(s(z), s(s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3108, 8309, 8307])).
% 2.04/2.25 tff(8311,plain,
% 2.04/2.25 (b(s(z), s(s(s(s(s(elem!1))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[749, 8310])).
% 2.04/2.25 tff(8312,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8313,plain,
% 2.04/2.25 (((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), 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(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8314,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), 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(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8313])).
% 2.04/2.25 tff(8315,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), 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(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8314, 8312])).
% 2.04/2.25 tff(8316,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), 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(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8317,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(z), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8316, 8315])).
% 2.04/2.25 tff(8318,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8317, 112, 102, 859, 803, 8311, 406, 762])).
% 2.04/2.25 tff(8319,plain,((~b(s(z), 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(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8320,plain,
% 2.04/2.25 (~b(s(s(s(z))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8319, 8305, 406, 762, 803])).
% 2.04/2.25 tff(8321,plain,
% 2.04/2.25 (r(s(s(s(z))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[527, 8320])).
% 2.04/2.25 tff(8322,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8323,plain,
% 2.04/2.25 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), 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))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(8324,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[8323])).
% 2.04/2.25 tff(8325,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[8324, 8322])).
% 2.04/2.25 tff(8326,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(8327,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[8326, 8325])).
% 2.04/2.25 tff(8328,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8327, 31, 8321, 3, 6653, 6467])).
% 2.04/2.25 tff(8329,plain,((~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))))) | (~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(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(8330,plain,
% 2.04/2.25 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8329, 803, 8303, 406, 762, 3])).
% 2.04/2.25 tff(8331,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[6377, 8330])).
% 2.04/2.25 tff(8332,plain,
% 2.04/2.25 (~b(s(s(s(s(z)))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[912, 112, 18, 673, 6625])).
% 2.04/2.25 tff(8333,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[8077, 31, 7847, 982])).
% 2.04/2.25 tff(8334,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[7114, 8333, 8332])).
% 2.04/2.26 tff(8335,plain,((~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8336,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8335, 673, 18, 408])).
% 2.04/2.26 tff(8337,plain,
% 2.04/2.26 (~r(s(s(s(s(z)))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6588, 8336])).
% 2.04/2.26 tff(8338,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6586, 8337])).
% 2.04/2.26 tff(8339,plain,
% 2.04/2.26 (b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6583, 8338])).
% 2.04/2.26 tff(8340,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8341,plain,
% 2.04/2.26 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8342,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8341])).
% 2.04/2.26 tff(8343,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8342, 8340])).
% 2.04/2.26 tff(8344,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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)))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8345,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8344, 8343])).
% 2.04/2.26 tff(8346,plain,
% 2.04/2.26 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8345, 112, 4, 196, 8221, 7332])).
% 2.04/2.26 tff(8347,plain,
% 2.04/2.26 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7012, 8346])).
% 2.04/2.26 tff(8348,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8349,plain,
% 2.04/2.26 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(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(s(elem!1))))))) <=> ((~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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8350,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(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(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8349])).
% 2.04/2.26 tff(8351,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(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(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8350, 8348])).
% 2.04/2.26 tff(8352,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(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(s(elem!1)))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8353,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8352, 8351])).
% 2.04/2.26 tff(8354,plain,
% 2.04/2.26 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8353, 112, 4, 196, 1273, 8221, 7332])).
% 2.04/2.26 tff(8355,plain,
% 2.04/2.26 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[6865, 8354])).
% 2.04/2.26 tff(8356,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3221, 8355, 8169, 8347])).
% 2.04/2.26 tff(8357,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(8358,plain,
% 2.04/2.26 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8357, 8339, 196, 4])).
% 2.04/2.26 tff(8359,plain,
% 2.04/2.26 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7342, 6458])).
% 2.04/2.26 tff(8360,plain,
% 2.04/2.26 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8359, 8358])).
% 2.04/2.26 tff(8361,plain,
% 2.04/2.26 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7353, 8360, 408])).
% 2.04/2.26 tff(8362,plain,
% 2.04/2.26 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[7184, 8361])).
% 2.04/2.26 tff(8363,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8364,plain,
% 2.04/2.26 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8365,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8364])).
% 2.04/2.26 tff(8366,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8365, 8363])).
% 2.04/2.26 tff(8367,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8368,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[8367, 8366])).
% 2.04/2.26 tff(8369,plain,
% 2.04/2.26 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[8368, 112, 18, 673, 4909, 8362])).
% 2.04/2.26 tff(8370,plain,
% 2.04/2.26 (r(z, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[194, 78, 8369, 17])).
% 2.04/2.26 tff(8371,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(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(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8372,plain,
% 2.04/2.26 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(8373,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(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(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[8372])).
% 2.04/2.26 tff(8374,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(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(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[8373, 8371])).
% 2.04/2.26 tff(8375,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(8376,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8375, 8374])).
% 2.04/2.27 tff(8377,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8376, 31, 408, 7847, 8360, 8370])).
% 2.04/2.27 tff(8378,plain,((~b(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(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(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8379,plain,
% 2.04/2.27 (~b(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8378, 8331, 8285, 408, 8267, 8301])).
% 2.04/2.27 tff(8380,plain,
% 2.04/2.27 (r(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[608, 8379])).
% 2.04/2.27 tff(8381,plain,
% 2.04/2.27 (~r(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5054, 8380, 3])).
% 2.04/2.27 tff(8382,plain,
% 2.04/2.27 (b(s(s(s(z))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[527, 8381])).
% 2.04/2.27 tff(8383,plain,
% 2.04/2.27 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[600, 8380, 408])).
% 2.04/2.27 tff(8384,plain,
% 2.04/2.27 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[398, 8383])).
% 2.04/2.27 tff(8385,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4333, 8384, 8382, 8301, 803])).
% 2.04/2.27 tff(8386,plain,((~b(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8387,plain,
% 2.04/2.27 (~b(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8386, 581, 3, 8299, 8295])).
% 2.04/2.27 tff(8388,plain,
% 2.04/2.27 (r(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[515, 8387])).
% 2.04/2.27 tff(8389,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[7262, 31, 8388, 8271])).
% 2.04/2.27 tff(8390,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8389])).
% 2.04/2.27 tff(8391,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6503, 31, 3, 6653, 6467])).
% 2.04/2.27 tff(8392,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8393,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8392, 8271, 3])).
% 2.04/2.27 tff(8394,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6377, 8393])).
% 2.04/2.27 tff(8395,plain,
% 2.04/2.27 (~b(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8378, 8394, 8285, 581, 8267, 8269])).
% 2.04/2.27 tff(8396,plain,
% 2.04/2.27 (r(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[608, 8395])).
% 2.04/2.27 tff(8397,plain,
% 2.04/2.27 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[600, 8396, 581])).
% 2.04/2.27 tff(8398,plain,
% 2.04/2.27 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[398, 8397])).
% 2.04/2.27 tff(8399,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8400,plain,
% 2.04/2.27 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8401,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8400])).
% 2.04/2.27 tff(8402,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8401, 8399])).
% 2.04/2.27 tff(8403,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8404,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8403, 8402])).
% 2.04/2.27 tff(8405,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8404, 112, 8285, 8398, 8394, 8221, 8390])).
% 2.04/2.27 tff(8406,plain,(b(s(s(s(s(elem!1)))), s(z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8407,plain,
% 2.04/2.27 (b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8406, 3])).
% 2.04/2.27 tff(8408,plain,
% 2.04/2.27 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4155, 21, 85])).
% 2.04/2.27 tff(8409,plain,
% 2.04/2.27 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[646, 8408])).
% 2.04/2.27 tff(8410,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[202, 112, 8409, 196, 8221])).
% 2.04/2.27 tff(8411,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[235, 8410])).
% 2.04/2.27 tff(8412,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8413,plain,
% 2.04/2.27 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8414,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8413])).
% 2.04/2.27 tff(8415,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), 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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8414, 8412])).
% 2.04/2.27 tff(8416,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8417,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8416, 8415])).
% 2.04/2.27 tff(8418,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8417, 31, 85, 8411])).
% 2.04/2.27 tff(8419,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[7184, 8418])).
% 2.04/2.27 tff(8420,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6661, 8411, 85])).
% 2.04/2.27 tff(8421,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6377, 8420])).
% 2.04/2.27 tff(8422,plain,
% 2.04/2.27 (~r(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1065, 31, 7847, 21])).
% 2.04/2.27 tff(8423,plain,
% 2.04/2.27 (b(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[608, 8422])).
% 2.04/2.27 tff(8424,plain,
% 2.04/2.27 (~r(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8274, 21])).
% 2.04/2.27 tff(8425,plain,
% 2.04/2.27 (b(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[182, 8424])).
% 2.04/2.27 tff(8426,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8427,plain,
% 2.04/2.27 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8428,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8427])).
% 2.04/2.27 tff(8429,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8428, 8426])).
% 2.04/2.27 tff(8430,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8431,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8430, 8429])).
% 2.04/2.27 tff(8432,plain,
% 2.04/2.27 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8431, 112, 8425, 19, 8423, 8421, 8419])).
% 2.04/2.27 tff(8433,plain,
% 2.04/2.27 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8359, 8432])).
% 2.04/2.27 tff(8434,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6388, 112, 8425, 8423, 8421])).
% 2.04/2.27 tff(8435,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8434])).
% 2.04/2.27 tff(8436,plain,
% 2.04/2.27 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1835, 8423, 19, 8425])).
% 2.04/2.27 tff(8437,plain,
% 2.04/2.27 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[398, 8436])).
% 2.04/2.27 tff(8438,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8439,plain,
% 2.04/2.27 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8440,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8439])).
% 2.04/2.27 tff(8441,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8440, 8438])).
% 2.04/2.27 tff(8442,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8443,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8442, 8441])).
% 2.04/2.27 tff(8444,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8443, 31, 8437, 8435, 8433])).
% 2.04/2.27 tff(8445,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(8446,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8445, 196, 85, 19])).
% 2.04/2.27 tff(8447,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[477, 8446])).
% 2.04/2.27 tff(8448,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8222, 8447, 19])).
% 2.04/2.27 tff(8449,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[6377, 8448])).
% 2.04/2.27 tff(8450,plain,
% 2.04/2.27 (((~![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))), 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(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8451,plain,
% 2.04/2.27 (((~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(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(8452,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[8451])).
% 2.04/2.27 tff(8453,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[8452, 8450])).
% 2.04/2.27 tff(8454,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(8455,plain,
% 2.04/2.27 ((~![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))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[8454, 8453])).
% 2.04/2.27 tff(8456,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[8455, 31, 3, 8449])).
% 2.04/2.27 tff(8457,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[7012, 8456])).
% 2.04/2.27 tff(8458,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8459,plain,
% 2.04/2.28 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8460,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8459])).
% 2.04/2.28 tff(8461,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8460, 8458])).
% 2.04/2.28 tff(8462,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8463,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8462, 8461])).
% 2.04/2.28 tff(8464,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8463, 112, 19, 196, 539, 8221, 7332, 7578])).
% 2.04/2.28 tff(8465,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), 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(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8466,plain,
% 2.04/2.28 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8465, 196, 19, 8447, 8457])).
% 2.04/2.28 tff(8467,plain,
% 2.04/2.28 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8359, 8466])).
% 2.04/2.28 tff(8468,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6661, 8449, 85])).
% 2.04/2.28 tff(8469,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[235, 8468])).
% 2.04/2.28 tff(8470,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[577, 20, 568, 569])).
% 2.04/2.28 tff(8471,plain,
% 2.04/2.28 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[646, 8470])).
% 2.04/2.28 tff(8472,plain,
% 2.04/2.28 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[202, 112, 8471, 7907, 184])).
% 2.04/2.28 tff(8473,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[235, 8472])).
% 2.04/2.28 tff(8474,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7262, 31, 20, 8473])).
% 2.04/2.28 tff(8475,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8474])).
% 2.04/2.28 tff(8476,plain,
% 2.04/2.28 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6661, 8473, 85])).
% 2.04/2.28 tff(8477,plain,
% 2.04/2.28 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6377, 8476])).
% 2.04/2.28 tff(8478,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6388, 112, 18, 4855, 8477, 8475])).
% 2.04/2.28 tff(8479,plain,((~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8480,plain,
% 2.04/2.28 ((~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8479, 7847, 8221])).
% 2.04/2.28 tff(8481,plain,
% 2.04/2.28 (~r(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8480, 568, 85, 18])).
% 2.04/2.28 tff(8482,plain,
% 2.04/2.28 (b(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[515, 8481])).
% 2.04/2.28 tff(8483,plain,
% 2.04/2.28 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6675, 112, 8482, 196, 6507, 8221])).
% 2.04/2.28 tff(8484,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8483])).
% 2.04/2.28 tff(8485,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8443, 31, 568, 8484, 7345])).
% 2.04/2.28 tff(8486,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8487,plain,
% 2.04/2.28 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8486, 18, 196, 8469, 85, 8467])).
% 2.04/2.28 tff(8488,plain,
% 2.04/2.28 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[398, 8487])).
% 2.04/2.28 tff(8489,plain,
% 2.04/2.28 (~b(s(z), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1835, 8488, 19, 18])).
% 2.04/2.28 tff(8490,plain,
% 2.04/2.28 (r(s(z), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[608, 8489])).
% 2.04/2.28 tff(8491,plain,
% 2.04/2.28 (~r(s(s(s(z))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5054, 8490, 3])).
% 2.04/2.28 tff(8492,plain,
% 2.04/2.28 (b(s(s(s(z))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[527, 8491])).
% 2.04/2.28 tff(8493,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8494,plain,
% 2.04/2.28 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(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)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8495,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8494])).
% 2.04/2.28 tff(8496,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8495, 8493])).
% 2.04/2.28 tff(8497,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8498,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8497, 8496])).
% 2.04/2.28 tff(8499,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8498, 112, 8492, 8488, 196, 8221, 8457])).
% 2.04/2.28 tff(8500,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8501,plain,
% 2.04/2.28 (~b(z, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8500, 196, 3, 19, 85])).
% 2.04/2.28 tff(8502,plain,
% 2.04/2.28 (r(z, s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[182, 8501])).
% 2.04/2.28 tff(8503,plain,
% 2.04/2.28 (~r(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8278, 8502])).
% 2.04/2.28 tff(8504,plain,
% 2.04/2.28 (~b(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6517, 8502, 3, 8449])).
% 2.04/2.28 tff(8505,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[515, 8504, 8503])).
% 2.04/2.28 tff(8506,plain,((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8507,plain,
% 2.04/2.28 (~r(s(z), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8506, 8407, 3, 8267])).
% 2.04/2.28 tff(8508,plain,
% 2.04/2.28 (b(s(z), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[99, 8507])).
% 2.04/2.28 tff(8509,plain,
% 2.04/2.28 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8222, 4909, 19])).
% 2.04/2.28 tff(8510,plain,
% 2.04/2.28 (r(s(z), s(s(s(s(elem!1)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[477, 8509])).
% 2.04/2.28 tff(8511,plain,
% 2.04/2.28 (~r(s(z), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1065, 31, 7847, 8510])).
% 2.04/2.28 tff(8512,plain,
% 2.04/2.28 (b(s(z), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[608, 8511])).
% 2.04/2.28 tff(8513,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8514,plain,
% 2.04/2.28 (((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8515,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8514])).
% 2.04/2.28 tff(8516,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8515, 8513])).
% 2.04/2.28 tff(8517,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8518,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[8517, 8516])).
% 2.04/2.28 tff(8519,plain,
% 2.04/2.28 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8518, 112, 102, 196, 8221])).
% 2.04/2.28 tff(8520,plain,
% 2.04/2.28 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8519, 4909])).
% 2.04/2.28 tff(8521,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[235, 8520])).
% 2.04/2.28 tff(8522,plain,
% 2.04/2.28 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6388, 112, 18, 8512, 4909])).
% 2.04/2.28 tff(8523,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8522])).
% 2.04/2.28 tff(8524,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[7262, 31, 20, 1792, 6653])).
% 2.04/2.28 tff(8525,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(8526,plain,
% 2.04/2.28 (~r(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[8525, 8523, 8521])).
% 2.04/2.28 tff(8527,plain,
% 2.04/2.28 (b(z, s(s(s(z))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[515, 8526])).
% 2.04/2.28 tff(8528,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8529,plain,
% 2.04/2.28 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(8530,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[8529])).
% 2.04/2.28 tff(8531,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[8530, 8528])).
% 2.04/2.28 tff(8532,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(8533,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8532, 8531])).
% 2.04/2.29 tff(8534,plain,
% 2.04/2.29 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8533, 112, 102, 8527, 18, 4909])).
% 2.04/2.29 tff(8535,plain,
% 2.04/2.29 (r(z, s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[194, 78, 8534, 17])).
% 2.04/2.29 tff(8536,plain,
% 2.04/2.29 (~b(s(s(s(s(elem!1)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1835, 8512, 19, 18])).
% 2.04/2.29 tff(8537,plain,
% 2.04/2.29 (r(s(s(s(s(elem!1)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[398, 8536])).
% 2.04/2.29 tff(8538,plain,
% 2.04/2.29 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8443, 31, 8537, 8523])).
% 2.04/2.29 tff(8539,plain,
% 2.04/2.29 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8359, 8538])).
% 2.04/2.29 tff(8540,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8541,plain,
% 2.04/2.29 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8542,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8541])).
% 2.04/2.29 tff(8543,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8542, 8540])).
% 2.04/2.29 tff(8544,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8545,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8544, 8543])).
% 2.04/2.29 tff(8546,plain,
% 2.04/2.29 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8545, 112, 196, 8221, 8539])).
% 2.04/2.29 tff(8547,plain,
% 2.04/2.29 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7012, 8546])).
% 2.04/2.29 tff(8548,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(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))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8549,plain,
% 2.04/2.29 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8550,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8549])).
% 2.04/2.29 tff(8551,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8550, 8548])).
% 2.04/2.29 tff(8552,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8553,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8552, 8551])).
% 2.04/2.29 tff(8554,plain,
% 2.04/2.29 (~r(s(s(s(z))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8553, 31, 8547, 8535])).
% 2.04/2.29 tff(8555,plain,
% 2.04/2.29 (b(s(s(s(z))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[527, 8554])).
% 2.04/2.29 tff(8556,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2519, 112, 102, 8555, 8527, 8512])).
% 2.04/2.29 tff(8557,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8558,plain,
% 2.04/2.29 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8557, 8508, 8285, 8267, 8407])).
% 2.04/2.29 tff(8559,plain,
% 2.04/2.29 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6377, 8558])).
% 2.04/2.29 tff(8560,plain,
% 2.04/2.29 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8392, 8559, 3])).
% 2.04/2.29 tff(8561,plain,
% 2.04/2.29 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[235, 8560])).
% 2.04/2.29 tff(8562,plain,
% 2.04/2.29 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8455, 31, 3, 8559])).
% 2.04/2.29 tff(8563,plain,
% 2.04/2.29 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[7012, 8562])).
% 2.04/2.29 tff(8564,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8545, 112, 196, 8221, 7332, 7578])).
% 2.04/2.29 tff(8565,plain,((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8566,plain,
% 2.04/2.29 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8565, 8267, 8563])).
% 2.04/2.29 tff(8567,plain,
% 2.04/2.29 (r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8359, 8566])).
% 2.04/2.29 tff(8568,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8443, 31, 568, 1792, 7345])).
% 2.04/2.29 tff(8569,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8570,plain,
% 2.04/2.29 (~r(s(s(s(s(elem!1)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8569, 1792, 7345])).
% 2.04/2.29 tff(8571,plain,
% 2.04/2.29 (b(s(s(s(s(elem!1)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[398, 8570])).
% 2.04/2.29 tff(8572,plain,
% 2.04/2.29 (~b(s(z), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1835, 8571, 19, 18])).
% 2.04/2.29 tff(8573,plain,
% 2.04/2.29 (r(s(z), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[608, 8572])).
% 2.04/2.29 tff(8574,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6644, 31, 8573, 1792, 6467])).
% 2.04/2.29 tff(8575,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8576,plain,
% 2.04/2.29 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8575, 8559, 8407, 8285, 8567])).
% 2.04/2.29 tff(8577,plain,
% 2.04/2.29 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8576])).
% 2.04/2.29 tff(8578,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6675, 112, 803, 196, 6507, 8221, 7468])).
% 2.04/2.29 tff(8579,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8580,plain,
% 2.04/2.29 (~b(z, s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8579, 8267, 8561, 8577])).
% 2.04/2.29 tff(8581,plain,
% 2.04/2.29 (r(z, s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[515, 8580])).
% 2.04/2.29 tff(8582,plain,
% 2.04/2.29 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3991, 8581, 3, 8267, 8285])).
% 2.04/2.29 tff(8583,plain,
% 2.04/2.29 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[646, 8582])).
% 2.04/2.29 tff(8584,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[202, 112, 8583, 8267, 8561, 8221])).
% 2.04/2.29 tff(8585,plain,(~r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(8586,plain,
% 2.04/2.29 (b(s(s(s(z))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[83, 8585])).
% 2.04/2.29 tff(8587,plain,
% 2.04/2.29 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1330, 1264])).
% 2.04/2.29 tff(8588,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[1337])).
% 2.04/2.29 tff(8589,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.29 inference(symmetry,[status(thm)],[8588])).
% 2.04/2.29 tff(8590,plain,
% 2.04/2.29 ((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8589])).
% 2.04/2.29 tff(8591,plain,
% 2.04/2.29 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~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(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8592,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8591])).
% 2.04/2.29 tff(8593,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8592, 6727])).
% 2.04/2.29 tff(8594,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8595,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8594, 8593])).
% 2.04/2.29 tff(8596,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8595, 112, 19, 539, 906])).
% 2.04/2.29 tff(8597,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8596, 8590])).
% 2.04/2.29 tff(8598,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1335, 8597, 8587])).
% 2.04/2.29 tff(8599,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1343, 8598, 1264])).
% 2.04/2.29 tff(8600,plain,
% 2.04/2.29 (((~![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(s(s(s(elem!1)))))) | (~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(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8601,plain,
% 2.04/2.29 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8602,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8601])).
% 2.04/2.29 tff(8603,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8602, 8600])).
% 2.04/2.29 tff(8604,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(8605,plain,
% 2.04/2.29 ((~![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(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[8604, 8603])).
% 2.04/2.29 tff(8606,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[8605, 31, 162, 569, 8599])).
% 2.04/2.29 tff(8607,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[917, 78, 224, 8606])).
% 2.04/2.29 tff(8608,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[6744, 31, 1, 8599])).
% 2.04/2.29 tff(8609,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[972, 78, 969, 8608])).
% 2.04/2.29 tff(8610,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8611,plain,
% 2.04/2.29 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(8612,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[8611])).
% 2.04/2.29 tff(8613,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[8612, 8610])).
% 2.13/2.30 tff(8614,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(8615,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[8614, 8613])).
% 2.13/2.30 tff(8616,plain,
% 2.13/2.30 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8615, 112, 2662, 101, 906])).
% 2.13/2.30 tff(8617,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8616, 8609, 8607])).
% 2.13/2.30 tff(8618,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8619,plain,
% 2.13/2.30 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(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))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8618, 6330])).
% 2.13/2.30 tff(8620,plain,
% 2.13/2.30 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8619, 7847])).
% 2.13/2.30 tff(8621,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8620, 7866, 1, 7863, 162, 8586])).
% 2.13/2.30 tff(8622,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1733, 8621])).
% 2.13/2.30 tff(8623,plain,
% 2.13/2.30 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2350, 31, 8622, 8224])).
% 2.13/2.30 tff(8624,plain,
% 2.13/2.30 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6486, 78, 6483, 8623])).
% 2.13/2.30 tff(8625,plain,
% 2.13/2.30 (~r(s(s(s(s(s(z))))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6473, 31, 162, 8224])).
% 2.13/2.30 tff(8626,plain,
% 2.13/2.30 (b(s(s(s(s(s(z))))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8625])).
% 2.13/2.30 tff(8627,plain,
% 2.13/2.30 (~r(z, s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6174, 31, 162, 8622])).
% 2.13/2.30 tff(8628,plain,
% 2.13/2.30 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7424, 6168])).
% 2.13/2.30 tff(8629,plain,
% 2.13/2.30 (b(z, s(s(s(s(z)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8628, 8627])).
% 2.13/2.30 tff(8630,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2940, 31, 162, 8622])).
% 2.13/2.30 tff(8631,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7114, 8630])).
% 2.13/2.30 tff(8632,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8633,plain,
% 2.13/2.30 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8634,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[8633])).
% 2.13/2.30 tff(8635,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[8634, 8632])).
% 2.13/2.30 tff(8636,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(8637,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[8636, 8635])).
% 2.13/2.30 tff(8638,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8637, 112, 8631, 8629, 8626, 8624])).
% 2.13/2.30 tff(8639,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8640,plain,
% 2.13/2.30 (~r(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8639, 1])).
% 2.13/2.30 tff(8641,plain,
% 2.13/2.30 (b(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[182, 8640])).
% 2.13/2.30 tff(8642,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2685, 112, 859, 8586, 18, 673])).
% 2.13/2.30 tff(8643,plain,((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8644,plain,
% 2.13/2.30 (~b(s(z), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8643, 7849, 8641])).
% 2.13/2.30 tff(8645,plain,
% 2.13/2.30 (r(s(z), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[608, 8644])).
% 2.13/2.30 tff(8646,plain,
% 2.13/2.30 ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1877, 7847])).
% 2.13/2.30 tff(8647,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8646, 408, 8586])).
% 2.13/2.30 tff(8648,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[646, 8647])).
% 2.13/2.30 tff(8649,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[600, 408, 592])).
% 2.13/2.30 tff(8650,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[398, 8649])).
% 2.13/2.30 tff(8651,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4333, 8650, 8648, 803, 859])).
% 2.13/2.30 tff(8652,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8653,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8652, 7852, 7849, 8645])).
% 2.13/2.30 tff(8654,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[429, 8653])).
% 2.13/2.30 tff(8655,plain,
% 2.13/2.30 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8222, 8654, 7863])).
% 2.13/2.30 tff(8656,plain,
% 2.13/2.30 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6377, 8655])).
% 2.13/2.30 tff(8657,plain,
% 2.13/2.30 (~b(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1867, 8641, 8586, 7852])).
% 2.13/2.30 tff(8658,plain,
% 2.13/2.30 (r(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[99, 8657])).
% 2.13/2.30 tff(8659,plain,
% 2.13/2.30 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6661, 8656, 8658])).
% 2.13/2.30 tff(8660,plain,
% 2.13/2.30 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[235, 8659])).
% 2.13/2.30 tff(8661,plain,
% 2.13/2.30 (r(s(s(s(s(s(z))))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6515, 8660, 7852, 7849])).
% 2.13/2.30 tff(8662,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8575, 8661, 8641, 8654, 8656])).
% 2.13/2.30 tff(8663,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8359, 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8665,plain,
% 2.13/2.30 (((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))))),
% 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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[8668, 8667])).
% 2.13/2.30 tff(8670,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8669, 112, 19, 539, 1273, 8221, 7332])).
% 2.13/2.30 tff(8671,plain,
% 2.13/2.30 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8222, 19, 539])).
% 2.13/2.30 tff(8672,plain,
% 2.13/2.30 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6377, 8671])).
% 2.13/2.30 tff(8673,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(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))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8674,plain,
% 2.13/2.30 (((~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))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8675,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[8674])).
% 2.13/2.30 tff(8676,plain,
% 2.13/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[8675, 8673])).
% 2.13/2.30 tff(8677,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(8678,plain,
% 2.13/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[8677, 8676])).
% 2.13/2.30 tff(8679,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8678, 31, 8006, 8672])).
% 2.13/2.30 tff(8680,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6865, 8679, 8670])).
% 2.13/2.30 tff(8681,plain,((~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8682,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8681, 8654, 7863, 8663])).
% 2.13/2.30 tff(8683,plain,
% 2.13/2.30 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6583, 8682])).
% 2.13/2.30 tff(8684,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6586, 8683])).
% 2.13/2.30 tff(8685,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6588, 8684])).
% 2.13/2.30 tff(8686,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8077, 31, 7847, 8685])).
% 2.13/2.30 tff(8687,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7114, 8686])).
% 2.13/2.30 tff(8688,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[6744, 31, 1, 8685])).
% 2.13/2.30 tff(8689,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1718, 8688])).
% 2.13/2.30 tff(8690,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1692, 8689, 8687, 7852, 7849])).
% 2.13/2.30 tff(8691,plain,(~r(s(s(s(z))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8692,plain,
% 2.13/2.30 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[160, 8691])).
% 2.13/2.30 tff(8693,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4251, 7866, 8276, 8586, 8692])).
% 2.13/2.30 tff(8694,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(8695,plain,
% 2.13/2.30 (b(z, s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[182, 8694])).
% 2.13/2.30 tff(8696,plain,
% 2.13/2.30 (~b(s(z), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8378, 4909, 8692, 8695, 408, 8648])).
% 2.13/2.30 tff(8697,plain,
% 2.13/2.30 (r(s(z), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[608, 8696])).
% 2.13/2.30 tff(8698,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[600, 8697, 408])).
% 2.13/2.30 tff(8699,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[398, 8698])).
% 2.13/2.30 tff(8700,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(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(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8701,plain,
% 2.13/2.30 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(8702,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8701])).
% 2.13/2.31 tff(8703,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8702, 8700])).
% 2.13/2.31 tff(8704,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8705,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8704, 8703])).
% 2.13/2.31 tff(8706,plain,
% 2.13/2.31 (~b(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8705, 112, 8586, 8695, 8648, 8699, 8692])).
% 2.13/2.31 tff(8707,plain,
% 2.13/2.31 (r(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[527, 8706])).
% 2.13/2.31 tff(8708,plain,
% 2.13/2.31 (~r(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7408, 31, 8707, 8697])).
% 2.13/2.31 tff(8709,plain,
% 2.13/2.31 (b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[99, 8708])).
% 2.13/2.31 tff(8710,plain,
% 2.13/2.31 (~b(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1867, 8709, 8586, 8695])).
% 2.13/2.31 tff(8711,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8712,plain,
% 2.13/2.31 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8713,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8712])).
% 2.13/2.31 tff(8714,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), 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(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8713, 8711])).
% 2.13/2.31 tff(8715,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8716,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8715, 8714])).
% 2.13/2.31 tff(8717,plain,
% 2.13/2.31 (~b(s(s(s(s(s(z))))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8716, 112, 8586, 8695, 8648, 8699, 4909, 8221])).
% 2.13/2.31 tff(8718,plain,
% 2.13/2.31 (r(s(s(s(s(s(z))))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6404, 78, 15, 8717])).
% 2.13/2.31 tff(8719,plain,
% 2.13/2.31 (~r(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7717, 8709, 8697, 8718, 8586])).
% 2.13/2.31 tff(8720,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[515, 8719, 8710])).
% 2.13/2.31 tff(8721,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8722,plain,
% 2.13/2.31 (~b(s(s(s(s(s(z))))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8721, 408])).
% 2.13/2.31 tff(8723,plain,
% 2.13/2.31 (r(s(s(s(s(s(z))))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6377, 8722])).
% 2.13/2.31 tff(8724,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8725,plain,
% 2.13/2.31 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(8726,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[8725])).
% 2.13/2.31 tff(8727,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), 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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[8726, 8724])).
% 2.13/2.31 tff(8728,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(8729,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8728, 8727])).
% 2.13/2.31 tff(8730,plain,
% 2.13/2.31 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8729, 31, 408, 8723])).
% 2.13/2.31 tff(8731,plain,
% 2.13/2.31 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8359, 8730])).
% 2.13/2.31 tff(8732,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8357, 8731, 8692, 8648])).
% 2.13/2.31 tff(8733,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6583, 8732])).
% 2.13/2.31 tff(8734,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6586, 8733])).
% 2.13/2.31 tff(8735,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[6588, 8734])).
% 2.13/2.31 tff(8736,plain,
% 2.13/2.31 (~b(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8335, 8735, 8695, 408])).
% 2.13/2.31 tff(8737,plain,
% 2.13/2.31 (r(s(z), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[608, 8736])).
% 2.13/2.31 tff(8738,plain,
% 2.13/2.31 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[600, 8737, 408])).
% 2.13/2.31 tff(8739,plain,
% 2.13/2.31 (b(s(s(s(s(elem!1)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[398, 8738])).
% 2.13/2.31 tff(8740,plain,
% 2.13/2.31 (~b(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8705, 112, 8586, 8695, 8648, 8739, 8692])).
% 2.13/2.31 tff(8741,plain,
% 2.13/2.31 (r(s(s(s(z))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[527, 8740])).
% 2.13/2.31 tff(8742,plain,
% 2.13/2.31 (~r(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7408, 31, 8741, 8737])).
% 2.13/2.31 tff(8743,plain,
% 2.13/2.31 (b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[99, 8742])).
% 2.13/2.31 tff(8744,plain,
% 2.13/2.31 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[3598, 8743, 8586, 8692, 8648])).
% 2.13/2.31 tff(8745,plain,
% 2.13/2.31 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[477, 8744])).
% 2.13/2.31 tff(8746,plain,
% 2.13/2.31 (r(s(z), elem!1)),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[8745, 7920])).
% 2.13/2.31 tff(8747,plain,
% 2.13/2.31 ((~r(s(z), elem!1)) | (~r(s(z), z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7938, 7878])).
% 2.13/2.31 tff(8748,plain,
% 2.13/2.31 (~r(s(z), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8747, 8737])).
% 2.13/2.31 tff(8749,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8748, 8746])).
% 2.13/2.31 tff(8750,plain,(~r(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(8751,plain,
% 2.13/2.31 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[429, 8750])).
% 2.13/2.31 tff(8752,plain,
% 2.13/2.31 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4251, 8751, 8586, 8692])).
% 2.13/2.31 tff(8753,plain,
% 2.13/2.31 (r(s(z), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[477, 8752])).
% 2.13/2.31 tff(8754,plain,
% 2.13/2.31 (~r(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8445, 8753, 8692, 8751])).
% 2.13/2.31 tff(8755,plain,
% 2.13/2.31 (b(s(z), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[99, 8754])).
% 2.13/2.31 tff(8756,plain,
% 2.13/2.31 (~b(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1867, 8755, 8586, 8695])).
% 2.13/2.31 tff(8757,plain,
% 2.13/2.31 (r(z, s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[515, 8756])).
% 2.13/2.31 tff(8758,plain,
% 2.13/2.31 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[120, 8755, 8586, 8751])).
% 2.13/2.31 tff(8759,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[646, 8758])).
% 2.13/2.31 tff(8760,plain,
% 2.13/2.31 ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~r(z, s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7941, 7878, 7847])).
% 2.13/2.31 tff(8761,plain,
% 2.13/2.31 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8760, 8759, 8695, 8757])).
% 2.13/2.31 tff(8762,plain,
% 2.13/2.31 ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[577, 7847])).
% 2.13/2.31 tff(8763,plain,
% 2.13/2.31 (~r(s(s(s(s(elem!1)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8762, 8759, 8757])).
% 2.13/2.31 tff(8764,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[398, 8763, 8761])).
% 2.13/2.31 % SZS output end Proof
% 2.13/2.32 % E exiting
%------------------------------------------------------------------------------