%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA132-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 1.54s 1.75s
% Output : Proof 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA132-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.34 % Computer : n007.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 22:47:10 EDT 2026
% 0.16/0.34 % CPUTime :
% 1.54/1.75 % SZS status Unsatisfiable
% 1.54/1.75 % SZS output start Proof
% 1.54/1.75 tff(b_type, type, (
% 1.54/1.75 b: ( $i * $i ) > $o)).
% 1.54/1.75 tff(z_type, type, (
% 1.54/1.75 z: $i)).
% 1.54/1.75 tff(s_type, type, (
% 1.54/1.75 s: $i > $i)).
% 1.54/1.75 tff(r_type, type, (
% 1.54/1.75 r: ( $i * $i ) > $o)).
% 1.54/1.75 tff(inj_0_type, type, (
% 1.54/1.75 inj_0: $i > $i)).
% 1.54/1.75 tff(elem_1_type, type, (
% 1.54/1.75 elem_1: $i)).
% 1.54/1.75 tff(1,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.75 tff(2,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.75 tff(3,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.75 tff(4,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.75 tff(5,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.75 tff(6,plain,
% 1.54/1.75 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(7,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(8,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(9,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 1.54/1.75 tff(10,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.54/1.75 tff(11,plain,(
% 1.54/1.75 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.54/1.75 inference(skolemize,[status(sab)],[10])).
% 1.54/1.75 tff(12,plain,
% 1.54/1.75 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[11, 7])).
% 1.54/1.75 tff(13,plain,
% 1.54/1.75 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[12, 6])).
% 1.54/1.75 tff(14,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(15,plain,
% 1.54/1.75 (inj_0(s(z)) = z),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[14, 13])).
% 1.54/1.75 tff(16,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.54/1.75 tff(17,plain,
% 1.54/1.75 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[16])).
% 1.54/1.75 tff(18,plain,
% 1.54/1.75 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[17])).
% 1.54/1.75 tff(19,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(20,plain,
% 1.54/1.75 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[19, 13])).
% 1.54/1.75 tff(21,plain,
% 1.54/1.75 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[20])).
% 1.54/1.75 tff(22,plain,
% 1.54/1.75 (s(s(s(z))) = z),
% 1.54/1.75 inference(transitivity,[status(thm)],[21, 18, 15])).
% 1.54/1.75 tff(23,plain,
% 1.54/1.75 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(24,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[23])).
% 1.54/1.75 tff(25,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(26,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 1.54/1.75 tff(27,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.54/1.75 tff(28,plain,(
% 1.54/1.75 ![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(skolemize,[status(sab)],[27])).
% 1.54/1.75 tff(29,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.54/1.75 tff(30,plain,
% 1.54/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(31,plain,
% 1.54/1.75 (~(s(s(s(z))) = z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.54/1.75 tff(32,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[31, 22])).
% 1.54/1.75 tff(33,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(34,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(35,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.54/1.75 tff(36,plain,
% 1.54/1.75 (s(z) = s(s(s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.54/1.75 tff(37,assumption,(~(s(z) = s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.75 tff(38,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[37, 36])).
% 1.54/1.75 tff(39,plain,((~(s(s(s(s(z)))) = s(z))) | (s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(40,plain,
% 1.54/1.75 (~(s(s(s(s(z)))) = s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[39, 33])).
% 1.54/1.75 tff(41,plain,
% 1.54/1.75 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(42,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[41])).
% 1.54/1.75 tff(43,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(44,plain,
% 1.54/1.75 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(45,plain,
% 1.54/1.75 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[44])).
% 1.54/1.75 tff(46,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 1.54/1.75 tff(47,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.54/1.75 tff(48,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[47, 43])).
% 1.54/1.75 tff(49,plain,(
% 1.54/1.75 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(skolemize,[status(sab)],[48])).
% 1.54/1.75 tff(50,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[49, 42])).
% 1.54/1.75 tff(51,plain,
% 1.54/1.75 (((~![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)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(52,plain,
% 1.54/1.75 ((~![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)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(53,plain,
% 1.54/1.75 ((~![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))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.54/1.75 tff(54,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[53, 50])).
% 1.54/1.75 tff(55,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[54, 40])).
% 1.54/1.75 tff(56,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[55, 5])).
% 1.54/1.75 tff(57,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.54/1.75 tff(58,plain,
% 1.54/1.75 (^[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))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(59,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))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[58])).
% 1.54/1.75 tff(60,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))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(61,plain,
% 1.54/1.75 (^[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)))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(62,plain,
% 1.54/1.75 (![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)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[61])).
% 1.54/1.75 tff(63,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 1.54/1.75 tff(64,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)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.54/1.75 tff(65,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)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.54/1.75 tff(66,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)))),
% 1.54/1.75 inference(skolemize,[status(sab)],[65])).
% 1.54/1.75 tff(67,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)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.54/1.75 tff(68,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(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)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(69,plain,
% 1.54/1.75 (((~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)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(70,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(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))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[69])).
% 1.54/1.75 tff(71,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(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)))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[70, 68])).
% 1.54/1.75 tff(72,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(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)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(73,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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.54/1.75 tff(74,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[73, 67, 57, 56])).
% 1.54/1.75 tff(75,plain,
% 1.54/1.75 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(76,plain,
% 1.54/1.75 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[75])).
% 1.54/1.75 tff(77,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(78,plain,
% 1.54/1.75 (inj_0(s(s(z))) = s(z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[77, 13])).
% 1.54/1.75 tff(79,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.54/1.75 tff(80,plain,
% 1.54/1.75 (s(s(s(z))) = s(s(s(s(z))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[79])).
% 1.54/1.75 tff(81,plain,
% 1.54/1.75 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[80])).
% 1.54/1.75 tff(82,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(83,plain,
% 1.54/1.75 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[82, 13])).
% 1.54/1.75 tff(84,plain,
% 1.54/1.75 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[83])).
% 1.54/1.75 tff(85,plain,
% 1.54/1.75 (s(s(z)) = s(s(s(z)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[84, 81, 20])).
% 1.54/1.75 tff(86,plain,
% 1.54/1.75 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[85])).
% 1.54/1.75 tff(87,plain,
% 1.54/1.75 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[86])).
% 1.54/1.75 tff(88,plain,
% 1.54/1.75 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(z))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[81])).
% 1.54/1.75 tff(89,plain,
% 1.54/1.75 (s(s(s(z))) = s(z)),
% 1.54/1.75 inference(transitivity,[status(thm)],[21, 88, 87, 78])).
% 1.54/1.75 tff(90,plain,
% 1.54/1.75 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(91,plain,
% 1.54/1.75 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[90])).
% 1.54/1.75 tff(92,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.54/1.75 tff(93,plain,
% 1.54/1.75 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[92])).
% 1.54/1.75 tff(94,plain,
% 1.54/1.75 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[93])).
% 1.54/1.75 tff(95,plain,
% 1.54/1.75 (s(s(z)) = z),
% 1.54/1.75 inference(transitivity,[status(thm)],[84, 94, 15])).
% 1.54/1.75 tff(96,plain,
% 1.54/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(97,plain,
% 1.54/1.75 (~(s(s(z)) = z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[96, 29])).
% 1.54/1.75 tff(98,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[97, 95])).
% 1.54/1.75 tff(99,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(100,plain,
% 1.54/1.75 (~(s(s(s(z))) = s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[99, 91])).
% 1.54/1.75 tff(101,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[100, 89])).
% 1.54/1.75 tff(102,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(103,plain,
% 1.54/1.75 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[102, 76])).
% 1.54/1.75 tff(104,plain,
% 1.54/1.75 (((~![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))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(105,plain,
% 1.54/1.75 ((~![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))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(106,plain,
% 1.54/1.75 ((~![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)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.54/1.75 tff(107,plain,
% 1.54/1.75 ((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)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[106, 50])).
% 1.54/1.75 tff(108,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[107, 103])).
% 1.54/1.75 tff(109,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[108, 74])).
% 1.54/1.75 tff(110,assumption,(r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.54/1.75 tff(111,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(112,plain,
% 1.54/1.75 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(113,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(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[112])).
% 1.54/1.75 tff(114,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(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[113, 111])).
% 1.54/1.75 tff(115,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(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(116,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.54/1.75 tff(117,plain,
% 1.54/1.75 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[116, 67, 57, 110])).
% 1.54/1.75 tff(118,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(119,plain,
% 1.54/1.75 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[118, 13])).
% 1.54/1.75 tff(120,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(121,plain,
% 1.54/1.75 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[120, 13])).
% 1.54/1.75 tff(122,assumption,(s(s(s(z))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.75 tff(123,plain,
% 1.54/1.75 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[122])).
% 1.54/1.75 tff(124,plain,
% 1.54/1.75 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[84, 123, 121])).
% 1.54/1.75 tff(125,plain,
% 1.54/1.75 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[124])).
% 1.54/1.75 tff(126,plain,
% 1.54/1.75 (s(z) = inj_0(s(s(z)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[78])).
% 1.54/1.75 tff(127,plain,
% 1.54/1.75 (s(z) = s(s(s(s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[126, 125, 119])).
% 1.54/1.75 tff(128,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[33, 127])).
% 1.54/1.75 tff(129,plain,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(130,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(131,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(132,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.54/1.75 tff(133,plain,
% 1.54/1.75 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[132, 50])).
% 1.54/1.75 tff(134,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[133, 129])).
% 1.54/1.75 tff(135,plain,
% 1.54/1.75 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[134, 117])).
% 1.54/1.75 tff(136,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.75 tff(137,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.75 tff(138,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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(139,plain,
% 1.54/1.75 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(140,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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[139])).
% 1.54/1.75 tff(141,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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[140, 138])).
% 1.54/1.75 tff(142,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(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))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(143,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.54/1.75 tff(144,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[143, 67, 57, 137, 136])).
% 1.54/1.75 tff(145,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(146,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[145, 136, 57])).
% 1.54/1.75 tff(147,plain,
% 1.54/1.75 (((~![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)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(148,plain,
% 1.54/1.76 ((~![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)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(149,plain,
% 1.54/1.76 ((~![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))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.54/1.76 tff(150,plain,
% 1.54/1.76 ((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))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[149, 50])).
% 1.54/1.76 tff(151,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[150, 102])).
% 1.54/1.76 tff(152,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[151, 146])).
% 1.54/1.76 tff(153,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.76 tff(154,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(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(155,plain,
% 1.54/1.76 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(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(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(156,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(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[155])).
% 1.54/1.76 tff(157,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(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[156, 154])).
% 1.54/1.76 tff(158,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(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(159,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.54/1.76 tff(160,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[159, 67, 136, 110, 1])).
% 1.54/1.76 tff(161,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(162,plain,
% 1.54/1.76 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[161, 136, 110])).
% 1.54/1.76 tff(163,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(164,plain,
% 1.54/1.76 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[163])).
% 1.54/1.76 tff(165,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.76 tff(166,plain,
% 1.54/1.76 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[165])).
% 1.54/1.76 tff(167,plain,
% 1.54/1.76 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[21, 166, 121])).
% 1.54/1.76 tff(168,plain,
% 1.54/1.76 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[167])).
% 1.54/1.76 tff(169,plain,
% 1.54/1.76 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[168])).
% 1.54/1.76 tff(170,plain,
% 1.54/1.76 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[119])).
% 1.54/1.76 tff(171,plain,
% 1.54/1.76 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[165])).
% 1.54/1.76 tff(172,plain,
% 1.54/1.76 (s(s(s(s(s(s(z)))))) = s(s(z))),
% 1.54/1.76 inference(transitivity,[status(thm)],[171, 170, 169, 83])).
% 1.54/1.76 tff(173,assumption,(s(s(s(s(s(s(z)))))) = s(s(z))), introduced(assumption)).
% 1.54/1.76 tff(174,plain,
% 1.54/1.76 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[173])).
% 1.54/1.76 tff(175,plain,
% 1.54/1.76 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[121])).
% 1.54/1.76 tff(176,plain,
% 1.54/1.76 (s(s(s(s(s(z))))) = s(z)),
% 1.54/1.76 inference(transitivity,[status(thm)],[175, 174, 78])).
% 1.54/1.76 tff(177,plain,
% 1.54/1.76 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[176])).
% 1.54/1.76 tff(178,plain,
% 1.54/1.76 (s(s(s(s(z)))) = z),
% 1.54/1.76 inference(transitivity,[status(thm)],[170, 177, 15])).
% 1.54/1.76 tff(179,plain,
% 1.54/1.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(180,plain,
% 1.54/1.76 (~(s(s(s(s(z)))) = z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[179, 29])).
% 1.54/1.76 tff(181,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[180, 178])).
% 1.54/1.76 tff(182,plain,(~(s(s(s(s(s(s(z)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(183,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[182, 172])).
% 1.54/1.76 tff(184,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(185,plain,
% 1.54/1.76 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[184, 164])).
% 1.54/1.76 tff(186,plain,
% 1.54/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(187,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(188,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.54/1.76 tff(189,plain,
% 1.54/1.76 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[188, 50])).
% 1.54/1.76 tff(190,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[189, 185])).
% 1.54/1.76 tff(191,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[190, 162])).
% 1.54/1.76 tff(192,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.76 tff(193,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.76 tff(194,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.76 tff(195,plain,
% 1.54/1.76 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(196,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[195])).
% 1.54/1.76 tff(197,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(198,plain,
% 1.54/1.76 (^[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(X1, X4))) <=> (((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X4))))), rewrite((((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X4))) <=> ((~b(X1, 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(X1, X4))) <=> ((~b(X1, 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(X1, X4))) | (~b(X2, X4))) <=> (((~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))))), rewrite((((~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, 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(X1, X4))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, 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(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> (((~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(199,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[198])).
% 1.54/1.76 tff(200,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X1, X4))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 1.54/1.76 tff(201,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.54/1.76 tff(202,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[201, 197])).
% 1.54/1.76 tff(203,plain,(
% 1.54/1.76 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[202])).
% 1.54/1.76 tff(204,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[203, 196])).
% 1.54/1.76 tff(205,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(206,plain,
% 1.54/1.76 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(207,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[206])).
% 1.54/1.76 tff(208,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[207, 205])).
% 1.54/1.76 tff(209,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(210,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.54/1.76 tff(211,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[210, 204, 194, 153, 193, 4, 192])).
% 1.54/1.76 tff(212,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(213,plain,
% 1.54/1.76 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[212, 191, 153, 152, 135])).
% 1.54/1.76 tff(214,plain,
% 1.54/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(215,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(216,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.54/1.76 tff(217,plain,
% 1.54/1.76 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[216, 50])).
% 1.54/1.76 tff(218,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[217, 184])).
% 1.54/1.76 tff(219,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[218, 213])).
% 1.54/1.76 tff(220,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(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(221,plain,
% 1.54/1.76 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(222,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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[221])).
% 1.54/1.76 tff(223,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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[222, 220])).
% 1.54/1.76 tff(224,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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(225,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.54/1.76 tff(226,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[225, 67, 136, 110, 219])).
% 1.54/1.76 tff(227,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(228,plain,
% 1.54/1.76 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[227, 109, 56, 57])).
% 1.54/1.76 tff(229,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 1.54/1.76 tff(230,plain,
% 1.54/1.76 (s(z) = s(s(s(s(s(s(z))))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[229])).
% 1.54/1.76 tff(231,plain,
% 1.54/1.76 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[230])).
% 1.54/1.76 tff(232,plain,
% 1.54/1.76 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[231])).
% 1.54/1.76 tff(233,plain,
% 1.54/1.76 (s(s(s(s(s(z))))) = z),
% 1.54/1.76 inference(transitivity,[status(thm)],[175, 232, 15])).
% 1.54/1.76 tff(234,plain,
% 1.54/1.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(235,plain,
% 1.54/1.76 (~(s(s(s(s(s(z))))) = z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[234, 29])).
% 1.54/1.76 tff(236,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[235, 233])).
% 1.54/1.76 tff(237,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(238,assumption,(~b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.54/1.76 tff(239,assumption,(~r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.54/1.76 tff(240,plain,
% 1.54/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(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(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(241,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(242,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.54/1.76 tff(243,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[242, 50, 239, 238, 237])).
% 1.54/1.76 tff(244,plain,(b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(245,plain,
% 1.54/1.76 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[244, 228])).
% 1.54/1.76 tff(246,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.76 tff(247,plain,
% 1.54/1.76 (s(s(s(s(s(s(z)))))) = s(z)),
% 1.54/1.76 inference(symmetry,[status(thm)],[246])).
% 1.54/1.76 tff(248,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[237, 247])).
% 1.54/1.76 tff(249,plain,(~(s(z) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(250,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.76 tff(251,plain,
% 1.54/1.76 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(252,plain,
% 1.54/1.76 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[251])).
% 1.54/1.76 tff(253,plain,
% 1.54/1.76 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[252])).
% 1.54/1.76 tff(254,plain,
% 1.54/1.76 (~(z = s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[31, 253])).
% 1.54/1.76 tff(255,plain,
% 1.54/1.76 (((~![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)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(256,plain,
% 1.54/1.76 ((~![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)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(257,plain,
% 1.54/1.76 ((~![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))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.54/1.76 tff(258,plain,
% 1.54/1.76 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[257, 50])).
% 1.54/1.76 tff(259,plain,
% 1.54/1.76 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[258, 254])).
% 1.54/1.76 tff(260,plain,
% 1.54/1.76 (r(z, s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[259, 250])).
% 1.54/1.76 tff(261,assumption,(r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 1.54/1.76 tff(262,plain,
% 1.54/1.76 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[73, 67, 57, 136])).
% 1.54/1.76 tff(263,plain,
% 1.54/1.76 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[108, 262])).
% 1.54/1.76 tff(264,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.76 tff(265,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(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(266,plain,
% 1.54/1.76 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(267,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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), 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(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[266])).
% 1.54/1.76 tff(268,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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), 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(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[267, 265])).
% 1.54/1.76 tff(269,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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(270,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[269, 268])).
% 1.54/1.76 tff(271,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[270, 67, 3, 261, 264])).
% 1.54/1.76 tff(272,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(273,plain,
% 1.54/1.77 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[272, 261, 3])).
% 1.54/1.77 tff(274,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(z)))), introduced(assumption)).
% 1.54/1.77 tff(275,plain,
% 1.54/1.77 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[274])).
% 1.54/1.77 tff(276,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[129, 275])).
% 1.54/1.77 tff(277,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(278,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.77 tff(279,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.77 tff(280,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(281,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(282,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.54/1.77 tff(283,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[282, 50, 279, 278, 277])).
% 1.54/1.77 tff(284,plain,(b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(285,plain,
% 1.54/1.77 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[284, 273])).
% 1.54/1.77 tff(286,assumption,(r(z, s(z))), introduced(assumption)).
% 1.54/1.77 tff(287,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(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(288,plain,
% 1.54/1.77 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(289,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(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[288])).
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% 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(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[289, 287])).
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% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
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% 1.54/1.77 inference(modus_ponens,[status(thm)],[291, 290])).
% 1.54/1.77 tff(293,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[292, 67, 286, 57, 3])).
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% 1.54/1.77 tff(295,plain,
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% 1.54/1.77 inference(unit_resolution,[status(thm)],[294, 3, 57])).
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% 1.54/1.77 ((z = s(z)) <=> (s(z) = z)),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
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% 1.54/1.77 ((s(z) = z) <=> (z = s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[296])).
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% 1.54/1.77 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[297])).
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% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(300,plain,
% 1.54/1.77 (~(s(z) = z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[299, 29])).
% 1.54/1.77 tff(301,plain,
% 1.54/1.77 (~(z = s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[300, 298])).
% 1.54/1.77 tff(302,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(303,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(304,plain,
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% 1.54/1.77 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.54/1.77 tff(305,plain,
% 1.54/1.77 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[304, 50])).
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% 1.54/1.77 inference(unit_resolution,[status(thm)],[305, 301])).
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% 1.54/1.77 (b(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[306, 295])).
% 1.54/1.77 tff(308,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.54/1.77 tff(309,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))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
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% 1.54/1.77 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(311,plain,
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% 1.54/1.77 inference(monotonicity,[status(thm)],[310])).
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% 1.54/1.77 inference(transitivity,[status(thm)],[311, 309])).
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% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
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% 1.54/1.77 inference(modus_ponens,[status(thm)],[313, 312])).
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% 1.54/1.77 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[314, 67, 308, 261])).
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% 1.54/1.77 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[284, 315])).
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% 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))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
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% 1.54/1.77 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
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% 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(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[318])).
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% 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(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[319, 317])).
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% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
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% 1.54/1.77 inference(modus_ponens,[status(thm)],[321, 320])).
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% 1.54/1.77 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[322, 67, 308, 261])).
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% 1.54/1.77 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[134, 323])).
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% 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(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
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% 1.54/1.77 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
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% 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(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[326])).
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% 1.54/1.77 inference(transitivity,[status(thm)],[327, 325])).
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% 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(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
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% 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(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[329, 328])).
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% 1.54/1.77 (~r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[330, 67, 3, 137])).
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% 1.54/1.77 (((~![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))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
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% 1.54/1.77 ((~![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))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
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% 1.54/1.77 ((~![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)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.54/1.77 tff(335,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[334, 50, 180])).
% 1.54/1.77 tff(336,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[335, 331])).
% 1.54/1.77 tff(337,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[145, 57, 137])).
% 1.54/1.77 tff(338,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[55, 337])).
% 1.54/1.77 tff(339,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.77 tff(340,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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(341,plain,
% 1.54/1.77 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(342,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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[341])).
% 1.54/1.77 tff(343,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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[342, 340])).
% 1.54/1.77 tff(344,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(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(345,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.54/1.77 tff(346,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[345, 67, 3, 339, 137])).
% 1.54/1.77 tff(347,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(348,plain,
% 1.54/1.77 (~r(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[347, 3, 137])).
% 1.54/1.77 tff(349,plain,
% 1.54/1.77 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(350,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[349])).
% 1.54/1.77 tff(351,plain,
% 1.54/1.77 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[350])).
% 1.54/1.77 tff(352,plain,
% 1.54/1.77 (~(z = s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[180, 351])).
% 1.54/1.77 tff(353,plain,
% 1.54/1.77 (((~![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))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(354,plain,
% 1.54/1.77 ((~![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))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(355,plain,
% 1.54/1.77 ((~![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)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.54/1.77 tff(356,plain,
% 1.54/1.77 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[355, 50])).
% 1.54/1.77 tff(357,plain,
% 1.54/1.77 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[356, 352])).
% 1.54/1.77 tff(358,plain,
% 1.54/1.77 (b(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[357, 348])).
% 1.54/1.77 tff(359,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.54/1.77 tff(360,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.77 tff(361,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.77 tff(362,assumption,(b(z, s(z))), introduced(assumption)).
% 1.54/1.77 tff(363,assumption,(b(s(z), z)), introduced(assumption)).
% 1.54/1.77 tff(364,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(365,plain,
% 1.54/1.77 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(366,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[365])).
% 1.54/1.77 tff(367,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[366, 364])).
% 1.54/1.78 tff(368,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(369,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.54/1.78 tff(370,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[369, 204, 363, 362, 361, 360, 359])).
% 1.54/1.78 tff(371,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(372,plain,
% 1.54/1.78 (~b(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[371, 336, 338, 307, 358])).
% 1.54/1.78 tff(373,plain,
% 1.54/1.78 (((~![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))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(374,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(375,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.54/1.78 tff(376,plain,
% 1.54/1.78 (b(s(z), z) | r(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[375, 50, 300])).
% 1.54/1.78 tff(377,plain,
% 1.54/1.78 (r(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[376, 372])).
% 1.54/1.78 tff(378,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.78 tff(379,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), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(380,plain,
% 1.54/1.78 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(381,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), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[380])).
% 1.54/1.78 tff(382,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), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[381, 379])).
% 1.54/1.78 tff(383,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), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(384,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.54/1.78 tff(385,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[384, 67, 57, 2, 378])).
% 1.54/1.78 tff(386,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(387,plain,
% 1.54/1.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[386, 57, 2])).
% 1.54/1.78 tff(388,plain,
% 1.54/1.78 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[108, 387])).
% 1.54/1.78 tff(389,assumption,(r(s(z), z)), introduced(assumption)).
% 1.54/1.78 tff(390,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(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(391,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(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(392,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(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[391])).
% 1.54/1.78 tff(393,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(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[392, 390])).
% 1.54/1.78 tff(394,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(395,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.54/1.78 tff(396,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[395, 67, 389, 57, 308])).
% 1.54/1.78 tff(397,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(398,plain,
% 1.54/1.78 (~r(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[397, 57, 389])).
% 1.54/1.78 tff(399,plain,
% 1.54/1.78 (((~![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))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(400,plain,
% 1.54/1.78 ((~![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))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(401,plain,
% 1.54/1.78 ((~![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)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.54/1.78 tff(402,plain,
% 1.54/1.78 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[401, 50, 31])).
% 1.54/1.78 tff(403,plain,
% 1.54/1.78 (b(s(s(s(z))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[402, 398])).
% 1.54/1.78 tff(404,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.54/1.78 tff(405,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.54/1.78 tff(406,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(407,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(408,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[407])).
% 1.54/1.78 tff(409,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[408, 406])).
% 1.54/1.78 tff(410,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(411,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.54/1.78 tff(412,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[411, 204, 405, 404, 361, 153, 359])).
% 1.54/1.78 tff(413,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(414,plain,
% 1.54/1.78 (~b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[413, 388, 403, 361, 359])).
% 1.54/1.78 tff(415,plain,
% 1.54/1.78 (r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[259, 414])).
% 1.54/1.78 tff(416,plain,
% 1.54/1.78 (~r(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[294, 57, 415])).
% 1.54/1.78 tff(417,plain,
% 1.54/1.78 (b(z, s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[306, 416])).
% 1.54/1.78 tff(418,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(419,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(420,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[419])).
% 1.54/1.78 tff(421,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[420, 418])).
% 1.54/1.78 tff(422,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(423,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.54/1.78 tff(424,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[423, 204, 417, 403, 361, 388, 360])).
% 1.54/1.78 tff(425,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(426,plain,
% 1.54/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[425, 377, 57, 338, 336, 358])).
% 1.54/1.78 tff(427,plain,
% 1.54/1.78 (((~![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))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(428,plain,
% 1.54/1.78 ((~![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))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(429,plain,
% 1.54/1.78 ((~![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)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.54/1.78 tff(430,plain,
% 1.54/1.78 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[429, 50])).
% 1.54/1.78 tff(431,plain,
% 1.54/1.78 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[430, 33])).
% 1.54/1.78 tff(432,plain,
% 1.54/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[431, 426])).
% 1.54/1.78 tff(433,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(434,plain,
% 1.54/1.78 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(435,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[434])).
% 1.54/1.78 tff(436,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[435, 433])).
% 1.54/1.78 tff(437,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(438,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.54/1.78 tff(439,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[438, 204, 307, 432, 358, 338, 336])).
% 1.54/1.78 tff(440,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(441,plain,
% 1.54/1.78 (~r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[440, 57, 137])).
% 1.54/1.78 tff(442,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[259, 441])).
% 1.54/1.78 tff(443,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.54/1.79 tff(444,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.54/1.79 tff(445,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.54/1.79 tff(446,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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(447,plain,
% 1.54/1.79 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(448,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(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[447])).
% 1.54/1.79 tff(449,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(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[448, 446])).
% 1.54/1.79 tff(450,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(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(451,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.54/1.79 tff(452,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[451, 67, 445, 2, 137])).
% 1.54/1.79 tff(453,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(454,plain,
% 1.54/1.79 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[453, 445, 137])).
% 1.54/1.79 tff(455,plain,
% 1.54/1.79 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[431, 454])).
% 1.54/1.79 tff(456,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.79 tff(457,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(458,plain,
% 1.54/1.79 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(459,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[458])).
% 1.54/1.79 tff(460,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[459, 457])).
% 1.54/1.79 tff(461,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(462,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[461, 460])).
% 1.54/1.79 tff(463,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[462, 204, 444, 456, 4, 443])).
% 1.54/1.79 tff(464,plain,
% 1.54/1.79 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[134, 463])).
% 1.54/1.79 tff(465,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(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(466,plain,
% 1.54/1.79 (((~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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(467,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(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(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[466])).
% 1.54/1.79 tff(468,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(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(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[467, 465])).
% 1.54/1.79 tff(469,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(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))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(470,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[469, 468])).
% 1.54/1.79 tff(471,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[470, 67, 445, 137, 136])).
% 1.54/1.79 tff(472,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(473,plain,
% 1.54/1.79 (~r(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[472, 136, 137])).
% 1.54/1.79 tff(474,plain,
% 1.54/1.79 (((~![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)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(475,plain,
% 1.54/1.79 ((~![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)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(476,plain,
% 1.54/1.79 ((~![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))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.54/1.79 tff(477,plain,
% 1.54/1.79 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[476, 50])).
% 1.54/1.79 tff(478,plain,
% 1.54/1.79 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[477, 99])).
% 1.54/1.79 tff(479,plain,
% 1.54/1.79 (b(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[478, 473])).
% 1.54/1.79 tff(480,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(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(481,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(482,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(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[481])).
% 1.54/1.79 tff(483,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(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[482, 480])).
% 1.54/1.79 tff(484,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(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(485,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(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.54/1.79 tff(486,plain,
% 1.54/1.79 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[485, 67, 389, 261])).
% 1.54/1.79 tff(487,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(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(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(488,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(489,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[488, 487])).
% 1.54/1.79 tff(490,plain,
% 1.54/1.79 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[489, 50, 486, 249])).
% 1.54/1.79 tff(491,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(492,plain,
% 1.54/1.79 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(493,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[492])).
% 1.54/1.79 tff(494,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[493, 491])).
% 1.54/1.79 tff(495,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(496,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.54/1.79 tff(497,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[496, 204, 444, 479, 490, 443])).
% 1.54/1.79 tff(498,plain,
% 1.54/1.79 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[134, 497])).
% 1.54/1.79 tff(499,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.79 tff(500,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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(501,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(502,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(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[501])).
% 1.54/1.79 tff(503,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(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[502, 500])).
% 1.54/1.79 tff(504,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(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(505,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.54/1.79 tff(506,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[505, 67, 378, 1, 499])).
% 1.54/1.79 tff(507,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(508,plain,
% 1.54/1.79 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[507, 498, 378])).
% 1.54/1.80 tff(509,plain,
% 1.54/1.80 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[190, 508])).
% 1.54/1.80 tff(510,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.54/1.80 tff(511,plain,
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% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(512,plain,
% 1.54/1.80 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(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(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(513,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~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(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[512])).
% 1.54/1.80 tff(514,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~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(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.80 inference(transitivity,[status(thm)],[513, 511])).
% 1.54/1.80 tff(515,plain,
% 1.54/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(516,plain,
% 1.54/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[515, 514])).
% 1.54/1.80 tff(517,plain,
% 1.54/1.80 ($false),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[516, 67, 137, 499, 510])).
% 1.54/1.80 tff(518,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.80 tff(519,plain,
% 1.54/1.80 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[518, 498, 137])).
% 1.54/1.80 tff(520,plain,
% 1.54/1.80 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[218, 519])).
% 1.54/1.80 tff(521,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(522,plain,
% 1.64/1.80 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(523,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[522])).
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% 1.64/1.80 inference(transitivity,[status(thm)],[523, 521])).
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% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
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% 1.64/1.80 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.64/1.80 tff(527,plain,
% 1.64/1.80 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[526, 204, 520, 509, 490, 443])).
% 1.64/1.80 tff(528,plain,
% 1.64/1.80 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[431, 527])).
% 1.64/1.80 tff(529,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), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(530,plain,
% 1.64/1.80 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(531,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(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[530])).
% 1.64/1.80 tff(532,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(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[531, 529])).
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% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(534,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.64/1.80 tff(535,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[534, 67, 389, 2, 339])).
% 1.64/1.80 tff(536,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(537,plain,
% 1.64/1.80 (~r(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[536, 528, 389])).
% 1.64/1.80 tff(538,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.64/1.80 tff(539,plain,
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% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(540,plain,
% 1.64/1.80 (((~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)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(541,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), 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))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[540])).
% 1.64/1.80 tff(542,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), 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)))),
% 1.64/1.80 inference(transitivity,[status(thm)],[541, 539])).
% 1.64/1.80 tff(543,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), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(544,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.64/1.80 tff(545,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[544, 67, 389, 538, 136])).
% 1.64/1.80 tff(546,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(547,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[546, 389, 136])).
% 1.64/1.80 tff(548,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[335, 547])).
% 1.64/1.80 tff(549,plain,
% 1.64/1.80 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(commutativity,[status(thm)],[])).
% 1.64/1.80 tff(550,plain,
% 1.64/1.80 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[549])).
% 1.64/1.80 tff(551,plain,
% 1.64/1.80 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[550])).
% 1.64/1.80 tff(552,plain,
% 1.64/1.80 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[129, 551])).
% 1.64/1.80 tff(553,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[145, 136, 137])).
% 1.64/1.80 tff(554,plain,
% 1.64/1.80 (((~![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)))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(555,plain,
% 1.64/1.80 ((~![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)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(556,plain,
% 1.64/1.80 ((~![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))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.64/1.80 tff(557,plain,
% 1.64/1.80 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[556, 50])).
% 1.64/1.80 tff(558,plain,
% 1.64/1.80 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[557, 100])).
% 1.64/1.80 tff(559,plain,
% 1.64/1.80 (b(s(s(s(z))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[558, 553])).
% 1.64/1.80 tff(560,plain,
% 1.64/1.80 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 1.64/1.80 inference(commutativity,[status(thm)],[])).
% 1.64/1.80 tff(561,plain,
% 1.64/1.80 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(symmetry,[status(thm)],[560])).
% 1.64/1.80 tff(562,plain,
% 1.64/1.80 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[561])).
% 1.64/1.80 tff(563,plain,
% 1.64/1.80 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[237, 562])).
% 1.64/1.80 tff(564,plain,
% 1.64/1.80 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[489, 50, 486])).
% 1.64/1.80 tff(565,plain,
% 1.64/1.80 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[564, 563])).
% 1.64/1.80 tff(566,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.64/1.80 tff(567,plain,
% 1.64/1.80 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[496, 204, 444, 566, 565, 443])).
% 1.64/1.80 tff(568,plain,
% 1.64/1.80 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[134, 567])).
% 1.64/1.80 tff(569,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(570,plain,
% 1.64/1.80 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(571,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[570])).
% 1.64/1.80 tff(572,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[571, 569])).
% 1.64/1.80 tff(573,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(574,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[573, 572])).
% 1.64/1.80 tff(575,plain,
% 1.64/1.80 ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[574, 204, 444, 566, 443])).
% 1.64/1.80 tff(576,plain,
% 1.64/1.80 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[575, 565])).
% 1.64/1.80 tff(577,plain,
% 1.64/1.80 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[282, 50, 576])).
% 1.64/1.80 tff(578,plain,
% 1.64/1.80 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[577, 552])).
% 1.64/1.80 tff(579,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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(580,plain,
% 1.64/1.80 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(581,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(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[580])).
% 1.64/1.81 tff(582,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(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[581, 579])).
% 1.64/1.81 tff(583,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(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(584,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(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.64/1.81 tff(585,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[584, 67, 137, 578])).
% 1.64/1.81 tff(586,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[190, 585])).
% 1.64/1.81 tff(587,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[518, 568, 137])).
% 1.64/1.81 tff(588,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[218, 587])).
% 1.64/1.81 tff(589,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(590,plain,
% 1.64/1.81 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(591,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(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(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[590])).
% 1.64/1.81 tff(592,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(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(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[591, 589])).
% 1.64/1.81 tff(593,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(594,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.64/1.81 tff(595,plain,
% 1.64/1.81 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[594, 204, 361, 359, 588, 586])).
% 1.64/1.81 tff(596,assumption,(z = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.81 tff(597,plain,
% 1.64/1.81 (s(s(s(s(s(s(z)))))) = z),
% 1.64/1.81 inference(symmetry,[status(thm)],[596])).
% 1.64/1.81 tff(598,plain,
% 1.64/1.81 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(599,plain,
% 1.64/1.81 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[598, 29])).
% 1.64/1.81 tff(600,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[599, 597])).
% 1.64/1.81 tff(601,plain,(~(z = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(602,plain,
% 1.64/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(603,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(604,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[603, 602])).
% 1.64/1.81 tff(605,plain,
% 1.64/1.81 (r(z, s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[604, 50, 601, 595])).
% 1.64/1.81 tff(606,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(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(607,plain,
% 1.64/1.81 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(608,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(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(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(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[607])).
% 1.64/1.81 tff(609,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(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(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(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[608, 606])).
% 1.64/1.81 tff(610,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(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(611,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(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[610, 609])).
% 1.64/1.81 tff(612,plain,
% 1.64/1.81 (~r(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[611, 67, 568, 605])).
% 1.64/1.81 tff(613,plain,
% 1.64/1.81 (b(s(s(s(z))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[402, 612])).
% 1.64/1.81 tff(614,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(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(615,plain,
% 1.64/1.81 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(616,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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[615])).
% 1.64/1.81 tff(617,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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[616, 614])).
% 1.64/1.81 tff(618,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(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(619,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(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[618, 617])).
% 1.64/1.81 tff(620,plain,
% 1.64/1.81 (~r(z, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[619, 67, 568, 605])).
% 1.64/1.81 tff(621,plain,
% 1.64/1.81 (b(z, s(s(s(z))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[259, 620])).
% 1.64/1.81 tff(622,plain,
% 1.64/1.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[413, 621, 613, 361, 359])).
% 1.64/1.81 tff(623,plain,
% 1.64/1.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[108, 622])).
% 1.64/1.81 tff(624,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[507, 378, 499])).
% 1.64/1.81 tff(625,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[189, 624, 185])).
% 1.64/1.81 tff(626,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[518, 137, 499])).
% 1.64/1.81 tff(627,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[217, 626, 184])).
% 1.64/1.81 tff(628,assumption,(~(s(s(elem!1)) = s(s(s(z))))), introduced(assumption)).
% 1.64/1.81 tff(629,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[546, 136, 389])).
% 1.64/1.81 tff(630,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[335, 629])).
% 1.64/1.81 tff(631,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(632,plain,
% 1.64/1.81 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(633,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[632])).
% 1.64/1.81 tff(634,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[633, 631])).
% 1.64/1.81 tff(635,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(636,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.64/1.81 tff(637,plain,
% 1.64/1.81 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[636, 204, 361, 630, 627, 625])).
% 1.64/1.81 tff(638,plain,
% 1.64/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(639,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(640,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.64/1.81 tff(641,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[640, 50, 599])).
% 1.64/1.81 tff(642,plain,
% 1.64/1.81 (r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[641, 637])).
% 1.64/1.81 tff(643,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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(644,plain,
% 1.64/1.81 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(645,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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[644])).
% 1.64/1.81 tff(646,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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[645, 643])).
% 1.64/1.81 tff(647,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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(648,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), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.64/1.81 tff(649,plain,
% 1.64/1.81 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[648, 67, 389, 642])).
% 1.64/1.81 tff(650,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[242, 50, 649, 237])).
% 1.64/1.81 tff(651,plain,
% 1.64/1.81 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[485, 67, 389, 642])).
% 1.64/1.81 tff(652,plain,
% 1.64/1.81 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[489, 50, 651])).
% 1.64/1.81 tff(653,plain,
% 1.64/1.81 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[652, 563])).
% 1.64/1.81 tff(654,plain,
% 1.64/1.81 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[526, 204, 627, 625, 653, 650])).
% 1.64/1.81 tff(655,plain,
% 1.64/1.81 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[431, 654])).
% 1.64/1.81 tff(656,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.81 tff(657,assumption,(s(s(s(s(s(s(elem!1)))))) = s(z)), introduced(assumption)).
% 1.64/1.81 tff(658,plain,
% 1.64/1.81 (s(z) = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[657])).
% 1.64/1.81 tff(659,assumption,(s(z) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.64/1.81 tff(660,plain,
% 1.64/1.81 (s(s(s(s(s(s(elem!1)))))) = s(z)),
% 1.64/1.81 inference(symmetry,[status(thm)],[659])).
% 1.64/1.81 tff(661,plain,
% 1.64/1.81 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[660])).
% 1.64/1.81 tff(662,plain,
% 1.64/1.81 ((~![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))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(663,plain,
% 1.64/1.81 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[662, 13])).
% 1.64/1.81 tff(664,plain,
% 1.64/1.81 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[663])).
% 1.64/1.81 tff(665,plain,
% 1.64/1.81 (s(s(s(s(s(elem!1))))) = z),
% 1.64/1.81 inference(transitivity,[status(thm)],[664, 661, 15])).
% 1.64/1.81 tff(666,plain,
% 1.64/1.81 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(667,plain,
% 1.64/1.81 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[666, 29])).
% 1.64/1.81 tff(668,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[667, 665])).
% 1.64/1.81 tff(669,plain,(~(s(z) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(670,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[669, 658])).
% 1.64/1.81 tff(671,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(672,assumption,(~r(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 1.64/1.81 tff(673,plain,
% 1.64/1.81 (((~![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)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(674,plain,
% 1.64/1.81 ((~![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)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(675,plain,
% 1.64/1.81 ((~![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))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[674, 673])).
% 1.64/1.81 tff(676,plain,
% 1.64/1.81 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[675, 50, 672, 671])).
% 1.64/1.81 tff(677,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(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(678,plain,
% 1.64/1.81 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(679,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(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[678])).
% 1.64/1.82 tff(680,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[679, 677])).
% 1.64/1.82 tff(681,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(682,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))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[681, 680])).
% 1.64/1.82 tff(683,plain,
% 1.64/1.82 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[682, 67, 656, 378])).
% 1.64/1.82 tff(684,plain,
% 1.64/1.82 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(commutativity,[status(thm)],[])).
% 1.64/1.82 tff(685,plain,
% 1.64/1.82 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[684])).
% 1.64/1.82 tff(686,plain,
% 1.64/1.82 ((~![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)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(687,plain,
% 1.64/1.82 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[686, 13])).
% 1.64/1.82 tff(688,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))), introduced(assumption)).
% 1.64/1.82 tff(689,plain,
% 1.64/1.82 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[688])).
% 1.64/1.82 tff(690,plain,
% 1.64/1.82 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 1.64/1.82 inference(transitivity,[status(thm)],[664, 689, 83])).
% 1.64/1.82 tff(691,plain,
% 1.64/1.82 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(z)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[690])).
% 1.64/1.82 tff(692,plain,
% 1.64/1.82 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[691])).
% 1.64/1.82 tff(693,plain,
% 1.64/1.82 (s(z) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[126, 692, 687])).
% 1.64/1.82 tff(694,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.82 tff(695,plain,
% 1.64/1.82 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[694])).
% 1.64/1.82 tff(696,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.64/1.82 inference(symmetry,[status(thm)],[695])).
% 1.64/1.82 tff(697,plain,
% 1.64/1.82 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(698,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[697, 13])).
% 1.64/1.82 tff(699,plain,
% 1.64/1.82 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[698])).
% 1.64/1.82 tff(700,plain,
% 1.64/1.82 (s(s(s(elem!1))) = z),
% 1.64/1.82 inference(transitivity,[status(thm)],[699, 696, 15])).
% 1.64/1.82 tff(701,plain,
% 1.64/1.82 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(702,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[701, 29])).
% 1.64/1.82 tff(703,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[702, 700])).
% 1.64/1.82 tff(704,plain,(~(s(z) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(705,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[704, 693])).
% 1.64/1.82 tff(706,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(707,plain,
% 1.64/1.82 (~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[706, 685])).
% 1.64/1.82 tff(708,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(709,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(710,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[709, 708])).
% 1.64/1.82 tff(711,plain,
% 1.64/1.82 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[710, 50, 707, 683])).
% 1.64/1.82 tff(712,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(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(713,plain,
% 1.64/1.82 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(714,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[713])).
% 1.64/1.82 tff(715,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[714, 712])).
% 1.64/1.82 tff(716,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(717,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(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[716, 715])).
% 1.64/1.82 tff(718,plain,
% 1.64/1.82 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[717, 67, 2, 656])).
% 1.64/1.82 tff(719,plain,
% 1.64/1.82 (((~![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))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(720,plain,
% 1.64/1.82 ((~![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))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(721,plain,
% 1.64/1.82 ((~![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)))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[720, 719])).
% 1.64/1.82 tff(722,plain,
% 1.64/1.82 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[721, 50, 669, 718])).
% 1.64/1.82 tff(723,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(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(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(724,plain,
% 1.64/1.82 (((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(725,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(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(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[724])).
% 1.64/1.82 tff(726,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(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(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[725, 723])).
% 1.64/1.82 tff(727,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(728,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[727, 726])).
% 1.64/1.82 tff(729,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[728, 204, 444, 566, 722, 711, 676])).
% 1.64/1.82 tff(730,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(731,plain,
% 1.64/1.82 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[730, 656, 566, 444, 378, 2])).
% 1.64/1.82 tff(732,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(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(733,plain,
% 1.64/1.82 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(734,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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[733])).
% 1.64/1.82 tff(735,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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[734, 732])).
% 1.64/1.82 tff(736,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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(737,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[736, 735])).
% 1.64/1.82 tff(738,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[737, 67, 389, 2, 656, 731])).
% 1.64/1.82 tff(739,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(740,plain,
% 1.64/1.82 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[739, 655, 389, 479, 559, 378])).
% 1.64/1.82 tff(741,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.64/1.82 tff(742,plain,
% 1.64/1.82 (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[741])).
% 1.64/1.82 tff(743,plain,
% 1.64/1.82 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[742])).
% 1.64/1.82 tff(744,plain,
% 1.64/1.82 (s(s(s(z))) = s(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[21, 743, 663])).
% 1.64/1.82 tff(745,plain,
% 1.64/1.82 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[744])).
% 1.64/1.82 tff(746,plain,
% 1.64/1.82 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[84, 745, 687])).
% 1.64/1.82 tff(747,plain,
% 1.64/1.82 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[746])).
% 1.64/1.82 tff(748,plain,
% 1.64/1.82 (s(z) = s(s(s(elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[126, 747, 698])).
% 1.64/1.82 tff(749,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.64/1.82 tff(750,plain,
% 1.64/1.82 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[749])).
% 1.64/1.82 tff(751,plain,
% 1.64/1.82 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.64/1.82 inference(symmetry,[status(thm)],[750])).
% 1.64/1.82 tff(752,plain,
% 1.64/1.82 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(753,plain,
% 1.64/1.82 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[752, 13])).
% 1.64/1.82 tff(754,plain,
% 1.64/1.82 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[753])).
% 1.64/1.82 tff(755,plain,
% 1.64/1.82 (s(s(elem!1)) = z),
% 1.64/1.82 inference(transitivity,[status(thm)],[754, 751, 15])).
% 1.64/1.82 tff(756,plain,
% 1.64/1.82 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(757,plain,
% 1.64/1.82 (~(s(s(elem!1)) = z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[756, 29])).
% 1.64/1.82 tff(758,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[757, 755])).
% 1.64/1.82 tff(759,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(760,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[759, 748])).
% 1.64/1.82 tff(761,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(762,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(763,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(764,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[763, 762])).
% 1.64/1.82 tff(765,plain,
% 1.64/1.82 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[764, 50])).
% 1.64/1.82 tff(766,plain,
% 1.64/1.82 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[765, 761])).
% 1.64/1.82 tff(767,plain,
% 1.64/1.82 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[766, 740])).
% 1.64/1.82 tff(768,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(769,plain,
% 1.64/1.82 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(770,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[769])).
% 1.64/1.82 tff(771,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[770, 768])).
% 1.64/1.82 tff(772,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(773,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.64/1.82 tff(774,plain,
% 1.64/1.82 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[773, 204, 627, 625])).
% 1.64/1.82 tff(775,plain,
% 1.64/1.82 ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[594, 204, 361, 627, 625])).
% 1.64/1.82 tff(776,plain,
% 1.64/1.82 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[775, 630])).
% 1.64/1.82 tff(777,plain,
% 1.64/1.82 (r(z, s(s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[604, 50, 601, 776])).
% 1.64/1.82 tff(778,plain,
% 1.64/1.82 (~r(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[611, 67, 499, 777])).
% 1.64/1.82 tff(779,plain,
% 1.64/1.82 (b(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[402, 778])).
% 1.64/1.82 tff(780,plain,
% 1.64/1.82 ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 1.64/1.83 inference(commutativity,[status(thm)],[])).
% 1.64/1.83 tff(781,plain,
% 1.64/1.83 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[780])).
% 1.64/1.83 tff(782,plain,
% 1.64/1.83 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[781])).
% 1.64/1.83 tff(783,plain,
% 1.64/1.83 (~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[761, 782])).
% 1.64/1.83 tff(784,assumption,(b(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 1.64/1.83 tff(785,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.83 tff(786,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(787,plain,
% 1.64/1.83 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(788,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[787])).
% 1.64/1.83 tff(789,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[788, 786])).
% 1.64/1.83 tff(790,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(791,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.64/1.83 tff(792,plain,
% 1.64/1.83 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[791, 204, 361, 785, 359])).
% 1.64/1.83 tff(793,plain,
% 1.64/1.83 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[792, 784])).
% 1.64/1.83 tff(794,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(795,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(796,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[795, 794])).
% 1.64/1.83 tff(797,plain,
% 1.64/1.83 ((s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[796, 50, 793])).
% 1.64/1.83 tff(798,plain,
% 1.64/1.83 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[797, 783])).
% 1.64/1.83 tff(799,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(800,plain,
% 1.64/1.83 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(801,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[800])).
% 1.64/1.83 tff(802,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[801, 799])).
% 1.64/1.83 tff(803,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(804,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.64/1.83 tff(805,plain,
% 1.64/1.83 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[804, 204, 404, 361, 785])).
% 1.64/1.83 tff(806,plain,
% 1.64/1.83 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[805, 784])).
% 1.64/1.83 tff(807,plain,
% 1.64/1.83 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[710, 50, 707, 806])).
% 1.64/1.83 tff(808,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))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(809,plain,
% 1.64/1.83 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(810,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(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[809])).
% 1.64/1.83 tff(811,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(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[810, 808])).
% 1.64/1.83 tff(812,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(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(813,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[812, 811])).
% 1.64/1.83 tff(814,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[813, 67, 378, 807, 798])).
% 1.64/1.83 tff(815,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(816,plain,
% 1.64/1.83 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[815, 767, 361, 378, 630, 779])).
% 1.64/1.83 tff(817,plain,
% 1.64/1.83 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(818,plain,
% 1.64/1.83 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[817, 29])).
% 1.64/1.83 tff(819,plain,
% 1.64/1.83 (((~![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))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(820,plain,
% 1.64/1.83 ((~![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))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(821,plain,
% 1.64/1.83 ((~![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)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[820, 819])).
% 1.64/1.83 tff(822,plain,
% 1.64/1.83 (b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[821, 50, 818])).
% 1.64/1.83 tff(823,plain,
% 1.64/1.83 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[822, 816])).
% 1.64/1.83 tff(824,assumption,(r(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 1.64/1.83 tff(825,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), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(826,plain,
% 1.64/1.83 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(827,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(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[826])).
% 1.64/1.83 tff(828,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(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[827, 825])).
% 1.64/1.83 tff(829,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(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(830,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), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.64/1.83 tff(831,plain,
% 1.64/1.83 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[830, 67, 389, 824])).
% 1.64/1.83 tff(832,plain,
% 1.64/1.83 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[721, 50, 669, 831])).
% 1.64/1.83 tff(833,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(834,plain,
% 1.64/1.83 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(835,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[834])).
% 1.64/1.83 tff(836,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[835, 833])).
% 1.64/1.84 tff(837,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(838,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.64/1.84 tff(839,plain,
% 1.64/1.84 ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[838, 204, 785, 4, 565])).
% 1.64/1.84 tff(840,plain,
% 1.64/1.84 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[839, 832])).
% 1.64/1.84 tff(841,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(842,plain,
% 1.64/1.84 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(843,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(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[842])).
% 1.64/1.84 tff(844,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(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[843, 841])).
% 1.64/1.84 tff(845,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(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(846,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.64/1.84 tff(847,plain,
% 1.64/1.84 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[846, 67, 824, 261])).
% 1.64/1.84 tff(848,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(849,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(850,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[849, 848])).
% 1.64/1.84 tff(851,plain,
% 1.64/1.84 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[850, 50, 847])).
% 1.64/1.84 tff(852,plain,
% 1.64/1.84 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[851, 840])).
% 1.64/1.84 tff(853,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 1.64/1.84 tff(854,plain,
% 1.64/1.84 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[853])).
% 1.64/1.84 tff(855,plain,
% 1.64/1.84 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[854])).
% 1.64/1.84 tff(856,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[855, 852])).
% 1.64/1.84 tff(857,plain,
% 1.64/1.84 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[856])).
% 1.64/1.84 tff(858,plain,
% 1.64/1.84 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[857])).
% 1.64/1.84 tff(859,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.64/1.84 tff(860,plain,
% 1.64/1.84 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[859, 858])).
% 1.64/1.84 tff(861,plain,
% 1.64/1.84 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[853])).
% 1.64/1.84 tff(862,plain,
% 1.64/1.84 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[861])).
% 1.64/1.84 tff(863,plain,
% 1.64/1.84 ((s(s(s(s(elem!1)))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[855])).
% 1.64/1.84 tff(864,plain,
% 1.64/1.84 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(z)))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[863])).
% 1.64/1.84 tff(865,plain,
% 1.64/1.84 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[864, 862])).
% 1.64/1.84 tff(866,plain,
% 1.64/1.84 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[865])).
% 1.64/1.84 tff(867,plain,
% 1.64/1.84 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[185, 866])).
% 1.64/1.84 tff(868,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.64/1.84 tff(869,plain,
% 1.64/1.84 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[868])).
% 1.64/1.84 tff(870,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[869])).
% 1.64/1.84 tff(871,plain,
% 1.64/1.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[870])).
% 1.64/1.84 tff(872,plain,
% 1.64/1.84 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[699, 871, 663])).
% 1.64/1.84 tff(873,plain,
% 1.64/1.84 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[872])).
% 1.64/1.84 tff(874,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[873])).
% 1.64/1.84 tff(875,plain,
% 1.64/1.84 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[687])).
% 1.64/1.84 tff(876,plain,
% 1.64/1.84 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.64/1.84 inference(transitivity,[status(thm)],[875, 874, 753])).
% 1.64/1.84 tff(877,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.64/1.84 tff(878,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[877, 876])).
% 1.64/1.84 tff(879,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(880,plain,
% 1.64/1.84 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[879, 867])).
% 1.64/1.84 tff(881,plain,
% 1.64/1.84 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[855])).
% 1.64/1.84 tff(882,plain,
% 1.64/1.84 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[881])).
% 1.64/1.84 tff(883,plain,
% 1.64/1.84 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[882])).
% 1.64/1.84 tff(884,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(885,plain,
% 1.64/1.84 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(886,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[885])).
% 1.64/1.84 tff(887,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[886, 884])).
% 1.64/1.84 tff(888,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(889,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[888, 887])).
% 1.64/1.84 tff(890,plain,
% 1.64/1.84 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[889, 67, 824, 261])).
% 1.64/1.84 tff(891,plain,
% 1.64/1.84 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[890, 883])).
% 1.64/1.84 tff(892,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(893,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(894,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.64/1.84 tff(895,plain,
% 1.64/1.84 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[894, 50])).
% 1.64/1.84 tff(896,plain,
% 1.64/1.84 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[895, 891, 880])).
% 1.64/1.84 tff(897,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[896, 860])).
% 1.64/1.84 tff(898,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(z))))))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(899,plain,
% 1.64/1.84 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[898, 823, 774, 767, 625, 642, 389])).
% 1.64/1.84 tff(900,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.64/1.84 tff(901,plain,
% 1.64/1.84 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(902,plain,
% 1.64/1.84 (inj_0(s(elem!1)) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[901, 13])).
% 1.64/1.84 tff(903,plain,
% 1.64/1.84 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(904,plain,
% 1.64/1.84 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[903, 13])).
% 1.64/1.84 tff(905,plain,
% 1.64/1.84 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[648, 67, 389, 261])).
% 1.64/1.84 tff(906,plain,
% 1.64/1.84 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[242, 50, 905, 237])).
% 1.64/1.84 tff(907,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.84 tff(908,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(s(z), z)) | (~r(s(z), 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(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(909,plain,
% 1.64/1.84 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(910,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(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[909])).
% 1.64/1.84 tff(911,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(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[910, 908])).
% 1.64/1.84 tff(912,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(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(913,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[912, 911])).
% 1.64/1.84 tff(914,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[913, 67, 907, 389, 900])).
% 1.64/1.84 tff(915,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(916,plain,
% 1.64/1.84 (~r(s(z), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[915, 900, 389])).
% 1.64/1.84 tff(917,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.64/1.84 tff(918,plain,
% 1.64/1.84 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[917])).
% 1.64/1.84 tff(919,plain,
% 1.64/1.84 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[904])).
% 1.64/1.84 tff(920,plain,
% 1.64/1.84 (s(elem!1) = z),
% 1.64/1.84 inference(transitivity,[status(thm)],[919, 918, 15])).
% 1.64/1.84 tff(921,plain,
% 1.64/1.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(922,plain,
% 1.64/1.84 (~(s(elem!1) = z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[921, 29])).
% 1.64/1.84 tff(923,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[922, 920])).
% 1.64/1.84 tff(924,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(925,plain,
% 1.64/1.84 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.64/1.84 inference(commutativity,[status(thm)],[])).
% 1.64/1.84 tff(926,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.64/1.84 tff(927,plain,
% 1.64/1.84 (s(s(elem!1)) = s(z)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.64/1.84 tff(928,assumption,(~(s(s(elem!1)) = s(z))), introduced(assumption)).
% 1.64/1.84 tff(929,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[928, 927])).
% 1.64/1.84 tff(930,plain,((~(s(z) = s(s(elem!1)))) | (s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(931,plain,
% 1.64/1.84 (~(s(z) = s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[930, 924])).
% 1.64/1.84 tff(932,plain,
% 1.64/1.84 (((~![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))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(933,plain,
% 1.64/1.84 ((~![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))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(934,plain,
% 1.64/1.84 ((~![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)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[933, 932])).
% 1.64/1.84 tff(935,plain,
% 1.64/1.84 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[934, 50])).
% 1.64/1.84 tff(936,plain,
% 1.64/1.84 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[935, 931])).
% 1.64/1.84 tff(937,plain,
% 1.64/1.84 (b(s(z), s(s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[936, 916])).
% 1.64/1.84 tff(938,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.64/1.84 tff(939,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(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))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(940,plain,
% 1.64/1.84 (((~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))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(941,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(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)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[940])).
% 1.64/1.84 tff(942,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(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))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[941, 939])).
% 1.64/1.84 tff(943,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(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(944,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[943, 942])).
% 1.64/1.84 tff(945,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[944, 67, 938, 389, 900])).
% 1.64/1.84 tff(946,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(947,plain,
% 1.64/1.84 (~r(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[946, 900, 389])).
% 1.64/1.84 tff(948,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(949,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(950,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[949, 948])).
% 1.64/1.84 tff(951,plain,
% 1.64/1.84 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[950, 50])).
% 1.64/1.84 tff(952,plain,
% 1.64/1.84 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[951, 924])).
% 1.64/1.84 tff(953,plain,
% 1.64/1.84 (b(s(s(elem!1)), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[952, 947])).
% 1.64/1.84 tff(954,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(955,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(956,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[955])).
% 1.64/1.85 tff(957,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[956, 954])).
% 1.64/1.85 tff(958,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(959,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[958, 957])).
% 1.64/1.85 tff(960,plain,
% 1.64/1.85 (~b(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[959, 204, 953, 937, 565, 906])).
% 1.64/1.85 tff(961,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)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(962,plain,
% 1.64/1.85 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(963,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)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[962])).
% 1.64/1.85 tff(964,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)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[963, 961])).
% 1.64/1.85 tff(965,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)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(966,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)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[965, 964])).
% 1.64/1.85 tff(967,plain,
% 1.64/1.85 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[966, 67, 900, 261])).
% 1.64/1.85 tff(968,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(969,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(970,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(z)))))), s(s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.64/1.85 tff(971,plain,
% 1.64/1.85 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[970, 50, 967, 960])).
% 1.64/1.85 tff(972,plain,
% 1.64/1.85 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[971])).
% 1.64/1.85 tff(973,plain,
% 1.64/1.85 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.64/1.85 inference(transitivity,[status(thm)],[175, 972, 904])).
% 1.64/1.85 tff(974,plain,
% 1.64/1.85 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[973])).
% 1.64/1.85 tff(975,plain,
% 1.64/1.85 (s(s(s(s(z)))) = elem!1),
% 1.64/1.85 inference(transitivity,[status(thm)],[170, 974, 902])).
% 1.64/1.85 tff(976,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[975])).
% 1.64/1.85 tff(977,plain,
% 1.64/1.85 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[971])).
% 1.64/1.85 tff(978,plain,
% 1.64/1.85 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[4, 977])).
% 1.64/1.85 tff(979,plain,
% 1.64/1.85 (b(s(s(elem!1)), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[978, 976])).
% 1.64/1.85 tff(980,plain,
% 1.64/1.85 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[975])).
% 1.64/1.85 tff(981,plain,
% 1.64/1.85 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[785, 980])).
% 1.64/1.85 tff(982,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)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(983,plain,
% 1.64/1.85 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(984,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(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z))))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[983])).
% 1.64/1.85 tff(985,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(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[984, 982])).
% 1.64/1.85 tff(986,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(s(z)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(987,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)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.64/1.85 tff(988,plain,
% 1.64/1.85 (~r(s(s(elem!1)), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[987, 67, 900, 261])).
% 1.64/1.85 tff(989,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.64/1.85 tff(990,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.64/1.85 tff(991,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(992,plain,
% 1.64/1.85 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(993,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z))))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[992])).
% 1.64/1.85 tff(994,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[993, 991])).
% 1.64/1.85 tff(995,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(996,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[995, 994])).
% 1.64/1.85 tff(997,plain,
% 1.64/1.85 ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[996, 204, 990, 565, 906])).
% 1.64/1.85 tff(998,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[997, 937])).
% 1.64/1.85 tff(999,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1000,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1001,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(z))))))) | b(s(s(elem!1)), s(s(s(s(s(s(z))))))) | r(s(s(elem!1)), s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1000, 999])).
% 1.64/1.85 tff(1002,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1001, 50, 998, 989, 988])).
% 1.64/1.85 tff(1003,plain,((~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1004,plain,
% 1.64/1.85 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1003, 953, 261, 900, 389])).
% 1.64/1.85 tff(1005,assumption,(s(s(elem!1)) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.85 tff(1006,plain,
% 1.64/1.85 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1005])).
% 1.64/1.85 tff(1007,plain,
% 1.64/1.85 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[919, 1006, 121])).
% 1.64/1.85 tff(1008,plain,
% 1.64/1.85 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1007])).
% 1.64/1.85 tff(1009,plain,
% 1.64/1.85 (elem!1 = inj_0(s(elem!1))),
% 1.64/1.85 inference(symmetry,[status(thm)],[902])).
% 1.64/1.85 tff(1010,plain,
% 1.64/1.85 (elem!1 = s(s(s(s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1009, 1008, 119])).
% 1.64/1.85 tff(1011,plain,
% 1.64/1.85 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1010])).
% 1.64/1.85 tff(1012,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[1011])).
% 1.64/1.85 tff(1013,plain,
% 1.64/1.85 (b(elem!1, z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[359, 1012])).
% 1.64/1.85 tff(1014,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.64/1.85 tff(1015,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1014, 1013])).
% 1.64/1.85 tff(1016,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(z)))))))) | b(elem!1, z) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1017,plain,
% 1.64/1.85 (b(elem!1, z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1016, 1004, 359])).
% 1.64/1.85 tff(1018,plain,
% 1.64/1.85 ((s(s(s(s(s(s(elem!1)))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(commutativity,[status(thm)],[])).
% 1.64/1.85 tff(1019,plain,
% 1.64/1.85 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[975])).
% 1.64/1.85 tff(1020,plain,
% 1.64/1.85 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1019, 1018])).
% 1.64/1.85 tff(1021,plain,
% 1.64/1.85 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1020])).
% 1.64/1.85 tff(1022,plain,
% 1.64/1.85 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[761, 1021])).
% 1.64/1.85 tff(1023,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[975])).
% 1.64/1.85 tff(1024,plain,
% 1.64/1.85 (r(elem!1, s(s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[137, 1023])).
% 1.64/1.85 tff(1025,assumption,(~(elem!1 = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.64/1.85 tff(1026,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.64/1.85 tff(1027,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1028,plain,
% 1.64/1.85 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1029,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1028])).
% 1.64/1.85 tff(1030,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1029, 1027])).
% 1.64/1.85 tff(1031,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1032,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.64/1.85 tff(1033,plain,
% 1.64/1.85 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1032, 204, 1026, 361, 785])).
% 1.64/1.85 tff(1034,plain,
% 1.64/1.85 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1033, 784])).
% 1.64/1.85 tff(1035,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1036,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1037,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.64/1.85 tff(1038,plain,
% 1.64/1.85 ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1037, 50])).
% 1.64/1.85 tff(1039,plain,
% 1.64/1.85 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1038, 1034, 1025])).
% 1.64/1.85 tff(1040,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.64/1.85 tff(1041,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(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1042,plain,
% 1.64/1.85 (((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1043,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(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1042])).
% 1.64/1.85 tff(1044,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(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1043, 1041])).
% 1.64/1.86 tff(1045,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(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1046,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 1.64/1.86 tff(1047,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1046, 67, 1040, 1039, 807])).
% 1.64/1.86 tff(1048,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~r(elem!1, s(s(s(z))))) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1049,plain,
% 1.64/1.86 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1048, 1024, 1022, 1017, 361, 785, 404])).
% 1.64/1.86 tff(1050,plain,
% 1.64/1.86 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[822, 1049])).
% 1.64/1.86 tff(1051,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))), introduced(assumption)).
% 1.64/1.86 tff(1052,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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1053,plain,
% 1.64/1.86 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1054,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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1053])).
% 1.64/1.86 tff(1055,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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1054, 1052])).
% 1.64/1.86 tff(1056,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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(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(1057,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)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 1.64/1.86 tff(1058,plain,
% 1.64/1.86 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1057, 67, 900, 824])).
% 1.64/1.86 tff(1059,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1060,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1061,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 1.64/1.86 tff(1062,plain,
% 1.64/1.86 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1061, 50])).
% 1.64/1.86 tff(1063,plain,
% 1.64/1.86 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1062, 1058, 1051])).
% 1.64/1.86 tff(1064,assumption,(b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.64/1.86 tff(1065,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.64/1.86 tff(1066,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1067,plain,
% 1.64/1.86 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1068,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1067])).
% 1.64/1.86 tff(1069,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1068, 1066])).
% 1.64/1.86 tff(1070,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1071,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.64/1.86 tff(1072,plain,
% 1.64/1.86 ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1071, 204, 937, 1065, 1064])).
% 1.64/1.86 tff(1073,plain,
% 1.64/1.86 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1072, 1063])).
% 1.64/1.86 tff(1074,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[721, 50, 669, 1073, 831])).
% 1.64/1.86 tff(1075,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1076,plain,
% 1.64/1.86 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1075, 1050, 981, 979, 900, 389])).
% 1.64/1.86 tff(1077,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))), introduced(assumption)).
% 1.64/1.86 tff(1078,plain,
% 1.64/1.86 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1077])).
% 1.64/1.86 tff(1079,plain,
% 1.64/1.86 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.64/1.86 inference(transitivity,[status(thm)],[664, 1078, 904])).
% 1.64/1.86 tff(1080,plain,
% 1.64/1.86 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1079])).
% 1.64/1.86 tff(1081,plain,
% 1.64/1.86 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.86 inference(transitivity,[status(thm)],[875, 1080, 902])).
% 1.64/1.86 tff(1082,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.64/1.86 tff(1083,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1082, 1081])).
% 1.64/1.86 tff(1084,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1085,plain,
% 1.64/1.86 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1084, 1076])).
% 1.64/1.86 tff(1086,plain,
% 1.64/1.86 (elem!1 = s(s(s(s(elem!1))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[1085])).
% 1.64/1.86 tff(1087,plain,
% 1.64/1.86 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[170, 974, 902, 1086])).
% 1.64/1.86 tff(1088,plain,
% 1.64/1.86 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1087])).
% 1.64/1.86 tff(1089,plain,
% 1.64/1.86 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[21, 1088, 698])).
% 1.64/1.86 tff(1090,plain,
% 1.64/1.86 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1089])).
% 1.64/1.86 tff(1091,plain,
% 1.64/1.86 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[1090])).
% 1.64/1.86 tff(1092,plain,
% 1.64/1.86 (s(s(s(s(s(s(z)))))) = s(s(z))),
% 1.64/1.86 inference(transitivity,[status(thm)],[971, 754, 1091, 83])).
% 1.64/1.86 tff(1093,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[182, 1092])).
% 1.64/1.86 tff(1094,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1095,plain,
% 1.64/1.86 (~r(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1094, 767, 361, 389, 779, 137, 625, 642, 630])).
% 1.64/1.86 tff(1096,plain,
% 1.64/1.86 (((~![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))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1097,plain,
% 1.64/1.86 ((~![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))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1098,plain,
% 1.64/1.86 ((~![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)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 1.64/1.86 tff(1099,plain,
% 1.64/1.86 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1098, 50, 757])).
% 1.64/1.86 tff(1100,plain,
% 1.64/1.86 (b(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1099, 1095])).
% 1.64/1.86 tff(1101,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.86 tff(1102,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.64/1.86 tff(1103,assumption,(r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.86 tff(1104,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(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1105,plain,
% 1.64/1.86 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1106,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(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1105])).
% 1.64/1.86 tff(1107,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(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1106, 1104])).
% 1.64/1.86 tff(1108,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(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1109,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.64/1.86 tff(1110,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1109, 67, 907, 2, 1103])).
% 1.64/1.86 tff(1111,plain,((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1112,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1111, 907, 2])).
% 1.64/1.86 tff(1113,assumption,(r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.86 tff(1114,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(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1115,plain,
% 1.64/1.86 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1116,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(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(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(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1115])).
% 1.64/1.86 tff(1117,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(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(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(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1116, 1114])).
% 1.64/1.86 tff(1118,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(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(elem!1)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1119,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.64/1.86 tff(1120,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1119, 67, 907, 1113, 2])).
% 1.64/1.86 tff(1121,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1122,plain,
% 1.64/1.86 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1121, 907, 2])).
% 1.64/1.86 tff(1123,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.64/1.86 inference(commutativity,[status(thm)],[])).
% 1.64/1.86 tff(1124,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 1.64/1.86 tff(1125,plain,
% 1.64/1.86 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 1.64/1.86 tff(1126,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1101, 1125])).
% 1.64/1.86 tff(1127,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1128,plain,
% 1.64/1.86 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1127, 1101])).
% 1.64/1.86 tff(1129,assumption,(~r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.64/1.86 tff(1130,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1131,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1132,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.64/1.86 tff(1133,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1132, 50, 1129])).
% 1.64/1.86 tff(1134,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1133, 1128])).
% 1.64/1.86 tff(1135,assumption,(~r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.86 tff(1136,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1137,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1138,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.64/1.86 tff(1139,plain,
% 1.64/1.86 ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1138, 50])).
% 1.64/1.86 tff(1140,plain,
% 1.64/1.86 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1139, 1101, 1135])).
% 1.64/1.86 tff(1141,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1142,plain,
% 1.64/1.86 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1143,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1142])).
% 1.64/1.86 tff(1144,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1143, 1141])).
% 1.64/1.86 tff(1145,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1146,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 1.64/1.87 tff(1147,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1146, 204, 1102, 1140, 361, 359, 1134])).
% 1.64/1.87 tff(1148,plain,((s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(1149,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1148, 1122, 1112, 361, 1102, 359, 1101])).
% 1.64/1.87 tff(1150,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(1151,plain,
% 1.64/1.87 (~r(s(z), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1150, 899, 361, 630, 1100, 655])).
% 1.64/1.87 tff(1152,plain,
% 1.64/1.87 (b(s(z), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[936, 1151])).
% 1.64/1.87 tff(1153,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1154,plain,
% 1.64/1.87 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(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(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1155,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1154])).
% 1.64/1.87 tff(1156,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1155, 1153])).
% 1.64/1.87 tff(1157,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1158,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 1.64/1.87 tff(1159,plain,
% 1.64/1.87 ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1158, 204, 1100, 779, 479])).
% 1.64/1.87 tff(1160,plain,
% 1.64/1.87 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1159, 1152])).
% 1.64/1.87 tff(1161,assumption,(~r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.64/1.87 tff(1162,assumption,(~b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.64/1.87 tff(1163,plain,
% 1.64/1.87 (((~![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)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1164,plain,
% 1.64/1.87 ((~![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)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1165,plain,
% 1.64/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.64/1.87 tff(1166,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1165, 50, 628, 1162, 1161])).
% 1.64/1.87 tff(1167,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,[]))).
% 1.64/1.87 tff(1168,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1167, 1160, 628])).
% 1.64/1.87 tff(1169,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1170,plain,
% 1.64/1.87 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1171,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1170])).
% 1.64/1.87 tff(1172,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1171, 1169])).
% 1.64/1.87 tff(1173,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1174,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 1.64/1.87 tff(1175,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1174, 67, 1168, 137])).
% 1.64/1.87 tff(1176,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(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(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1177,plain,
% 1.64/1.87 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1178,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(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(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1177])).
% 1.64/1.87 tff(1179,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(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(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1178, 1176])).
% 1.64/1.87 tff(1180,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1181,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 1.64/1.87 tff(1182,plain,
% 1.64/1.87 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1181, 67, 1168, 137])).
% 1.64/1.87 tff(1183,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1148, 1182, 1175, 361, 1100, 630, 899])).
% 1.64/1.87 tff(1184,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(1185,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1184, 361, 137, 628, 389, 378, 499])).
% 1.64/1.87 tff(1186,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[55, 1185])).
% 1.64/1.87 tff(1187,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1188,plain,
% 1.64/1.87 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1189,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1188])).
% 1.64/1.87 tff(1190,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1189, 1187])).
% 1.64/1.87 tff(1191,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1192,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 1.64/1.87 tff(1193,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1192, 67, 389, 2, 538])).
% 1.64/1.87 tff(1194,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(1195,plain,
% 1.64/1.87 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1194, 538, 389])).
% 1.64/1.87 tff(1196,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[431, 1195])).
% 1.64/1.87 tff(1197,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1198,plain,
% 1.64/1.87 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1199,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1198])).
% 1.64/1.88 tff(1200,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1199, 1197])).
% 1.64/1.88 tff(1201,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1202,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 1.64/1.88 tff(1203,plain,
% 1.64/1.88 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1202, 204, 1196, 360, 193, 625])).
% 1.64/1.88 tff(1204,plain,
% 1.64/1.88 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[242, 50, 1203, 237])).
% 1.64/1.88 tff(1205,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(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)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1206,plain,
% 1.64/1.88 (((~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)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1207,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(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))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1206])).
% 1.64/1.88 tff(1208,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(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)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1207, 1205])).
% 1.64/1.88 tff(1209,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(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)))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1210,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 1.64/1.88 tff(1211,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1210, 67, 308, 538, 378])).
% 1.64/1.88 tff(1212,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1213,plain,
% 1.64/1.88 (~r(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1212, 538, 378])).
% 1.64/1.88 tff(1214,plain,
% 1.64/1.88 (b(s(s(s(z))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[402, 1213])).
% 1.64/1.88 tff(1215,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1216,plain,
% 1.64/1.88 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1217,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1216])).
% 1.64/1.88 tff(1218,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1217, 1215])).
% 1.64/1.88 tff(1219,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1220,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 1.64/1.88 tff(1221,plain,
% 1.64/1.88 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1220, 204, 1196, 360, 193, 625])).
% 1.64/1.88 tff(1222,plain,
% 1.64/1.88 ((s(z) = s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[489, 50, 1221])).
% 1.64/1.88 tff(1223,plain,
% 1.64/1.88 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1222, 563])).
% 1.64/1.88 tff(1224,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(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1225,plain,
% 1.64/1.88 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1226,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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1225])).
% 1.64/1.88 tff(1227,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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1226, 1224])).
% 1.64/1.88 tff(1228,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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1229,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(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.64/1.88 tff(1230,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1229, 67, 499, 1223])).
% 1.64/1.88 tff(1231,plain,
% 1.64/1.88 (b(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[558, 1230])).
% 1.64/1.88 tff(1232,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1233,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(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(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1234,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1233])).
% 1.64/1.88 tff(1235,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1234, 1232])).
% 1.64/1.88 tff(1236,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1237,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 1.64/1.88 tff(1238,plain,
% 1.64/1.88 (~b(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1237, 204, 1231, 1214, 1196, 361])).
% 1.64/1.88 tff(1239,plain,
% 1.64/1.88 (r(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[306, 1238])).
% 1.64/1.88 tff(1240,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1241,plain,
% 1.64/1.88 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1242,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(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1241])).
% 1.64/1.88 tff(1243,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(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.64/1.88 tff(1244,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(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1245,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.64/1.88 tff(1246,plain,
% 1.64/1.88 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1245, 67, 1239, 1204])).
% 1.64/1.88 tff(1247,plain,
% 1.64/1.88 (b(z, s(s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[604, 50, 601, 1246])).
% 1.64/1.88 tff(1248,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(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1249,plain,
% 1.64/1.88 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1250,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1249])).
% 1.64/1.88 tff(1251,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1250, 1248])).
% 1.64/1.88 tff(1252,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1253,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(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 1.64/1.88 tff(1254,plain,
% 1.64/1.88 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1253, 67, 1239, 1204])).
% 1.64/1.88 tff(1255,plain,
% 1.64/1.88 (b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[641, 1254])).
% 1.64/1.88 tff(1256,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1257,plain,
% 1.64/1.88 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1258,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1257])).
% 1.64/1.89 tff(1259,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.64/1.89 tff(1260,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1261,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.64/1.89 tff(1262,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1261, 204, 361, 193, 625, 1255, 1247])).
% 1.64/1.89 tff(1263,plain,((~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1264,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1263, 361, 627, 499, 1186, 389, 378])).
% 1.64/1.89 tff(1265,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[335, 1264])).
% 1.64/1.89 tff(1266,plain,
% 1.64/1.89 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[636, 204, 361, 1265, 627, 625])).
% 1.64/1.89 tff(1267,plain,
% 1.64/1.89 (r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[641, 1266])).
% 1.64/1.89 tff(1268,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[648, 67, 389, 1267])).
% 1.64/1.89 tff(1269,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[242, 50, 1268, 237])).
% 1.64/1.89 tff(1270,plain,
% 1.64/1.89 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[485, 67, 389, 1267])).
% 1.64/1.89 tff(1271,plain,
% 1.64/1.89 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[489, 50, 1270])).
% 1.64/1.89 tff(1272,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1271, 563])).
% 1.64/1.89 tff(1273,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1274,plain,
% 1.64/1.89 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1275,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1274])).
% 1.64/1.89 tff(1276,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1275, 1273])).
% 1.64/1.89 tff(1277,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1278,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 1.64/1.89 tff(1279,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1278, 204, 1186, 627, 625, 1272, 1269])).
% 1.64/1.89 tff(1280,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1281,plain,
% 1.64/1.89 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1280, 623, 361, 137, 389, 568])).
% 1.64/1.89 tff(1282,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.64/1.89 tff(1283,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)],[1282])).
% 1.64/1.89 tff(1284,plain,
% 1.64/1.89 (s(elem!1) = s(s(z))),
% 1.64/1.89 inference(transitivity,[status(thm)],[919, 1283, 83])).
% 1.64/1.89 tff(1285,plain,
% 1.64/1.89 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1284])).
% 1.64/1.89 tff(1286,plain,
% 1.64/1.89 (elem!1 = s(z)),
% 1.64/1.89 inference(transitivity,[status(thm)],[1009, 1285, 78])).
% 1.64/1.89 tff(1287,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.64/1.89 tff(1288,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1287, 1286])).
% 1.64/1.89 tff(1289,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1290,plain,
% 1.64/1.89 (elem!1 = s(z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1289, 1281])).
% 1.64/1.89 tff(1291,plain,
% 1.64/1.89 (s(elem!1) = s(s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1290])).
% 1.64/1.89 tff(1292,plain,
% 1.64/1.89 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1291])).
% 1.64/1.89 tff(1293,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1292])).
% 1.64/1.89 tff(1294,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)],[1293])).
% 1.64/1.89 tff(1295,plain,
% 1.64/1.89 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1294])).
% 1.64/1.89 tff(1296,plain,
% 1.64/1.89 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1295])).
% 1.64/1.89 tff(1297,plain,
% 1.64/1.89 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1296])).
% 1.64/1.89 tff(1298,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[739, 623, 2, 566, 444, 389])).
% 1.64/1.89 tff(1299,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[766, 1298])).
% 1.64/1.89 tff(1300,plain,
% 1.64/1.89 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[815, 1299, 361, 623, 359, 613])).
% 1.64/1.89 tff(1301,plain,
% 1.64/1.89 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[822, 1300])).
% 1.64/1.89 tff(1302,plain,
% 1.64/1.89 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1301, 1297])).
% 1.64/1.89 tff(1303,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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1304,plain,
% 1.64/1.89 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1305,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(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1304])).
% 1.64/1.89 tff(1306,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(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1305, 1303])).
% 1.64/1.89 tff(1307,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(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1308,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 1.64/1.89 tff(1309,plain,
% 1.64/1.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1308, 67, 261, 1302])).
% 1.64/1.89 tff(1310,plain,
% 1.64/1.89 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1292])).
% 1.64/1.89 tff(1311,plain,
% 1.64/1.89 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1310])).
% 1.64/1.89 tff(1312,plain,
% 1.64/1.89 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1311])).
% 1.64/1.89 tff(1313,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 1.64/1.89 tff(1314,plain,
% 1.64/1.89 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1313])).
% 1.64/1.89 tff(1315,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(s(z))),
% 1.64/1.89 inference(transitivity,[status(thm)],[699, 1314, 83])).
% 1.64/1.89 tff(1316,plain,
% 1.64/1.89 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1315])).
% 1.64/1.89 tff(1317,plain,
% 1.64/1.89 (s(s(elem!1)) = s(z)),
% 1.64/1.89 inference(transitivity,[status(thm)],[754, 1316, 78])).
% 1.64/1.89 tff(1318,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[924, 1317])).
% 1.64/1.89 tff(1319,plain,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1320,plain,
% 1.64/1.89 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1319, 1312])).
% 1.64/1.89 tff(1321,plain,
% 1.64/1.89 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[879, 1320])).
% 1.64/1.89 tff(1322,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.64/1.89 tff(1323,plain,
% 1.64/1.89 (s(elem!1) = s(s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1322])).
% 1.64/1.89 tff(1324,plain,
% 1.64/1.89 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1323])).
% 1.64/1.89 tff(1325,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1324])).
% 1.64/1.89 tff(1326,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)],[1325])).
% 1.64/1.89 tff(1327,plain,
% 1.64/1.89 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1326])).
% 1.64/1.89 tff(1328,plain,
% 1.64/1.89 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1327])).
% 1.64/1.89 tff(1329,plain,
% 1.64/1.89 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1328])).
% 1.64/1.89 tff(1330,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.64/1.89 tff(1331,plain,
% 1.64/1.89 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1332,plain,
% 1.64/1.89 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1331, 13])).
% 1.64/1.89 tff(1333,plain,
% 1.64/1.89 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1330])).
% 1.64/1.89 tff(1334,plain,
% 1.64/1.89 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1326, 175, 1333, 1332, 1330, 1329])).
% 1.64/1.89 tff(1335,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.64/1.89 tff(1336,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1335, 1334])).
% 1.64/1.89 tff(1337,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1338,plain,
% 1.64/1.89 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1337, 1321, 1290])).
% 1.64/1.89 tff(1339,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1340,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1341,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 1.64/1.89 tff(1342,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1341, 50, 1338, 1309])).
% 1.64/1.89 tff(1343,plain,
% 1.64/1.89 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1296])).
% 1.64/1.89 tff(1344,plain,
% 1.64/1.89 (s(z) = elem!1),
% 1.64/1.89 inference(symmetry,[status(thm)],[1290])).
% 1.64/1.89 tff(1345,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1344, 1343])).
% 1.64/1.89 tff(1346,plain,
% 1.64/1.89 (b(elem!1, s(s(s(s(s(s(elem!1))))))) <=> b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1345])).
% 1.64/1.89 tff(1347,plain,
% 1.64/1.89 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1290])).
% 1.64/1.89 tff(1348,plain,
% 1.64/1.89 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1347])).
% 1.64/1.89 tff(1349,plain,
% 1.64/1.89 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1348])).
% 1.64/1.89 tff(1350,plain,
% 1.64/1.89 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[669, 1349])).
% 1.64/1.89 tff(1351,assumption,(r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.64/1.89 tff(1352,plain,
% 1.64/1.89 (s(z) = elem!1),
% 1.64/1.89 inference(symmetry,[status(thm)],[1322])).
% 1.64/1.89 tff(1353,plain,
% 1.64/1.89 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1352, 1329])).
% 1.64/1.89 tff(1354,plain,
% 1.64/1.89 (r(elem!1, s(s(s(s(s(s(elem!1))))))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1353])).
% 1.64/1.89 tff(1355,assumption,(r(elem!1, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.64/1.89 tff(1356,plain,
% 1.64/1.89 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 1.64/1.89 tff(1357,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), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1358,plain,
% 1.64/1.89 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1359,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(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1358])).
% 1.64/1.89 tff(1360,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(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1359, 1357])).
% 1.64/1.89 tff(1361,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(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1362,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 1.64/1.89 tff(1363,plain,
% 1.64/1.89 ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1362, 67, 389])).
% 1.64/1.89 tff(1364,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1363, 1356, 1351])).
% 1.64/1.89 tff(1365,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1366,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1365, 1302, 1290, 389])).
% 1.64/1.89 tff(1367,plain,
% 1.64/1.89 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1038, 1366, 1350])).
% 1.64/1.89 tff(1368,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1367, 1346])).
% 1.64/1.89 tff(1369,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1343])).
% 1.64/1.89 tff(1370,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1369])).
% 1.64/1.89 tff(1371,plain,
% 1.64/1.89 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1299, 1370])).
% 1.64/1.89 tff(1372,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1373,plain,
% 1.64/1.89 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1374,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1373])).
% 1.74/1.90 tff(1375,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1374, 1372])).
% 1.74/1.90 tff(1376,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1377,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(s(z)))))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 1.74/1.90 tff(1378,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1377, 204, 586, 565, 1371, 1368, 1342])).
% 1.74/1.90 tff(1379,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1380,plain,
% 1.74/1.90 (~r(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1379, 479, 361, 359, 2, 261, 559, 137, 443])).
% 1.74/1.90 tff(1381,plain,
% 1.74/1.90 (b(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[376, 1380])).
% 1.74/1.90 tff(1382,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1383,plain,
% 1.74/1.90 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1384,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1383])).
% 1.74/1.90 tff(1385,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1384, 1382])).
% 1.74/1.90 tff(1386,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1387,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.74/1.90 tff(1388,plain,
% 1.74/1.90 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1387, 204, 363, 444, 404, 443])).
% 1.74/1.90 tff(1389,plain,
% 1.74/1.90 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[282, 50, 1388])).
% 1.74/1.90 tff(1390,plain,
% 1.74/1.90 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1389, 552])).
% 1.74/1.90 tff(1391,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1392,plain,
% 1.74/1.90 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1393,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1392])).
% 1.74/1.90 tff(1394,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1393, 1391])).
% 1.74/1.90 tff(1395,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1396,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.74/1.90 tff(1397,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1396, 204, 363, 444, 405, 404, 566])).
% 1.74/1.90 tff(1398,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1399,plain,
% 1.74/1.90 (~b(z, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1398, 404, 363, 566, 444])).
% 1.74/1.90 tff(1400,plain,
% 1.74/1.90 (r(z, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[259, 1399])).
% 1.74/1.90 tff(1401,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1402,plain,
% 1.74/1.90 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), 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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1403,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1402])).
% 1.74/1.90 tff(1404,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1403, 1401])).
% 1.74/1.90 tff(1405,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1406,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.74/1.90 tff(1407,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1406, 204, 363, 362, 444, 404, 566])).
% 1.74/1.90 tff(1408,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1409,plain,
% 1.74/1.90 (~b(z, s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1408, 404, 363, 566, 444])).
% 1.74/1.90 tff(1410,plain,
% 1.74/1.90 (r(z, s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[306, 1409])).
% 1.74/1.90 tff(1411,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1412,plain,
% 1.74/1.90 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1413,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1412])).
% 1.74/1.90 tff(1414,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1413, 1411])).
% 1.74/1.90 tff(1415,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1416,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 1.74/1.90 tff(1417,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1416, 67, 1410, 1400, 261, 1390])).
% 1.74/1.90 tff(1418,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1419,plain,
% 1.74/1.90 (~b(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1418, 1381, 261, 559, 443, 479])).
% 1.74/1.90 tff(1420,plain,
% 1.74/1.90 (r(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[402, 1419])).
% 1.74/1.90 tff(1421,plain,
% 1.74/1.90 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[314, 67, 1420, 261])).
% 1.74/1.90 tff(1422,plain,
% 1.74/1.90 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[282, 50, 1421])).
% 1.74/1.90 tff(1423,plain,
% 1.74/1.90 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1422, 552])).
% 1.74/1.90 tff(1424,plain,
% 1.74/1.90 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[322, 67, 1420, 261])).
% 1.74/1.90 tff(1425,plain,
% 1.74/1.90 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[134, 1424])).
% 1.74/1.90 tff(1426,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1427,plain,
% 1.74/1.90 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1428,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1427])).
% 1.74/1.90 tff(1429,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1428, 1426])).
% 1.74/1.90 tff(1430,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1431,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.74/1.91 tff(1432,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1431, 204, 559, 479, 1425, 443, 1423])).
% 1.74/1.91 tff(1433,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1434,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1433, 137, 261, 361, 359, 2, 443])).
% 1.74/1.91 tff(1435,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[55, 1434])).
% 1.74/1.91 tff(1436,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[425, 389, 1435, 359, 361, 2])).
% 1.74/1.91 tff(1437,plain,
% 1.74/1.91 (~r(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[453, 137, 2])).
% 1.74/1.91 tff(1438,plain,
% 1.74/1.91 (b(s(z), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[478, 1437])).
% 1.74/1.91 tff(1439,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1379, 389, 361, 359, 2, 261, 1438, 137, 443])).
% 1.74/1.91 tff(1440,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[558, 1439, 1436])).
% 1.74/1.91 tff(1441,plain,((~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1442,plain,
% 1.74/1.91 (~b(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1441, 528, 137, 389, 261, 548, 443])).
% 1.74/1.91 tff(1443,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[357, 1442, 537])).
% 1.74/1.91 tff(1444,plain,((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1445,plain,
% 1.74/1.91 (~r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1444, 261, 137, 443, 378, 444, 136])).
% 1.74/1.91 tff(1446,plain,
% 1.74/1.91 (b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[376, 1445])).
% 1.74/1.91 tff(1447,plain,
% 1.74/1.91 (~b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1418, 1446, 444, 261, 443, 479])).
% 1.74/1.91 tff(1448,plain,
% 1.74/1.91 (r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[402, 1447])).
% 1.74/1.91 tff(1449,plain,
% 1.74/1.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[314, 67, 1448, 261])).
% 1.74/1.91 tff(1450,plain,
% 1.74/1.91 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[282, 50, 1449, 277])).
% 1.74/1.91 tff(1451,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[322, 67, 1448, 261])).
% 1.74/1.91 tff(1452,plain,
% 1.74/1.91 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[134, 1451])).
% 1.74/1.91 tff(1453,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1431, 204, 444, 479, 1452, 443, 1450])).
% 1.74/1.91 tff(1454,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1455,plain,
% 1.74/1.91 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1454, 378, 443, 137, 444, 136])).
% 1.74/1.91 tff(1456,plain,
% 1.74/1.91 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[641, 1455])).
% 1.74/1.91 tff(1457,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1458,plain,
% 1.74/1.91 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1459,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1458])).
% 1.74/1.91 tff(1460,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1459, 1457])).
% 1.74/1.91 tff(1461,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1462,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.74/1.91 tff(1463,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1462, 204, 363, 444, 1456, 443])).
% 1.74/1.91 tff(1464,plain,
% 1.74/1.91 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[134, 1463])).
% 1.74/1.91 tff(1465,plain,
% 1.74/1.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[507, 1464, 378])).
% 1.74/1.91 tff(1466,plain,
% 1.74/1.91 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[190, 1465])).
% 1.74/1.91 tff(1467,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[518, 1464, 137])).
% 1.74/1.91 tff(1468,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[218, 1467])).
% 1.74/1.91 tff(1469,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 1.74/1.91 tff(1470,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1212, 308, 378])).
% 1.74/1.91 tff(1471,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[335, 1470])).
% 1.74/1.91 tff(1472,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(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1473,plain,
% 1.74/1.91 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1474,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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1473])).
% 1.74/1.91 tff(1475,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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1474, 1472])).
% 1.74/1.91 tff(1476,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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1477,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.74/1.91 tff(1478,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1477, 67, 308, 339, 378])).
% 1.74/1.91 tff(1479,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1480,plain,
% 1.74/1.91 (~r(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1479, 308, 378])).
% 1.74/1.91 tff(1481,plain,
% 1.74/1.91 (b(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[357, 1480])).
% 1.74/1.91 tff(1482,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[636, 204, 1481, 1471, 193, 4, 1469])).
% 1.74/1.91 tff(1483,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1484,plain,
% 1.74/1.91 (~r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1483, 1468, 1466, 1456, 378])).
% 1.74/1.91 tff(1485,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[402, 1484])).
% 1.74/1.91 tff(1486,plain,
% 1.74/1.91 (~b(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1408, 1485, 479, 363, 444])).
% 1.74/1.91 tff(1487,plain,
% 1.74/1.91 (r(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[306, 1486])).
% 1.74/1.91 tff(1488,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(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)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1489,plain,
% 1.74/1.91 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1490,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(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))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1489])).
% 1.74/1.91 tff(1491,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(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)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1490, 1488])).
% 1.74/1.91 tff(1492,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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1493,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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 1.74/1.91 tff(1494,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1493, 67, 1487, 136])).
% 1.74/1.91 tff(1495,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[335, 1494])).
% 1.74/1.91 tff(1496,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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1497,plain,
% 1.74/1.91 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1498,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(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1497])).
% 1.74/1.91 tff(1499,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(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1498, 1496])).
% 1.74/1.91 tff(1500,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(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)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1501,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.74/1.91 tff(1502,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1501, 67, 286, 339, 136])).
% 1.74/1.91 tff(1503,plain,((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1504,plain,
% 1.74/1.91 (~r(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1503, 1487, 136])).
% 1.74/1.91 tff(1505,plain,
% 1.74/1.91 (b(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[357, 1504])).
% 1.74/1.91 tff(1506,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[636, 204, 1505, 1495, 1468, 1466, 1456])).
% 1.74/1.91 tff(1507,plain,((~b(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1508,plain,
% 1.74/1.91 (~b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1507, 378, 444, 136, 137, 443])).
% 1.74/1.91 tff(1509,plain,
% 1.74/1.91 (r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[376, 1508])).
% 1.74/1.91 tff(1510,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[546, 1509, 136])).
% 1.74/1.91 tff(1511,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[335, 1510])).
% 1.74/1.91 tff(1512,plain,
% 1.74/1.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[507, 499, 378])).
% 1.74/1.91 tff(1513,plain,
% 1.74/1.91 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[190, 1512])).
% 1.74/1.91 tff(1514,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[518, 499, 137])).
% 1.74/1.91 tff(1515,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[218, 1514])).
% 1.74/1.91 tff(1516,plain,
% 1.74/1.91 (~r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1483, 1515, 1513, 1469, 378])).
% 1.74/1.91 tff(1517,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[402, 1516])).
% 1.74/1.91 tff(1518,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[636, 204, 361, 359, 193, 4, 1469])).
% 1.74/1.91 tff(1519,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1520,plain,
% 1.74/1.91 (~b(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1519, 1515, 359, 1513, 1469])).
% 1.74/1.91 tff(1521,plain,
% 1.74/1.91 (r(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[357, 1520])).
% 1.74/1.91 tff(1522,plain,
% 1.74/1.91 (~r(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[347, 1521, 137])).
% 1.74/1.91 tff(1523,plain,
% 1.74/1.91 (b(z, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[259, 1522])).
% 1.74/1.91 tff(1524,plain,
% 1.74/1.91 (~r(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1503, 1521, 136])).
% 1.74/1.91 tff(1525,plain,
% 1.74/1.91 (b(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[306, 1524])).
% 1.74/1.91 tff(1526,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1527,plain,
% 1.74/1.91 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1528,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1527])).
% 1.74/1.91 tff(1529,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.74/1.91 tff(1530,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1531,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.74/1.91 tff(1532,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1531, 204, 362, 444, 405, 404, 566])).
% 1.74/1.91 tff(1533,plain,((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1534,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1533, 1525, 1523, 479, 1517, 444])).
% 1.74/1.91 tff(1535,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1536,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1535, 1511, 136, 137, 444, 1456, 378])).
% 1.74/1.92 tff(1537,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[134, 1536])).
% 1.74/1.92 tff(1538,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.74/1.92 tff(1539,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1431, 204, 444, 566, 192, 443, 1538])).
% 1.74/1.92 tff(1540,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(1541,plain,
% 1.74/1.92 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1540, 1537, 479, 444, 443])).
% 1.74/1.92 tff(1542,plain,
% 1.74/1.92 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[282, 50, 1541, 277])).
% 1.74/1.92 tff(1543,plain,
% 1.74/1.92 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[584, 67, 137, 1542])).
% 1.74/1.92 tff(1544,plain,
% 1.74/1.92 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[190, 1543])).
% 1.74/1.92 tff(1545,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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1546,plain,
% 1.74/1.92 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1547,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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1546])).
% 1.74/1.92 tff(1548,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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1547, 1545])).
% 1.74/1.92 tff(1549,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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1550,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 1.74/1.92 tff(1551,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1550, 67, 137, 1542])).
% 1.74/1.92 tff(1552,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[218, 1551])).
% 1.74/1.92 tff(1553,plain,
% 1.74/1.92 (~r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1483, 1552, 1544, 1456, 378])).
% 1.74/1.92 tff(1554,plain,
% 1.74/1.92 (b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[402, 1553])).
% 1.74/1.92 tff(1555,plain,
% 1.74/1.92 (~b(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1519, 1552, 1511, 1544, 1456])).
% 1.74/1.92 tff(1556,plain,
% 1.74/1.92 (r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[357, 1555])).
% 1.74/1.92 tff(1557,plain,
% 1.74/1.92 (~r(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[347, 1556, 137])).
% 1.74/1.92 tff(1558,plain,
% 1.74/1.92 (b(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[259, 1557])).
% 1.74/1.92 tff(1559,plain,
% 1.74/1.92 (~r(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1503, 1556, 136])).
% 1.74/1.92 tff(1560,plain,
% 1.74/1.92 (b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[306, 1559])).
% 1.74/1.92 tff(1561,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1533, 1560, 1558, 479, 1554, 444])).
% 1.74/1.92 tff(1562,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(1563,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1562, 136, 444, 137, 443])).
% 1.74/1.92 tff(1564,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[108, 1563])).
% 1.74/1.92 tff(1565,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[518, 510, 137])).
% 1.74/1.92 tff(1566,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[134, 1565])).
% 1.74/1.92 tff(1567,plain,
% 1.74/1.92 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1540, 1566, 566, 444, 443])).
% 1.74/1.92 tff(1568,plain,
% 1.74/1.92 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[282, 50, 1567, 277])).
% 1.74/1.92 tff(1569,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1550, 67, 137, 510, 1568])).
% 1.74/1.92 tff(1570,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~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(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(1571,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1570, 479, 137, 444, 443])).
% 1.74/1.92 tff(1572,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[218, 1571])).
% 1.74/1.92 tff(1573,plain,
% 1.74/1.92 (~r(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[347, 339, 137])).
% 1.74/1.92 tff(1574,plain,
% 1.74/1.92 (b(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[259, 1573])).
% 1.74/1.92 tff(1575,plain,
% 1.74/1.92 (~r(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1503, 339, 136])).
% 1.74/1.92 tff(1576,plain,
% 1.74/1.92 (b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[306, 1575])).
% 1.74/1.92 tff(1577,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1578,plain,
% 1.74/1.92 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1579,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1578])).
% 1.74/1.92 tff(1580,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1579, 1577])).
% 1.74/1.92 tff(1581,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1582,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.74/1.92 tff(1583,plain,
% 1.74/1.92 (~b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1582, 204, 1576, 444, 1574, 479])).
% 1.74/1.92 tff(1584,plain,
% 1.74/1.92 (r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[376, 1583])).
% 1.74/1.92 tff(1585,plain,
% 1.74/1.92 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[536, 1584, 339])).
% 1.74/1.92 tff(1586,plain,
% 1.74/1.92 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[431, 1585])).
% 1.74/1.92 tff(1587,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1588,plain,
% 1.74/1.92 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1589,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1588])).
% 1.74/1.92 tff(1590,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1589, 1587])).
% 1.74/1.92 tff(1591,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1592,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.74/1.92 tff(1593,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1592, 204, 1576, 1574, 479, 1586, 153])).
% 1.74/1.92 tff(1594,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(1595,plain,
% 1.74/1.92 (~r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1594, 1564, 444, 136, 137])).
% 1.74/1.92 tff(1596,plain,
% 1.74/1.92 (b(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[357, 1595])).
% 1.74/1.92 tff(1597,plain,
% 1.74/1.92 (~r(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[472, 137, 136])).
% 1.74/1.92 tff(1598,plain,
% 1.74/1.92 (b(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[478, 1597])).
% 1.74/1.92 tff(1599,plain,
% 1.74/1.92 (~r(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[347, 137, 339])).
% 1.74/1.92 tff(1600,plain,
% 1.74/1.92 (b(z, s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[259, 1599])).
% 1.74/1.92 tff(1601,plain,
% 1.74/1.92 (~r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[546, 136, 538])).
% 1.74/1.92 tff(1602,plain,
% 1.74/1.92 (b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[376, 1601])).
% 1.74/1.92 tff(1603,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[145, 137, 136])).
% 1.74/1.92 tff(1604,plain,
% 1.74/1.92 (b(s(s(s(z))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[558, 1603])).
% 1.74/1.92 tff(1605,plain,
% 1.74/1.92 (~b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1398, 1604, 1602, 1600, 1598])).
% 1.74/1.92 tff(1606,plain,
% 1.74/1.92 (r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[402, 1605])).
% 1.74/1.92 tff(1607,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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1608,plain,
% 1.74/1.92 (((~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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1609,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))), 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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1608])).
% 1.74/1.92 tff(1610,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))), 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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1609, 1607])).
% 1.74/1.92 tff(1611,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))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1612,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 1.74/1.92 tff(1613,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1612, 67, 1606, 538, 137])).
% 1.74/1.92 tff(1614,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(1615,plain,
% 1.74/1.92 (~r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1614, 538, 137, 136])).
% 1.74/1.92 tff(1616,plain,
% 1.74/1.92 (b(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[357, 1615])).
% 1.74/1.92 tff(1617,plain,
% 1.74/1.92 (~r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[546, 538, 136])).
% 1.74/1.92 tff(1618,plain,
% 1.74/1.92 (b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[376, 1617])).
% 1.74/1.92 tff(1619,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1620,plain,
% 1.74/1.92 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1621,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(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(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1620])).
% 1.74/1.92 tff(1622,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(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(X1, 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(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.74/1.92 tff(1623,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(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))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1624,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.74/1.92 tff(1625,plain,
% 1.74/1.92 (~b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1624, 204, 1618, 479, 1616, 153])).
% 1.74/1.92 tff(1626,plain,
% 1.74/1.92 (r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[402, 1625])).
% 1.74/1.92 tff(1627,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1612, 67, 1626, 538, 137])).
% 1.74/1.92 tff(1628,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(1629,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1628, 1564, 137, 136])).
% 1.74/1.92 tff(1630,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[335, 1629])).
% 1.74/1.92 tff(1631,plain,
% 1.74/1.92 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1433, 2, 137, 136, 1596, 1630, 443])).
% 1.74/1.92 tff(1632,plain,
% 1.74/1.92 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[641, 1631])).
% 1.74/1.92 tff(1633,plain,
% 1.74/1.92 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1519, 1632, 1630, 1596, 1572])).
% 1.74/1.92 tff(1634,plain,
% 1.74/1.92 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[190, 1633])).
% 1.74/1.92 tff(1635,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(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1636,plain,
% 1.74/1.93 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1637,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(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1636])).
% 1.74/1.93 tff(1638,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(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1637, 1635])).
% 1.74/1.93 tff(1639,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(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1640,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1639, 1638])).
% 1.74/1.93 tff(1641,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1640, 67, 2, 1634])).
% 1.74/1.93 tff(1642,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[489, 50, 1641, 249])).
% 1.74/1.93 tff(1643,plain,
% 1.74/1.93 ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[574, 204, 444, 479, 443])).
% 1.74/1.93 tff(1644,plain,
% 1.74/1.93 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1643, 1642])).
% 1.74/1.93 tff(1645,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[282, 50, 1644, 277])).
% 1.74/1.93 tff(1646,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[584, 67, 137, 1634, 1645])).
% 1.74/1.93 tff(1647,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1648,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1647, 136, 444, 443, 137])).
% 1.74/1.93 tff(1649,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[431, 1648])).
% 1.74/1.93 tff(1650,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1651,plain,
% 1.74/1.93 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1652,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1651])).
% 1.74/1.93 tff(1653,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1652, 1650])).
% 1.74/1.93 tff(1654,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1655,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 1.74/1.93 tff(1656,plain,
% 1.74/1.93 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1655, 204, 444, 1649, 1564, 443])).
% 1.74/1.93 tff(1657,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[282, 50, 1656, 277])).
% 1.74/1.93 tff(1658,plain,
% 1.74/1.93 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[584, 67, 137, 1657])).
% 1.74/1.93 tff(1659,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[190, 1658])).
% 1.74/1.93 tff(1660,plain,
% 1.74/1.93 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1519, 1659, 1630, 1596, 1572])).
% 1.74/1.93 tff(1661,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[641, 1660])).
% 1.74/1.93 tff(1662,plain,
% 1.74/1.93 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1433, 261, 137, 136, 1596, 1630, 443])).
% 1.74/1.93 tff(1663,plain,
% 1.74/1.93 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[431, 1662])).
% 1.74/1.93 tff(1664,plain,
% 1.74/1.93 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1655, 204, 444, 1663, 1564, 443])).
% 1.74/1.93 tff(1665,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[282, 50, 1664, 277])).
% 1.74/1.93 tff(1666,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1550, 67, 137, 1665])).
% 1.74/1.93 tff(1667,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[218, 1666])).
% 1.74/1.93 tff(1668,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1669,plain,
% 1.74/1.93 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1670,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1669])).
% 1.74/1.93 tff(1671,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1670, 1668])).
% 1.74/1.93 tff(1672,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1673,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.74/1.93 tff(1674,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1673, 204, 444, 1663, 1564, 1667, 490])).
% 1.74/1.93 tff(1675,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1676,plain,
% 1.74/1.93 (~r(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1675, 1661, 137, 443, 444, 136])).
% 1.74/1.93 tff(1677,plain,
% 1.74/1.93 (b(s(z), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[376, 1676])).
% 1.74/1.93 tff(1678,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1679,plain,
% 1.74/1.93 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1680,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1679])).
% 1.74/1.93 tff(1681,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1680, 1678])).
% 1.74/1.93 tff(1682,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1683,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.74/1.93 tff(1684,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1683, 204, 363, 444, 404, 456, 361])).
% 1.74/1.93 tff(1685,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1686,plain,
% 1.74/1.93 (~b(s(s(s(z))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1685, 1677, 1596, 444, 1649])).
% 1.74/1.93 tff(1687,plain,
% 1.74/1.93 (r(s(s(s(z))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[402, 1686])).
% 1.74/1.93 tff(1688,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[314, 67, 1687, 1661, 1657])).
% 1.74/1.93 tff(1689,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1690,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1689, 444, 137, 443])).
% 1.74/1.93 tff(1691,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[55, 1690])).
% 1.74/1.93 tff(1692,plain,
% 1.74/1.93 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1202, 204, 456, 1691, 4, 443])).
% 1.74/1.93 tff(1693,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[218, 1692])).
% 1.74/1.93 tff(1694,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[518, 1693, 464, 137])).
% 1.74/1.93 tff(1695,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1696,plain,
% 1.74/1.93 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1695, 455, 137, 443, 444])).
% 1.74/1.93 tff(1697,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[190, 1696])).
% 1.74/1.93 tff(1698,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[584, 67, 137, 1, 264])).
% 1.74/1.93 tff(1699,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1700,plain,
% 1.74/1.93 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1699, 1697, 137])).
% 1.74/1.93 tff(1701,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[282, 50, 1700, 277])).
% 1.74/1.93 tff(1702,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1655, 204, 444, 456, 153, 443, 1538])).
% 1.74/1.93 tff(1703,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1704,plain,
% 1.74/1.93 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1703, 455, 444, 443, 1701])).
% 1.74/1.93 tff(1705,plain,
% 1.74/1.93 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[108, 1704])).
% 1.74/1.93 tff(1706,plain,
% 1.74/1.93 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[507, 1705, 1697])).
% 1.74/1.93 tff(1707,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[134, 1706])).
% 1.74/1.93 tff(1708,assumption,(b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.74/1.93 tff(1709,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1710,plain,
% 1.74/1.93 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1711,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1710])).
% 1.74/1.93 tff(1712,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1711, 1709])).
% 1.74/1.93 tff(1713,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1714,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 1.74/1.93 tff(1715,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1714, 204, 444, 405, 192, 443, 1708])).
% 1.74/1.93 tff(1716,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1717,plain,
% 1.74/1.93 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1716, 1574, 192, 444, 443])).
% 1.74/1.93 tff(1718,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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1719,plain,
% 1.74/1.93 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1720,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(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1719])).
% 1.74/1.93 tff(1721,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(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1720, 1718])).
% 1.74/1.93 tff(1722,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(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1723,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 1.74/1.94 tff(1724,plain,
% 1.74/1.94 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1723, 67, 339, 1])).
% 1.74/1.94 tff(1725,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[604, 50, 601, 1724, 1717])).
% 1.74/1.94 tff(1726,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1727,plain,
% 1.74/1.94 (~r(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1726, 1707, 1697, 444, 443, 137])).
% 1.74/1.94 tff(1728,plain,
% 1.74/1.94 (b(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[357, 1727])).
% 1.74/1.94 tff(1729,plain,
% 1.74/1.94 (~b(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[438, 204, 456, 361, 360, 359])).
% 1.74/1.94 tff(1730,plain,
% 1.74/1.94 (r(z, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[306, 1729])).
% 1.74/1.94 tff(1731,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(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1732,plain,
% 1.74/1.94 (((~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(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1733,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), 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(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1732])).
% 1.74/1.94 tff(1734,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), 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(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1733, 1731])).
% 1.74/1.94 tff(1735,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), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1736,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 1.74/1.94 tff(1737,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1736, 67, 286, 3, 445])).
% 1.74/1.94 tff(1738,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1739,plain,
% 1.74/1.94 (~r(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1738, 1730, 445])).
% 1.74/1.94 tff(1740,plain,
% 1.74/1.94 (b(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[259, 1739])).
% 1.74/1.94 tff(1741,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1742,plain,
% 1.74/1.94 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1743,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1742])).
% 1.74/1.94 tff(1744,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1743, 1741])).
% 1.74/1.94 tff(1745,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1746,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.74/1.94 tff(1747,plain,
% 1.74/1.94 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1746, 204, 444, 361, 360])).
% 1.74/1.94 tff(1748,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1747, 1740])).
% 1.74/1.94 tff(1749,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[108, 1748])).
% 1.74/1.94 tff(1750,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(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1751,plain,
% 1.74/1.94 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1752,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(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1751])).
% 1.74/1.94 tff(1753,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(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1752, 1750])).
% 1.74/1.94 tff(1754,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(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1755,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(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 1.74/1.94 tff(1756,plain,
% 1.74/1.94 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1755, 67, 1749, 1])).
% 1.74/1.94 tff(1757,plain,
% 1.74/1.94 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[282, 50, 1756, 277])).
% 1.74/1.94 tff(1758,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1759,plain,
% 1.74/1.94 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1760,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1759])).
% 1.74/1.94 tff(1761,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1760, 1758])).
% 1.74/1.94 tff(1762,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(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))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1763,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.74/1.94 tff(1764,plain,
% 1.74/1.94 (~b(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1763, 204, 456, 361, 360, 359])).
% 1.74/1.94 tff(1765,plain,
% 1.74/1.94 (r(s(z), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[376, 1764])).
% 1.74/1.94 tff(1766,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(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)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1767,plain,
% 1.74/1.94 (((~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)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1768,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(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))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1767])).
% 1.74/1.94 tff(1769,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(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)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1768, 1766])).
% 1.74/1.94 tff(1770,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(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1771,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 1.74/1.94 tff(1772,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1771, 67, 389, 308, 445])).
% 1.74/1.94 tff(1773,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1774,plain,
% 1.74/1.94 (~r(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1773, 1765, 445])).
% 1.74/1.94 tff(1775,plain,
% 1.74/1.94 (b(s(s(s(z))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[402, 1774])).
% 1.74/1.94 tff(1776,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1777,plain,
% 1.74/1.94 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1778,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1777])).
% 1.74/1.94 tff(1779,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1778, 1776])).
% 1.74/1.94 tff(1780,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1781,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.74/1.94 tff(1782,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1781, 204, 405, 404, 1469, 192, 1538])).
% 1.74/1.94 tff(1783,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1784,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1783, 1757, 1740, 1775, 192])).
% 1.74/1.94 tff(1785,plain,
% 1.74/1.94 (r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[641, 1784])).
% 1.74/1.94 tff(1786,plain,
% 1.74/1.94 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[485, 67, 1765, 1785])).
% 1.74/1.94 tff(1787,plain,
% 1.74/1.94 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[489, 50, 1786, 249])).
% 1.74/1.94 tff(1788,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1789,plain,
% 1.74/1.95 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1790,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(X1, 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(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[1789])).
% 1.74/1.95 tff(1791,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(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(X1, 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(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1790, 1788])).
% 1.74/1.95 tff(1792,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1793,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.74/1.95 tff(1794,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1793, 204, 444, 192, 1787, 443, 1757])).
% 1.74/1.95 tff(1795,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1796,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1795, 1728, 1707, 443, 1697, 1691, 445, 455, 444])).
% 1.74/1.95 tff(1797,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[335, 1796])).
% 1.74/1.95 tff(1798,plain,
% 1.74/1.95 (~r(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1212, 1797, 1705])).
% 1.74/1.95 tff(1799,plain,
% 1.74/1.95 (b(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[402, 1798])).
% 1.74/1.95 tff(1800,plain,
% 1.74/1.95 (~b(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1685, 1799, 1728, 444, 455])).
% 1.74/1.95 tff(1801,plain,
% 1.74/1.95 (r(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[376, 1800])).
% 1.74/1.95 tff(1802,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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1803,plain,
% 1.74/1.95 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1804,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(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[1803])).
% 1.74/1.95 tff(1805,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(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1804, 1802])).
% 1.74/1.95 tff(1806,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(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1807,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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 1.74/1.95 tff(1808,plain,
% 1.74/1.95 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1807, 67, 538, 261])).
% 1.74/1.95 tff(1809,plain,
% 1.74/1.95 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[190, 1808])).
% 1.74/1.95 tff(1810,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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1811,plain,
% 1.74/1.95 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1812,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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[1811])).
% 1.74/1.95 tff(1813,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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1812, 1810])).
% 1.74/1.95 tff(1814,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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1815,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.74/1.95 tff(1816,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1815, 67, 538, 261])).
% 1.74/1.95 tff(1817,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[218, 1816])).
% 1.74/1.95 tff(1818,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1202, 204, 456, 360, 1817, 1809, 443])).
% 1.74/1.95 tff(1819,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1820,plain,
% 1.74/1.95 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1819, 1797, 1691, 443, 455])).
% 1.74/1.95 tff(1821,plain,
% 1.74/1.95 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[641, 1820])).
% 1.74/1.95 tff(1822,plain,
% 1.74/1.95 (~b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1783, 1799, 1701, 1821, 1707])).
% 1.74/1.95 tff(1823,plain,
% 1.74/1.95 (r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[259, 1822])).
% 1.74/1.95 tff(1824,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), z)) | (~r(z, 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), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1825,plain,
% 1.74/1.95 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1826,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(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[1825])).
% 1.74/1.95 tff(1827,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(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1826, 1824])).
% 1.74/1.95 tff(1828,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(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1829,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.74/1.95 tff(1830,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1829, 67, 389, 3, 445])).
% 1.74/1.95 tff(1831,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1832,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1831, 1823, 1801, 445])).
% 1.74/1.95 tff(1833,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1834,plain,
% 1.74/1.95 (~r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1833, 444, 443, 137])).
% 1.74/1.95 tff(1835,plain,
% 1.74/1.95 (b(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[478, 1834])).
% 1.74/1.95 tff(1836,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1570, 1835, 137, 444, 443])).
% 1.74/1.95 tff(1837,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[218, 1836])).
% 1.74/1.95 tff(1838,plain,
% 1.74/1.95 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1519, 336, 4, 358, 1837])).
% 1.74/1.95 tff(1839,plain,
% 1.74/1.95 (r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[641, 1838])).
% 1.74/1.95 tff(1840,plain,
% 1.74/1.95 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1695, 4, 137, 443, 444])).
% 1.74/1.95 tff(1841,plain,
% 1.74/1.95 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[431, 1840])).
% 1.74/1.95 tff(1842,plain,
% 1.74/1.95 (~r(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1379, 1839, 444, 1841, 358, 336, 1835, 137, 443])).
% 1.74/1.95 tff(1843,plain,
% 1.74/1.95 (b(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[376, 1842])).
% 1.74/1.95 tff(1844,plain,
% 1.74/1.95 (~b(s(s(s(z))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1418, 363, 261, 404, 443, 566])).
% 1.74/1.95 tff(1845,plain,
% 1.74/1.95 (r(s(s(s(z))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[558, 1844])).
% 1.74/1.95 tff(1846,plain,
% 1.74/1.95 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[386, 1845, 2])).
% 1.74/1.95 tff(1847,plain,
% 1.74/1.95 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[108, 1846])).
% 1.74/1.95 tff(1848,plain,
% 1.74/1.95 (~b(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[371, 363, 361, 360, 359])).
% 1.74/1.95 tff(1849,plain,
% 1.74/1.95 (r(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[306, 1848])).
% 1.74/1.95 tff(1850,plain,
% 1.74/1.95 (~r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[294, 1845, 1849])).
% 1.74/1.95 tff(1851,plain,
% 1.74/1.95 (b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[259, 1850])).
% 1.74/1.95 tff(1852,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[413, 1851, 1847, 404, 361, 359])).
% 1.74/1.95 tff(1853,plain,((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1854,plain,
% 1.74/1.95 (~b(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1853, 1843, 336, 1839, 358, 1841, 443, 1835, 1691])).
% 1.74/1.95 tff(1855,plain,
% 1.74/1.95 (r(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[402, 1854])).
% 1.74/1.95 tff(1856,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[322, 67, 1855, 1839, 499])).
% 1.74/1.95 tff(1857,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1858,plain,
% 1.74/1.95 (~r(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1857, 499, 443, 444, 137, 4])).
% 1.74/1.95 tff(1859,plain,
% 1.74/1.95 (b(z, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[259, 1858])).
% 1.74/1.95 tff(1860,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1861,plain,
% 1.74/1.95 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1862,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[1861])).
% 1.74/1.95 tff(1863,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1862, 1860])).
% 1.74/1.95 tff(1864,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1865,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1864, 1863])).
% 1.74/1.95 tff(1866,plain,
% 1.74/1.95 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1865, 204, 361, 1691, 4, 443])).
% 1.74/1.95 tff(1867,plain,
% 1.74/1.95 (r(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[604, 50, 601, 1866])).
% 1.74/1.95 tff(1868,plain,
% 1.74/1.95 (~r(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[611, 67, 499, 1867])).
% 1.74/1.95 tff(1869,plain,
% 1.74/1.95 (b(s(s(s(z))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[402, 1868])).
% 1.74/1.95 tff(1870,plain,
% 1.74/1.95 (~b(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1398, 1869, 444, 1835, 1859])).
% 1.74/1.95 tff(1871,plain,
% 1.74/1.95 (r(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[376, 1870])).
% 1.74/1.95 tff(1872,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1194, 1871, 1841])).
% 1.74/1.95 tff(1873,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[335, 1872])).
% 1.74/1.95 tff(1874,plain,
% 1.74/1.95 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1519, 1873, 4, 361, 1837])).
% 1.74/1.95 tff(1875,plain,
% 1.74/1.95 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1441, 1873, 137, 1841, 361, 1871, 443])).
% 1.74/1.95 tff(1876,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[641, 1875, 1874])).
% 1.74/1.95 tff(1877,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1878,plain,
% 1.74/1.95 (~b(z, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1877, 499, 443, 4, 444, 137])).
% 1.74/1.95 tff(1879,plain,
% 1.74/1.95 (r(z, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[357, 1878])).
% 1.74/1.95 tff(1880,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(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1881,plain,
% 1.74/1.95 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1882,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(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[1881])).
% 1.74/1.95 tff(1883,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(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1882, 1880])).
% 1.74/1.95 tff(1884,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(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1885,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 1.74/1.95 tff(1886,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1885, 67, 286, 2, 339])).
% 1.74/1.95 tff(1887,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1888,plain,
% 1.74/1.95 (~r(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1887, 1879, 1841])).
% 1.74/1.95 tff(1889,plain,
% 1.74/1.95 (b(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[306, 1888])).
% 1.74/1.95 tff(1890,plain,
% 1.74/1.95 (~r(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[536, 1879, 1841])).
% 1.74/1.95 tff(1891,plain,
% 1.74/1.95 (b(s(z), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[376, 1890])).
% 1.74/1.95 tff(1892,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1582, 204, 1891, 1889, 444, 1859, 1835])).
% 1.74/1.95 tff(1893,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1894,plain,
% 1.74/1.95 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1893, 4, 443, 444, 137])).
% 1.74/1.96 tff(1895,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[134, 1894])).
% 1.74/1.96 tff(1896,plain,
% 1.74/1.96 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1540, 1895, 1835, 444, 443])).
% 1.74/1.96 tff(1897,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[282, 50, 1896, 277])).
% 1.74/1.96 tff(1898,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[270, 67, 3, 264])).
% 1.74/1.96 tff(1899,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[641, 1898])).
% 1.74/1.96 tff(1900,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1519, 1899, 336, 4, 358, 193])).
% 1.74/1.96 tff(1901,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1902,plain,
% 1.74/1.96 (~r(z, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1901, 4, 1837, 1897, 137])).
% 1.74/1.96 tff(1903,plain,
% 1.74/1.96 (b(z, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[259, 1902])).
% 1.74/1.96 tff(1904,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1905,plain,
% 1.74/1.96 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1906,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1905])).
% 1.74/1.96 tff(1907,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[1906, 1904])).
% 1.74/1.96 tff(1908,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(1909,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 1.74/1.96 tff(1910,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1909, 204, 1691, 1837, 1895, 443])).
% 1.74/1.96 tff(1911,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[108, 1910])).
% 1.74/1.96 tff(1912,plain,
% 1.74/1.96 (~r(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1479, 339, 378])).
% 1.74/1.96 tff(1913,plain,
% 1.74/1.96 (~r(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[536, 339, 2])).
% 1.74/1.96 tff(1914,plain,
% 1.74/1.96 (b(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[376, 1913])).
% 1.74/1.96 tff(1915,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(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1916,plain,
% 1.74/1.96 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1917,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(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1916])).
% 1.74/1.96 tff(1918,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(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[1917, 1915])).
% 1.74/1.96 tff(1919,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(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(1920,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1919, 1918])).
% 1.74/1.96 tff(1921,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1920, 67, 3, 339, 378])).
% 1.74/1.96 tff(1922,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1923,plain,
% 1.74/1.96 (~r(z, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1922, 339, 378])).
% 1.74/1.96 tff(1924,plain,
% 1.74/1.96 (b(z, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[259, 1923])).
% 1.74/1.96 tff(1925,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1398, 1924, 1914, 404, 566, 444])).
% 1.74/1.96 tff(1926,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1927,plain,
% 1.74/1.96 (~b(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1926, 339, 2, 566, 378, 444])).
% 1.74/1.96 tff(1928,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[402, 1927, 1912])).
% 1.74/1.96 tff(1929,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1930,plain,
% 1.74/1.96 (~r(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1929, 1841, 1835, 1911, 444])).
% 1.74/1.96 tff(1931,plain,
% 1.74/1.96 (b(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[357, 1930])).
% 1.74/1.96 tff(1932,plain,
% 1.74/1.96 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1519, 359, 4, 1931, 1837])).
% 1.74/1.96 tff(1933,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[641, 1932])).
% 1.74/1.96 tff(1934,plain,
% 1.74/1.96 (~r(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1379, 1933, 444, 1841, 1931, 359, 1835, 137, 443])).
% 1.74/1.96 tff(1935,plain,
% 1.74/1.96 (b(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[376, 1934])).
% 1.74/1.96 tff(1936,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1937,plain,
% 1.74/1.96 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1938,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1937])).
% 1.74/1.96 tff(1939,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.74/1.96 tff(1940,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(1941,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.74/1.96 tff(1942,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1941, 204, 1935, 1903, 1835, 1691, 359])).
% 1.74/1.96 tff(1943,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1944,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1943, 4, 137, 443, 444])).
% 1.74/1.96 tff(1945,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[335, 1944])).
% 1.74/1.96 tff(1946,plain,
% 1.74/1.96 (~r(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1212, 1945, 1911])).
% 1.74/1.96 tff(1947,plain,
% 1.74/1.96 (b(s(s(s(z))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[402, 1946])).
% 1.74/1.96 tff(1948,plain,
% 1.74/1.96 (~r(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1194, 1945, 1841])).
% 1.74/1.96 tff(1949,plain,
% 1.74/1.96 (b(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[376, 1948])).
% 1.74/1.96 tff(1950,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1398, 1949, 1947, 444, 1835, 1903])).
% 1.74/1.96 tff(1951,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1952,plain,
% 1.74/1.96 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1951, 444, 137, 443])).
% 1.74/1.96 tff(1953,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[190, 1952])).
% 1.74/1.96 tff(1954,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1699, 1953, 137])).
% 1.74/1.96 tff(1955,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[284, 1954])).
% 1.74/1.96 tff(1956,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1957,plain,
% 1.74/1.96 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1958,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1957])).
% 1.74/1.96 tff(1959,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[1958, 1956])).
% 1.74/1.96 tff(1960,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(1961,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1960, 1959])).
% 1.74/1.96 tff(1962,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1961, 204, 1835, 1691, 1837, 443, 1955])).
% 1.74/1.96 tff(1963,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1964,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1963, 443, 137])).
% 1.74/1.96 tff(1965,plain,
% 1.74/1.96 (r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[558, 1964])).
% 1.74/1.96 tff(1966,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[145, 1965, 137])).
% 1.74/1.96 tff(1967,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[55, 1966])).
% 1.74/1.96 tff(1968,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1969,plain,
% 1.74/1.96 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1970,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1969])).
% 1.74/1.96 tff(1971,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[1970, 1968])).
% 1.74/1.96 tff(1972,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(1973,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.74/1.96 tff(1974,plain,
% 1.74/1.96 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1973, 204, 363, 1967, 359, 443])).
% 1.74/1.96 tff(1975,plain,
% 1.74/1.96 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[190, 1974])).
% 1.74/1.96 tff(1976,plain,
% 1.74/1.96 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1699, 1, 137])).
% 1.74/1.96 tff(1977,plain,
% 1.74/1.96 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[284, 1976])).
% 1.74/1.96 tff(1978,plain,
% 1.74/1.96 (~r(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1831, 3, 445])).
% 1.74/1.96 tff(1979,plain,
% 1.74/1.96 (b(s(z), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[376, 1978])).
% 1.74/1.96 tff(1980,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[371, 1979, 338, 358, 307])).
% 1.74/1.96 tff(1981,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[335, 1980])).
% 1.74/1.96 tff(1982,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[330, 67, 3, 1981, 137])).
% 1.74/1.96 tff(1983,plain,((~r(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(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(1984,plain,
% 1.74/1.96 (~r(z, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1983, 445, 137, 1965])).
% 1.74/1.96 tff(1985,plain,
% 1.74/1.96 (b(z, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[259, 1984])).
% 1.74/1.96 tff(1986,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1987,plain,
% 1.74/1.96 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(1988,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[1987])).
% 1.74/1.97 tff(1989,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[1988, 1986])).
% 1.74/1.97 tff(1990,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(1991,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 1.74/1.97 tff(1992,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1991, 204, 363, 362, 1469, 443, 1708])).
% 1.74/1.97 tff(1993,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(1994,plain,
% 1.74/1.97 (~b(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1993, 363, 443, 1469, 1708])).
% 1.74/1.97 tff(1995,plain,
% 1.74/1.97 (r(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[306, 1994])).
% 1.74/1.97 tff(1996,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(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(1997,plain,
% 1.74/1.97 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(1998,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(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[1997])).
% 1.74/1.97 tff(1999,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(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[1998, 1996])).
% 1.74/1.97 tff(2000,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(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2001,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 1.74/1.97 tff(2002,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2001, 67, 286, 57, 308])).
% 1.74/1.97 tff(2003,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2004,plain,
% 1.74/1.97 (~r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2003, 1995, 1965])).
% 1.74/1.97 tff(2005,plain,
% 1.74/1.97 (b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[402, 2004])).
% 1.74/1.97 tff(2006,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1783, 2005, 1538, 405, 1469])).
% 1.74/1.97 tff(2007,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[134, 2006])).
% 1.74/1.97 tff(2008,plain,
% 1.74/1.97 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[518, 2007, 137])).
% 1.74/1.97 tff(2009,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[218, 2008])).
% 1.74/1.97 tff(2010,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2011,plain,
% 1.74/1.97 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2012,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2011])).
% 1.74/1.97 tff(2013,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2012, 2010])).
% 1.74/1.97 tff(2014,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2015,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2014, 2013])).
% 1.74/1.97 tff(2016,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2015, 204, 363, 1967, 2009, 1469, 443])).
% 1.74/1.97 tff(2017,plain,((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2018,plain,
% 1.74/1.97 (~b(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2017, 1708, 443, 137, 1538, 1985, 1469])).
% 1.74/1.97 tff(2019,plain,
% 1.74/1.97 (r(s(z), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[376, 2018])).
% 1.74/1.97 tff(2020,plain,
% 1.74/1.97 (~r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1773, 2019, 445])).
% 1.74/1.97 tff(2021,plain,
% 1.74/1.97 (b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[402, 2020])).
% 1.74/1.97 tff(2022,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2023,plain,
% 1.74/1.97 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2024,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2023])).
% 1.74/1.97 tff(2025,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2024, 2022])).
% 1.74/1.97 tff(2026,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2027,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2026, 2025])).
% 1.74/1.97 tff(2028,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2027, 204, 1985, 2021, 1469, 1538, 1708])).
% 1.74/1.97 tff(2029,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2030,plain,
% 1.74/1.97 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2029, 1469, 1977, 445, 443, 137])).
% 1.74/1.97 tff(2031,plain,
% 1.74/1.97 (r(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[604, 50, 601, 2030])).
% 1.74/1.97 tff(2032,assumption,(r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.74/1.97 tff(2033,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1723, 67, 339, 1, 2032])).
% 1.74/1.97 tff(2034,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2035,plain,
% 1.74/1.97 (~r(z, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2034, 2031, 1])).
% 1.74/1.97 tff(2036,plain,
% 1.74/1.97 (b(z, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[357, 2035])).
% 1.74/1.97 tff(2037,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2038,plain,
% 1.74/1.97 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2039,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2038])).
% 1.74/1.97 tff(2040,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2039, 2037])).
% 1.74/1.97 tff(2041,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2042,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 1.74/1.97 tff(2043,plain,
% 1.74/1.97 (~b(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2042, 204, 455, 2036, 1469, 443])).
% 1.74/1.97 tff(2044,plain,
% 1.74/1.97 (r(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[306, 2043])).
% 1.74/1.97 tff(2045,plain,
% 1.74/1.97 (~r(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2003, 2044, 1965])).
% 1.74/1.97 tff(2046,plain,
% 1.74/1.97 (b(s(s(s(z))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[402, 2045])).
% 1.74/1.97 tff(2047,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1783, 2046, 1977, 1985, 1469])).
% 1.74/1.97 tff(2048,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[134, 2047])).
% 1.74/1.97 tff(2049,plain,
% 1.74/1.97 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[507, 2048, 1])).
% 1.74/1.97 tff(2050,plain,
% 1.74/1.97 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[108, 2049])).
% 1.74/1.97 tff(2051,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2052,plain,
% 1.74/1.97 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2053,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2052])).
% 1.74/1.97 tff(2054,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2053, 2051])).
% 1.74/1.98 tff(2055,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2056,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 1.74/1.98 tff(2057,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2056, 204, 2046, 2036, 2050, 1469, 1977])).
% 1.74/1.98 tff(2058,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2059,plain,
% 1.74/1.98 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2058, 445, 443, 1, 137])).
% 1.74/1.98 tff(2060,plain,
% 1.74/1.98 (r(s(s(s(s(s(s(z)))))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[641, 2059])).
% 1.74/1.98 tff(2061,plain,
% 1.74/1.98 (~r(s(s(s(s(z)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1819, 261, 360, 443, 456])).
% 1.74/1.98 tff(2062,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[335, 2061])).
% 1.74/1.98 tff(2063,plain,
% 1.74/1.98 (~b(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[438, 204, 456, 361, 360, 2062])).
% 1.74/1.98 tff(2064,plain,
% 1.74/1.98 (r(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[306, 2063])).
% 1.74/1.98 tff(2065,plain,
% 1.74/1.98 (~r(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2003, 2064, 57])).
% 1.74/1.98 tff(2066,plain,
% 1.74/1.98 (b(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[402, 2065])).
% 1.74/1.98 tff(2067,plain,
% 1.74/1.98 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[413, 2066, 2062, 405, 361])).
% 1.74/1.98 tff(2068,plain,
% 1.74/1.98 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[108, 2067])).
% 1.74/1.98 tff(2069,plain,
% 1.74/1.98 (~b(s(z), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1763, 204, 456, 361, 360, 2062])).
% 1.74/1.98 tff(2070,plain,
% 1.74/1.98 (r(s(z), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[376, 2069])).
% 1.74/1.98 tff(2071,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[507, 2068, 1])).
% 1.74/1.98 tff(2072,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[134, 2071])).
% 1.74/1.98 tff(2073,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2074,plain,
% 1.74/1.98 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2075,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2074])).
% 1.74/1.98 tff(2076,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2075, 2073])).
% 1.74/1.98 tff(2077,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2078,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2077, 2076])).
% 1.74/1.98 tff(2079,plain,
% 1.74/1.98 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2078, 204, 405, 2066, 2072, 1538])).
% 1.74/1.98 tff(2080,plain,
% 1.74/1.98 (r(z, s(s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[604, 50, 601, 2079])).
% 1.74/1.98 tff(2081,plain,
% 1.74/1.98 ((s(s(elem!1)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.74/1.98 inference(commutativity,[status(thm)],[])).
% 1.74/1.98 tff(2082,plain,
% 1.74/1.98 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2081])).
% 1.74/1.98 tff(2083,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.74/1.98 tff(2084,plain,
% 1.74/1.98 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2083])).
% 1.74/1.98 tff(2085,plain,
% 1.74/1.98 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2084])).
% 1.74/1.98 tff(2086,plain,
% 1.74/1.98 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.74/1.98 inference(commutativity,[status(thm)],[])).
% 1.74/1.98 tff(2087,plain,
% 1.74/1.98 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2083])).
% 1.74/1.98 tff(2088,plain,
% 1.74/1.98 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[175, 2087, 663])).
% 1.74/1.98 tff(2089,plain,
% 1.74/1.98 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2088])).
% 1.74/1.98 tff(2090,plain,
% 1.74/1.98 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[170, 2089, 687])).
% 1.74/1.98 tff(2091,plain,
% 1.74/1.98 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2090])).
% 1.74/1.98 tff(2092,plain,
% 1.74/1.98 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[21, 2091, 698])).
% 1.74/1.98 tff(2093,plain,
% 1.74/1.98 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2092])).
% 1.74/1.98 tff(2094,plain,
% 1.74/1.98 (s(s(z)) = s(s(elem!1))),
% 1.74/1.98 inference(transitivity,[status(thm)],[84, 2093, 753])).
% 1.74/1.98 tff(2095,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2094])).
% 1.74/1.98 tff(2096,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2095, 2086])).
% 1.74/1.98 tff(2097,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2096, 2085, 2082])).
% 1.74/1.98 tff(2098,plain,
% 1.74/1.98 ((~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2097])).
% 1.74/1.98 tff(2099,plain,
% 1.74/1.98 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(commutativity,[status(thm)],[])).
% 1.74/1.98 tff(2100,plain,
% 1.74/1.98 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2083])).
% 1.74/1.98 tff(2101,plain,
% 1.74/1.98 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2100, 2099])).
% 1.74/1.98 tff(2102,plain,
% 1.74/1.98 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2101])).
% 1.74/1.98 tff(2103,plain,
% 1.74/1.98 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[182, 2102])).
% 1.74/1.98 tff(2104,plain,
% 1.74/1.98 (~(s(s(elem!1)) = s(s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2103, 2098])).
% 1.74/1.98 tff(2105,plain,
% 1.74/1.98 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2091])).
% 1.74/1.98 tff(2106,plain,
% 1.74/1.98 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[699, 2105, 20])).
% 1.74/1.98 tff(2107,plain,
% 1.74/1.98 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2106])).
% 1.74/1.98 tff(2108,plain,
% 1.74/1.98 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.98 inference(commutativity,[status(thm)],[])).
% 1.74/1.98 tff(2109,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2094, 2092])).
% 1.74/1.98 tff(2110,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2109, 2108])).
% 1.74/1.98 tff(2111,plain,
% 1.74/1.98 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2110, 2107])).
% 1.74/1.98 tff(2112,plain,
% 1.74/1.98 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2111])).
% 1.74/1.98 tff(2113,plain,
% 1.74/1.98 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.74/1.98 inference(commutativity,[status(thm)],[])).
% 1.74/1.98 tff(2114,plain,
% 1.74/1.98 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2113])).
% 1.74/1.98 tff(2115,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.74/1.98 tff(2116,plain,
% 1.74/1.98 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2115])).
% 1.74/1.98 tff(2117,plain,
% 1.74/1.98 (s(s(s(s(z)))) = s(s(z))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2116, 2115])).
% 1.74/1.98 tff(2118,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.74/1.98 tff(2119,plain,
% 1.74/1.98 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2118])).
% 1.74/1.98 tff(2120,plain,
% 1.74/1.98 (s(s(s(z))) = s(z)),
% 1.74/1.98 inference(transitivity,[status(thm)],[21, 2119, 78])).
% 1.74/1.98 tff(2121,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[100, 2120])).
% 1.74/1.98 tff(2122,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2123,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2122, 2117])).
% 1.74/1.98 tff(2124,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2125,plain,
% 1.74/1.98 (~(s(s(z)) = s(s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2124, 2114])).
% 1.74/1.98 tff(2126,plain,
% 1.74/1.98 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2125, 2112])).
% 1.74/1.98 tff(2127,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.98 tff(2128,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(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2129,plain,
% 1.74/1.98 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2130,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(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), 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(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2129])).
% 1.74/1.98 tff(2131,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(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), 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(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2130, 2128])).
% 1.74/1.98 tff(2132,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(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2133,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 1.74/1.98 tff(2134,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2133, 67, 907, 445, 2127])).
% 1.74/1.98 tff(2135,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2136,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2135, 907, 445])).
% 1.74/1.98 tff(2137,plain,
% 1.74/1.98 (~r(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1773, 389, 445])).
% 1.74/1.98 tff(2138,plain,
% 1.74/1.98 (b(s(s(s(z))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[402, 2137])).
% 1.74/1.98 tff(2139,plain,
% 1.74/1.98 (~r(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[915, 907, 389])).
% 1.74/1.98 tff(2140,plain,
% 1.74/1.98 (b(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1099, 2139])).
% 1.74/1.98 tff(2141,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.98 tff(2142,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.74/1.98 tff(2143,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(z), s(s(elem!1)))) | (~r(z, 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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2144,plain,
% 1.74/1.98 (((~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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2145,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(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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2144])).
% 1.74/1.98 tff(2146,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(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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2145, 2143])).
% 1.74/1.98 tff(2147,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(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2148,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.74/1.98 tff(2149,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2148, 67, 907, 2142, 286])).
% 1.74/1.98 tff(2150,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2151,plain,
% 1.74/1.98 (~r(z, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2150, 286, 907])).
% 1.74/1.98 tff(2152,plain,
% 1.74/1.98 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.74/1.98 inference(commutativity,[status(thm)],[])).
% 1.74/1.98 tff(2153,plain,
% 1.74/1.98 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2152])).
% 1.74/1.98 tff(2154,plain,
% 1.74/1.98 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2153])).
% 1.74/1.98 tff(2155,plain,
% 1.74/1.98 (~(z = s(s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[757, 2154])).
% 1.74/1.98 tff(2156,plain,
% 1.74/1.98 (((~![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))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2157,plain,
% 1.74/1.98 ((~![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))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2158,plain,
% 1.74/1.98 ((~![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)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 1.74/1.98 tff(2159,plain,
% 1.74/1.98 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2158, 50])).
% 1.74/1.98 tff(2160,plain,
% 1.74/1.98 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2159, 2155])).
% 1.74/1.98 tff(2161,plain,
% 1.74/1.98 (b(z, s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2160, 2151])).
% 1.74/1.98 tff(2162,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2163,plain,
% 1.74/1.98 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2164,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2163])).
% 1.74/1.98 tff(2165,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2164, 2162])).
% 1.74/1.98 tff(2166,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2167,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 1.74/1.98 tff(2168,plain,
% 1.74/1.98 (~b(z, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2167, 204, 2161, 1102, 404, 2141])).
% 1.74/1.98 tff(2169,plain,
% 1.74/1.98 (r(z, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[259, 2168])).
% 1.74/1.98 tff(2170,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(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, 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(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2171,plain,
% 1.74/1.98 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2172,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(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2171])).
% 1.74/1.98 tff(2173,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(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~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(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2172, 2170])).
% 1.74/1.99 tff(2174,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(z, s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2175,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 1.74/1.99 tff(2176,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2175, 67, 907, 286, 2169, 445])).
% 1.74/1.99 tff(2177,plain,((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2178,plain,
% 1.74/1.99 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2177, 2140, 286, 445, 2138, 907])).
% 1.74/1.99 tff(2179,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.74/1.99 tff(2180,plain,
% 1.74/1.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2181,plain,
% 1.74/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2182,plain,
% 1.74/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.74/1.99 tff(2183,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2182, 50, 2179, 2178, 2136])).
% 1.74/1.99 tff(2184,plain,((~r(s(z), s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2185,plain,
% 1.74/1.99 (~r(s(z), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2184, 2126, 389, 445, 286])).
% 1.74/1.99 tff(2186,plain,
% 1.74/1.99 (b(s(z), s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[936, 2185])).
% 1.74/1.99 tff(2187,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2092, 2090])).
% 1.74/1.99 tff(2188,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[378, 2187])).
% 1.74/1.99 tff(2189,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2083, 2092])).
% 1.74/1.99 tff(2190,plain,
% 1.74/1.99 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[1538, 2189])).
% 1.74/1.99 tff(2191,plain,
% 1.74/1.99 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2094])).
% 1.74/1.99 tff(2192,plain,
% 1.74/1.99 (s(z) = s(elem!1)),
% 1.74/1.99 inference(transitivity,[status(thm)],[126, 2191, 904])).
% 1.74/1.99 tff(2193,plain,
% 1.74/1.99 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2192])).
% 1.74/1.99 tff(2194,plain,
% 1.74/1.99 (z = inj_0(s(z))),
% 1.74/1.99 inference(symmetry,[status(thm)],[15])).
% 1.74/1.99 tff(2195,plain,
% 1.74/1.99 (z = elem!1),
% 1.74/1.99 inference(transitivity,[status(thm)],[2194, 2193, 902])).
% 1.74/1.99 tff(2196,plain,
% 1.74/1.99 (r(z, s(s(s(s(s(s(elem!1))))))) <=> r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2195])).
% 1.74/1.99 tff(2197,plain,
% 1.74/1.99 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2083])).
% 1.74/1.99 tff(2198,plain,
% 1.74/1.99 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2032, 2197])).
% 1.74/1.99 tff(2199,plain,
% 1.74/1.99 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2198, 2196])).
% 1.74/1.99 tff(2200,plain,
% 1.74/1.99 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.74/1.99 inference(commutativity,[status(thm)],[])).
% 1.74/1.99 tff(2201,plain,
% 1.74/1.99 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2195])).
% 1.74/1.99 tff(2202,plain,
% 1.74/1.99 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2201, 2200])).
% 1.74/1.99 tff(2203,plain,
% 1.74/1.99 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2202])).
% 1.74/1.99 tff(2204,plain,
% 1.74/1.99 (~(elem!1 = s(s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[757, 2203])).
% 1.74/1.99 tff(2205,plain,
% 1.74/1.99 ((elem!1 = z) <=> (z = elem!1)),
% 1.74/1.99 inference(commutativity,[status(thm)],[])).
% 1.74/1.99 tff(2206,plain,
% 1.74/1.99 ((z = elem!1) <=> (elem!1 = z)),
% 1.74/1.99 inference(symmetry,[status(thm)],[2205])).
% 1.74/1.99 tff(2207,assumption,(z = elem!1), introduced(assumption)).
% 1.74/1.99 tff(2208,plain,
% 1.74/1.99 (elem!1 = z),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.74/1.99 tff(2209,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.74/1.99 tff(2210,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2209, 2208])).
% 1.74/1.99 tff(2211,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2212,plain,
% 1.74/1.99 (elem!1 = z),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2211, 2195])).
% 1.74/1.99 tff(2213,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.99 tff(2214,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.99 inference(commutativity,[status(thm)],[])).
% 1.74/1.99 tff(2215,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2090])).
% 1.74/1.99 tff(2216,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2215, 2214])).
% 1.74/1.99 tff(2217,plain,
% 1.74/1.99 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2216])).
% 1.74/1.99 tff(2218,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2090, 2094])).
% 1.74/1.99 tff(2219,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2218, 2217])).
% 1.74/1.99 tff(2220,plain,
% 1.74/1.99 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2219])).
% 1.74/1.99 tff(2221,plain,
% 1.74/1.99 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2122, 2220])).
% 1.74/1.99 tff(2222,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.74/1.99 tff(2223,plain,
% 1.74/1.99 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.74/1.99 inference(commutativity,[status(thm)],[])).
% 1.74/1.99 tff(2224,plain,
% 1.74/1.99 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2223])).
% 1.74/1.99 tff(2225,plain,
% 1.74/1.99 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2110, 2107, 2224])).
% 1.74/1.99 tff(2226,plain,
% 1.74/1.99 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2225])).
% 1.74/1.99 tff(2227,plain,
% 1.74/1.99 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2125, 2226])).
% 1.74/1.99 tff(2228,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(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2229,plain,
% 1.74/1.99 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2230,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(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $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(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2229])).
% 1.74/1.99 tff(2231,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(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $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(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2230, 2228])).
% 1.74/1.99 tff(2232,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(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2233,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(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 1.74/1.99 tff(2234,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2233, 67, 938, 57])).
% 1.74/1.99 tff(2235,plain,
% 1.74/1.99 (~r(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2003, 57, 286])).
% 1.74/1.99 tff(2236,plain,
% 1.74/1.99 (b(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[402, 2235])).
% 1.74/1.99 tff(2237,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(z))) | (~r(z, 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(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2238,plain,
% 1.74/1.99 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2239,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(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2238])).
% 1.74/1.99 tff(2240,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(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.74/1.99 tff(2241,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(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2242,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.74/1.99 tff(2243,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2242, 67, 938, 2142, 286])).
% 1.74/1.99 tff(2244,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2245,plain,
% 1.74/1.99 (~r(z, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2244, 938, 286])).
% 1.74/1.99 tff(2246,plain,
% 1.74/1.99 (b(z, s(s(elem!1)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2160, 2245])).
% 1.74/1.99 tff(2247,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2248,plain,
% 1.74/1.99 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2249,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2248])).
% 1.74/1.99 tff(2250,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2249, 2247])).
% 1.74/1.99 tff(2251,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(elem!1)))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2252,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 1.74/1.99 tff(2253,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2252, 204, 2246, 1102, 405, 2236])).
% 1.74/1.99 tff(2254,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1167, 2253, 2234, 628])).
% 1.74/1.99 tff(2255,plain,((~r(s(s(s(z))), s(z))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2256,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2255, 1102, 57, 286, 405, 2227])).
% 1.74/1.99 tff(2257,plain,
% 1.74/1.99 (b(s(s(elem!1)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[952, 2256])).
% 1.74/1.99 tff(2258,assumption,(b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.99 tff(2259,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2260,plain,
% 1.74/1.99 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2261,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2260])).
% 1.74/1.99 tff(2262,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2261, 2259])).
% 1.74/1.99 tff(2263,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1)))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2264,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.74/1.99 tff(2265,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2264, 204, 990, 2222, 2258, 456, 360])).
% 1.74/1.99 tff(2266,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2267,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2266, 2257, 360, 2222, 456])).
% 1.74/1.99 tff(2268,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1139, 2267, 2221])).
% 1.74/1.99 tff(2269,plain,
% 1.74/1.99 (s(z) = s(elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2207])).
% 1.74/1.99 tff(2270,plain,
% 1.74/1.99 (s(s(z)) = s(s(elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2269])).
% 1.74/1.99 tff(2271,plain,
% 1.74/1.99 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2270])).
% 1.74/1.99 tff(2272,plain,
% 1.74/1.99 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2271])).
% 1.74/1.99 tff(2273,plain,
% 1.74/1.99 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2272])).
% 1.74/1.99 tff(2274,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2273])).
% 1.74/1.99 tff(2275,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2274])).
% 1.74/1.99 tff(2276,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[1113, 2275])).
% 1.74/1.99 tff(2277,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.99 tff(2278,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(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2279,plain,
% 1.74/1.99 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2280,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(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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2279])).
% 1.74/1.99 tff(2281,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(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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2280, 2278])).
% 1.74/1.99 tff(2282,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(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(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2283,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.74/1.99 tff(2284,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2283, 67, 2277, 2213])).
% 1.74/1.99 tff(2285,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2284, 2276])).
% 1.74/1.99 tff(2286,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2287,plain,
% 1.74/1.99 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2286, 2268, 2213, 2195])).
% 1.74/1.99 tff(2288,plain,
% 1.74/1.99 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2270])).
% 1.74/1.99 tff(2289,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2288])).
% 1.74/1.99 tff(2290,plain,
% 1.74/1.99 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2271])).
% 1.74/1.99 tff(2291,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2290])).
% 1.74/2.00 tff(2292,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2291, 2289])).
% 1.74/2.00 tff(2293,plain,
% 1.74/2.00 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2292])).
% 1.74/2.00 tff(2294,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/2.00 tff(2295,plain,
% 1.74/2.00 (~r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 1.74/2.00 tff(2296,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.74/2.00 tff(2297,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2296, 2295])).
% 1.74/2.00 tff(2298,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2299,plain,
% 1.74/2.00 (~r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2298, 2287, 2195])).
% 1.74/2.00 tff(2300,assumption,(elem!1 = z), introduced(assumption)).
% 1.74/2.00 tff(2301,plain,
% 1.74/2.00 (s(elem!1) = s(z)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2300])).
% 1.74/2.00 tff(2302,plain,
% 1.74/2.00 (s(s(elem!1)) = s(s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2301])).
% 1.74/2.00 tff(2303,plain,
% 1.74/2.00 (s(s(z)) = s(s(elem!1))),
% 1.74/2.00 inference(symmetry,[status(thm)],[2302])).
% 1.74/2.00 tff(2304,plain,
% 1.74/2.00 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2303])).
% 1.74/2.00 tff(2305,plain,
% 1.74/2.00 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2304, 2223])).
% 1.74/2.00 tff(2306,plain,
% 1.74/2.00 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[2305])).
% 1.74/2.00 tff(2307,plain,
% 1.74/2.00 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2306])).
% 1.74/2.00 tff(2308,plain,
% 1.74/2.00 (~(s(s(z)) = s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2179, 2307])).
% 1.74/2.00 tff(2309,plain,
% 1.74/2.00 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2303])).
% 1.74/2.00 tff(2310,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[2309])).
% 1.74/2.00 tff(2311,plain,
% 1.74/2.00 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2310])).
% 1.74/2.00 tff(2312,plain,
% 1.74/2.00 (~b(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[1162, 2311])).
% 1.74/2.00 tff(2313,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.74/2.00 tff(2314,plain,
% 1.74/2.00 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2315,plain,
% 1.74/2.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2316,plain,
% 1.74/2.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2315, 2314])).
% 1.74/2.00 tff(2317,plain,
% 1.74/2.00 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2316, 50, 2313])).
% 1.74/2.00 tff(2318,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2317, 2312, 2308])).
% 1.74/2.00 tff(2319,plain,(r(s(s(z)), s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | (~(elem!1 = z)) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2320,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2319, 2299, 2212, 2126])).
% 1.74/2.00 tff(2321,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2290])).
% 1.74/2.00 tff(2322,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[2321])).
% 1.74/2.00 tff(2323,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.74/2.00 tff(2324,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 1.74/2.00 tff(2325,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/2.00 tff(2326,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2325, 2324])).
% 1.74/2.00 tff(2327,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2328,plain,
% 1.74/2.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2327, 2320, 2195])).
% 1.74/2.00 tff(2329,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2195])).
% 1.74/2.00 tff(2330,plain,
% 1.74/2.00 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2092])).
% 1.74/2.00 tff(2331,plain,
% 1.74/2.00 (~r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2003, 286, 57])).
% 1.74/2.00 tff(2332,plain,
% 1.74/2.00 (b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[402, 2331])).
% 1.74/2.00 tff(2333,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), z)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2332, 2330])).
% 1.74/2.00 tff(2334,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2333, 2329])).
% 1.74/2.00 tff(2335,plain,
% 1.74/2.00 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2195])).
% 1.74/2.00 tff(2336,plain,
% 1.74/2.00 (b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[1102, 2335])).
% 1.74/2.00 tff(2337,plain,
% 1.74/2.00 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2195])).
% 1.74/2.00 tff(2338,plain,
% 1.74/2.00 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2092])).
% 1.74/2.00 tff(2339,plain,
% 1.74/2.00 (b(z, s(s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[405, 2338])).
% 1.74/2.00 tff(2340,plain,
% 1.74/2.00 (b(elem!1, s(s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2339, 2337])).
% 1.74/2.00 tff(2341,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2342,plain,
% 1.74/2.00 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2343,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2342])).
% 1.74/2.00 tff(2344,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2343, 2341])).
% 1.74/2.00 tff(2345,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2346,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 1.74/2.00 tff(2347,plain,
% 1.74/2.00 (~b(elem!1, s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2346, 204, 2340, 2336, 2334, 2328])).
% 1.74/2.00 tff(2348,plain,
% 1.74/2.00 (((~![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))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2349,plain,
% 1.74/2.00 ((~![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))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2350,plain,
% 1.74/2.00 ((~![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)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2349, 2348])).
% 1.74/2.00 tff(2351,plain,
% 1.74/2.00 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2350, 50])).
% 1.74/2.00 tff(2352,plain,
% 1.74/2.00 (r(elem!1, s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2351, 2347, 2204])).
% 1.74/2.00 tff(2353,plain,
% 1.74/2.00 ((~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2096])).
% 1.74/2.00 tff(2354,plain,
% 1.74/2.00 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2103, 2353])).
% 1.74/2.00 tff(2355,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/2.00 tff(2356,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2357,plain,
% 1.74/2.00 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2358,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2357])).
% 1.74/2.00 tff(2359,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2358, 2356])).
% 1.74/2.00 tff(2360,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2361,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 1.74/2.00 tff(2362,plain,
% 1.74/2.00 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2361, 204, 2336, 2334, 2328, 2355])).
% 1.74/2.00 tff(2363,plain,
% 1.74/2.00 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1062, 2362, 2354])).
% 1.74/2.00 tff(2364,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), introduced(assumption)).
% 1.74/2.00 tff(2365,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.74/2.00 tff(2366,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2367,plain,
% 1.74/2.00 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2368,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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2367])).
% 1.74/2.00 tff(2369,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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2368, 2366])).
% 1.74/2.00 tff(2370,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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2371,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 1.74/2.00 tff(2372,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2371, 67, 2365, 2364, 1355])).
% 1.74/2.00 tff(2373,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2374,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2373, 2363, 2352, 1355])).
% 1.74/2.00 tff(2375,plain,((~b(s(s(elem!1)), z)) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2376,plain,
% 1.74/2.00 (~b(s(s(elem!1)), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2375, 2199, 2190, 2083, 2188, 360, 2186, 456, 57, 286, 405])).
% 1.74/2.00 tff(2377,plain,
% 1.74/2.00 (r(s(s(elem!1)), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1099, 2376])).
% 1.74/2.00 tff(2378,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1003, 2377, 261, 389, 2104])).
% 1.74/2.00 tff(2379,plain,
% 1.74/2.00 (~r(s(s(elem!1)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[946, 2377, 389])).
% 1.74/2.00 tff(2380,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[952, 2379, 2378])).
% 1.74/2.00 tff(2381,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2382,plain,
% 1.74/2.00 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2381, 2070, 261, 360, 456, 57, 2064, 405, 445, 1538, 2068, 2080])).
% 1.74/2.00 tff(2383,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(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2384,plain,
% 1.74/2.00 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2385,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(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2384])).
% 1.74/2.00 tff(2386,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(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2385, 2383])).
% 1.74/2.00 tff(2387,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(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2388,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(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 1.74/2.00 tff(2389,plain,
% 1.74/2.00 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2388, 67, 2070, 1, 261])).
% 1.74/2.00 tff(2390,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[489, 50, 2389, 249])).
% 1.74/2.00 tff(2391,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(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), 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)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2392,plain,
% 1.74/2.00 (((~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2393,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(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2392])).
% 1.74/2.00 tff(2394,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(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2393, 2391])).
% 1.74/2.00 tff(2395,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(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2396,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(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 1.74/2.01 tff(2397,plain,
% 1.74/2.01 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2396, 67, 389, 824])).
% 1.74/2.01 tff(2398,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[675, 50, 2397, 671])).
% 1.74/2.01 tff(2399,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.74/2.01 tff(2400,plain,
% 1.74/2.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2401,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2402,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2401, 2400])).
% 1.74/2.01 tff(2403,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2402, 50, 2399, 890])).
% 1.74/2.01 tff(2404,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.74/2.01 tff(2405,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2406,plain,
% 1.74/2.01 (((~b(s(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(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2407,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2406])).
% 1.74/2.01 tff(2408,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2407, 2405])).
% 1.74/2.01 tff(2409,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2410,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 1.74/2.01 tff(2411,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2410, 204, 2404, 443, 832, 2403, 2398])).
% 1.74/2.01 tff(2412,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(2413,plain,
% 1.74/2.01 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2412, 2390, 443, 2382, 2070, 261])).
% 1.74/2.01 tff(2414,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[822, 2413])).
% 1.74/2.01 tff(2415,plain,
% 1.74/2.01 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[815, 2414, 2068, 361, 2062, 2066])).
% 1.74/2.01 tff(2416,plain,
% 1.74/2.01 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[766, 2415])).
% 1.74/2.01 tff(2417,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2418,plain,
% 1.74/2.01 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2419,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2418])).
% 1.74/2.01 tff(2420,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2419, 2417])).
% 1.74/2.01 tff(2421,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2422,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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2421, 2420])).
% 1.74/2.01 tff(2423,plain,
% 1.74/2.01 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2422, 67, 2416, 1])).
% 1.74/2.01 tff(2424,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2402, 50, 2382, 2423])).
% 1.74/2.01 tff(2425,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(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(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(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2426,plain,
% 1.74/2.01 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2427,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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2426])).
% 1.74/2.01 tff(2428,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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2427, 2425])).
% 1.74/2.01 tff(2429,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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(2430,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(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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2429, 2428])).
% 1.74/2.01 tff(2431,plain,
% 1.74/2.01 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2430, 67, 57, 2416, 2068])).
% 1.74/2.01 tff(2432,plain,
% 1.74/2.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2433,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2434,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.74/2.01 tff(2435,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2434, 50, 706, 2431])).
% 1.74/2.01 tff(2436,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2437,plain,
% 1.74/2.01 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2438,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2437])).
% 1.74/2.01 tff(2439,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2438, 2436])).
% 1.74/2.01 tff(2440,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2441,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 1.74/2.01 tff(2442,plain,
% 1.74/2.01 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2441, 204, 2066, 2414, 1538])).
% 1.74/2.01 tff(2443,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2442, 2435, 2424])).
% 1.74/2.01 tff(2444,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(2445,plain,
% 1.74/2.01 (~b(z, s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2444, 2060, 1965, 1, 443, 1977, 1967, 455, 1985, 445])).
% 1.74/2.01 tff(2446,plain,
% 1.74/2.01 (r(z, s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[357, 2445])).
% 1.74/2.01 tff(2447,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(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2448,plain,
% 1.74/2.01 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2449,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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2448])).
% 1.74/2.01 tff(2450,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(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2449, 2447])).
% 1.74/2.02 tff(2451,plain,
% 1.74/2.02 ((~![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(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(2452,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 1.74/2.02 tff(2453,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2452, 67, 2446, 1, 2060])).
% 1.74/2.02 tff(2454,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2455,plain,
% 1.74/2.02 (~r(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2454, 1975, 443, 137])).
% 1.74/2.02 tff(2456,plain,
% 1.74/2.02 (b(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[478, 2455])).
% 1.74/2.02 tff(2457,plain,
% 1.74/2.02 (~r(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[440, 1965, 137])).
% 1.74/2.02 tff(2458,plain,
% 1.74/2.02 (b(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[259, 2457])).
% 1.74/2.02 tff(2459,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1941, 204, 363, 2458, 2456, 1967, 359])).
% 1.74/2.02 tff(2460,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2461,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2460, 363, 443, 137])).
% 1.74/2.02 tff(2462,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[335, 2461])).
% 1.74/2.02 tff(2463,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1612, 67, 308, 538, 137])).
% 1.74/2.02 tff(2464,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2465,plain,
% 1.74/2.02 (~r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2464, 538, 137])).
% 1.74/2.02 tff(2466,plain,
% 1.74/2.02 (b(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[402, 2465])).
% 1.74/2.02 tff(2467,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1819, 538, 1967, 443, 456])).
% 1.74/2.02 tff(2468,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[641, 2467])).
% 1.74/2.02 tff(2469,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2015, 204, 363, 1967, 2468, 443])).
% 1.74/2.02 tff(2470,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[218, 2469])).
% 1.74/2.02 tff(2471,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[518, 2470, 137])).
% 1.74/2.02 tff(2472,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[134, 2471])).
% 1.74/2.02 tff(2473,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1550, 67, 137, 510, 264])).
% 1.74/2.02 tff(2474,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2475,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2474, 2470, 137])).
% 1.74/2.02 tff(2476,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[284, 2475])).
% 1.74/2.02 tff(2477,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1783, 2476, 2472, 2468, 2458, 2466])).
% 1.74/2.02 tff(2478,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2479,plain,
% 1.74/2.02 (~b(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2478, 2462, 363, 443, 137])).
% 1.74/2.02 tff(2480,plain,
% 1.74/2.02 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[431, 2479])).
% 1.74/2.02 tff(2481,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[386, 2480, 1965])).
% 1.74/2.02 tff(2482,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[108, 2481])).
% 1.74/2.02 tff(2483,plain,
% 1.74/2.02 (~r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2464, 2462, 137])).
% 1.74/2.02 tff(2484,plain,
% 1.74/2.02 (b(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[402, 2483])).
% 1.74/2.02 tff(2485,plain,
% 1.74/2.02 (~r(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[453, 2, 137])).
% 1.74/2.02 tff(2486,plain,
% 1.74/2.02 (b(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[478, 2485])).
% 1.74/2.02 tff(2487,plain,
% 1.74/2.02 (~r(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1887, 2, 339])).
% 1.74/2.02 tff(2488,plain,
% 1.74/2.02 (b(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[306, 2487])).
% 1.74/2.02 tff(2489,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2490,plain,
% 1.74/2.02 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2491,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2490])).
% 1.74/2.02 tff(2492,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2491, 2489])).
% 1.74/2.02 tff(2493,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(2494,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 1.74/2.02 tff(2495,plain,
% 1.74/2.02 ((~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2494, 204, 363, 405, 404])).
% 1.74/2.02 tff(2496,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2495, 2488, 2486])).
% 1.74/2.02 tff(2497,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2498,plain,
% 1.74/2.02 (~r(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2497, 2480, 2458, 363, 2484, 137])).
% 1.74/2.02 tff(2499,plain,
% 1.74/2.02 (b(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[357, 2498])).
% 1.74/2.02 tff(2500,plain,
% 1.74/2.02 (~r(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[453, 2480, 137])).
% 1.74/2.02 tff(2501,plain,
% 1.74/2.02 (b(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[478, 2500])).
% 1.74/2.02 tff(2502,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1624, 204, 363, 2484, 2501, 2499, 2482])).
% 1.74/2.02 tff(2503,plain,((~b(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2504,plain,
% 1.74/2.02 (~b(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2503, 443, 137])).
% 1.74/2.02 tff(2505,plain,
% 1.74/2.02 (r(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[376, 2504])).
% 1.74/2.02 tff(2506,plain,
% 1.74/2.02 (~r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1194, 538, 2505])).
% 1.74/2.02 tff(2507,plain,
% 1.74/2.02 (b(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[431, 2506])).
% 1.74/2.02 tff(2508,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1699, 264, 137])).
% 1.74/2.02 tff(2509,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[190, 2508])).
% 1.74/2.02 tff(2510,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2474, 264, 137])).
% 1.74/2.02 tff(2511,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[218, 2510])).
% 1.74/2.02 tff(2512,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1202, 204, 456, 360, 193, 4, 443])).
% 1.74/2.02 tff(2513,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2514,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2513, 2511, 2509, 1967, 456, 443])).
% 1.74/2.02 tff(2515,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2516,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2515, 2507, 443, 137])).
% 1.74/2.02 tff(2517,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[284, 2516])).
% 1.74/2.02 tff(2518,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1819, 2507, 1967, 443, 538])).
% 1.74/2.02 tff(2519,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[641, 2518])).
% 1.74/2.02 tff(2520,plain,
% 1.74/2.02 (~r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[397, 2505, 1965])).
% 1.74/2.02 tff(2521,plain,
% 1.74/2.02 (b(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[402, 2520])).
% 1.74/2.02 tff(2522,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1783, 2517, 2519, 2458, 2521])).
% 1.74/2.02 tff(2523,plain,
% 1.74/2.02 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[134, 2522])).
% 1.74/2.02 tff(2524,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[518, 2523, 137])).
% 1.74/2.02 tff(2525,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[218, 2524])).
% 1.74/2.02 tff(2526,plain,
% 1.74/2.02 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2513, 2525, 1967, 2507, 443])).
% 1.74/2.02 tff(2527,plain,
% 1.74/2.02 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[190, 2526])).
% 1.74/2.02 tff(2528,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[507, 2527, 2523])).
% 1.74/2.02 tff(2529,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[108, 2528])).
% 1.74/2.02 tff(2530,plain,
% 1.74/2.02 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2027, 204, 2458, 2521, 2519])).
% 1.74/2.02 tff(2531,plain,
% 1.74/2.02 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2530, 2517])).
% 1.74/2.02 tff(2532,plain,
% 1.74/2.02 (r(z, s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[604, 50, 601, 2531])).
% 1.74/2.02 tff(2533,plain,
% 1.74/2.02 (~r(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2034, 2532, 2527])).
% 1.74/2.02 tff(2534,plain,
% 1.74/2.02 (b(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[357, 2533])).
% 1.74/2.02 tff(2535,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2056, 204, 2521, 2534, 2529, 2519, 2517])).
% 1.74/2.02 tff(2536,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2537,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2536, 443, 137])).
% 1.74/2.02 tff(2538,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[335, 2537])).
% 1.74/2.02 tff(2539,plain,
% 1.74/2.02 (~r(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[536, 2, 389])).
% 1.74/2.02 tff(2540,plain,
% 1.74/2.02 (~b(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[425, 2, 57, 360, 389, 359])).
% 1.74/2.02 tff(2541,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[357, 2540, 2539])).
% 1.74/2.02 tff(2542,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2543,plain,
% 1.74/2.02 (~r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2542, 1965, 1967, 2505, 2538])).
% 1.74/2.02 tff(2544,plain,
% 1.74/2.02 (b(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[431, 2543])).
% 1.74/2.02 tff(2545,plain,
% 1.74/2.02 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2515, 2544, 443, 137])).
% 1.74/2.02 tff(2546,plain,
% 1.74/2.02 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[284, 2545])).
% 1.74/2.02 tff(2547,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2548,plain,
% 1.74/2.02 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2549,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2548])).
% 1.74/2.02 tff(2550,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.74/2.02 tff(2551,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(2552,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.74/2.02 tff(2553,plain,
% 1.74/2.02 ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2552, 204, 2544, 1967, 443])).
% 1.74/2.02 tff(2554,plain,
% 1.74/2.02 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2553, 4])).
% 1.74/2.02 tff(2555,plain,
% 1.74/2.02 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[489, 50, 2554, 249])).
% 1.74/2.02 tff(2556,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2513, 4, 1967, 2544, 443])).
% 1.74/2.02 tff(2557,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[218, 2556])).
% 1.74/2.02 tff(2558,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[518, 2557, 137])).
% 1.74/2.02 tff(2559,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[134, 2558])).
% 1.74/2.02 tff(2560,plain,
% 1.74/2.02 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1783, 2559, 2546, 2458, 2521])).
% 1.74/2.02 tff(2561,plain,
% 1.74/2.02 (r(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[641, 2560])).
% 1.74/2.02 tff(2562,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[485, 67, 2505, 2561, 2555])).
% 1.74/2.02 tff(2563,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2564,plain,
% 1.74/2.02 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2563, 443, 137])).
% 1.74/2.02 tff(2565,plain,
% 1.74/2.02 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[190, 2564])).
% 1.74/2.02 tff(2566,plain,
% 1.74/2.02 (~r(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2454, 2565, 443, 137])).
% 1.74/2.02 tff(2567,plain,
% 1.74/2.02 (b(s(z), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[478, 2566])).
% 1.74/2.02 tff(2568,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2569,plain,
% 1.74/2.02 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2570,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2569])).
% 1.74/2.02 tff(2571,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2570, 2568])).
% 1.74/2.02 tff(2572,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(2573,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 1.74/2.02 tff(2574,plain,
% 1.74/2.02 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2573, 204, 2521, 2544, 2538])).
% 1.74/2.02 tff(2575,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2574, 2567])).
% 1.74/2.02 tff(2576,plain,
% 1.74/2.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[108, 2575])).
% 1.74/2.02 tff(2577,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[507, 2576, 2565])).
% 1.74/2.02 tff(2578,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[134, 2577])).
% 1.74/2.02 tff(2579,plain,
% 1.74/2.02 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1783, 2578, 2546, 2458, 2521])).
% 1.74/2.02 tff(2580,plain,
% 1.74/2.02 (r(s(s(s(s(s(s(z)))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[641, 2579])).
% 1.74/2.02 tff(2581,plain,
% 1.74/2.02 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2388, 67, 2505, 2565, 2580])).
% 1.74/2.02 tff(2582,plain,
% 1.74/2.02 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[489, 50, 2581, 249])).
% 1.74/2.02 tff(2583,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/2.03 inference(rewrite,[status(thm)],[])).
% 1.74/2.03 tff(2584,plain,
% 1.74/2.03 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/2.03 inference(rewrite,[status(thm)],[])).
% 1.74/2.03 tff(2585,plain,
% 1.74/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(X1, 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(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/2.03 inference(monotonicity,[status(thm)],[2584])).
% 1.74/2.03 tff(2586,plain,
% 1.74/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(X1, 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(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/2.03 inference(transitivity,[status(thm)],[2585, 2583])).
% 1.74/2.03 tff(2587,plain,
% 1.74/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/2.03 inference(quant_inst,[status(thm)],[])).
% 1.74/2.03 tff(2588,plain,
% 1.74/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/2.03 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 1.74/2.03 tff(2589,plain,
% 1.74/2.03 ($false),
% 1.74/2.03 inference(unit_resolution,[status(thm)],[2588, 204, 2567, 2578, 2582, 443, 2546])).
% 1.74/2.03 tff(2590,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.03 tff(2591,plain,
% 1.74/2.03 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/2.03 inference(unit_resolution,[status(thm)],[2590, 137])).
% 1.74/2.03 tff(2592,plain,
% 1.74/2.03 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/2.03 inference(unit_resolution,[status(thm)],[244, 2591])).
% 1.74/2.03 tff(2593,plain,
% 1.74/2.03 ($false),
% 1.74/2.03 inference(unit_resolution,[status(thm)],[330, 67, 3, 538, 137])).
% 1.74/2.03 tff(2594,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2595,plain,
% 1.86/2.03 (~r(z, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2594, 538, 137])).
% 1.86/2.03 tff(2596,plain,
% 1.86/2.03 (b(z, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[259, 2595])).
% 1.86/2.03 tff(2597,plain,
% 1.86/2.03 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1783, 1977, 1469, 405, 404])).
% 1.86/2.03 tff(2598,plain,
% 1.86/2.03 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[134, 2597])).
% 1.86/2.03 tff(2599,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2600,plain,
% 1.86/2.03 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2601,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2600])).
% 1.86/2.03 tff(2602,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2601, 2599])).
% 1.86/2.03 tff(2603,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2604,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 1.86/2.03 tff(2605,plain,
% 1.86/2.03 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2604, 67, 57, 110])).
% 1.86/2.03 tff(2606,plain,
% 1.86/2.03 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[282, 50, 2605])).
% 1.86/2.03 tff(2607,plain,
% 1.86/2.03 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2606, 552])).
% 1.86/2.03 tff(2608,plain,
% 1.86/2.03 (~b(z, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1783, 404, 1469, 135, 2607])).
% 1.86/2.03 tff(2609,plain,
% 1.86/2.03 (r(z, s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[259, 2608])).
% 1.86/2.03 tff(2610,plain,
% 1.86/2.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1922, 2609, 339])).
% 1.86/2.03 tff(2611,plain,
% 1.86/2.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[108, 2610])).
% 1.86/2.03 tff(2612,plain,
% 1.86/2.03 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[347, 2609, 339])).
% 1.86/2.03 tff(2613,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[151, 2612])).
% 1.86/2.03 tff(2614,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2615,plain,
% 1.86/2.03 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2616,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2615])).
% 1.86/2.03 tff(2617,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2616, 2614])).
% 1.86/2.03 tff(2618,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2619,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 1.86/2.03 tff(2620,plain,
% 1.86/2.03 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2619, 204, 2613, 2611, 135, 2607])).
% 1.86/2.03 tff(2621,plain,
% 1.86/2.03 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[190, 2620])).
% 1.86/2.03 tff(2622,plain,
% 1.86/2.03 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1723, 67, 339, 2621])).
% 1.86/2.03 tff(2623,plain,
% 1.86/2.03 (b(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[604, 50, 601, 2622])).
% 1.86/2.03 tff(2624,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2625,plain,
% 1.86/2.03 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2626,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2625])).
% 1.86/2.03 tff(2627,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2626, 2624])).
% 1.86/2.03 tff(2628,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2629,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 1.86/2.03 tff(2630,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2629, 204, 404, 1469, 135, 2607, 2623])).
% 1.86/2.03 tff(2631,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2632,plain,
% 1.86/2.03 (~r(s(s(s(z))), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2631, 339, 2592, 404, 1469])).
% 1.86/2.03 tff(2633,plain,
% 1.86/2.03 (b(s(s(s(z))), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[558, 2632])).
% 1.86/2.03 tff(2634,plain,
% 1.86/2.03 (~b(s(z), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1398, 2633, 363, 404, 405])).
% 1.86/2.03 tff(2635,plain,
% 1.86/2.03 (r(s(z), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[478, 2634])).
% 1.86/2.03 tff(2636,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2637,plain,
% 1.86/2.03 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2638,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2637])).
% 1.86/2.03 tff(2639,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2638, 2636])).
% 1.86/2.03 tff(2640,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2641,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.86/2.03 tff(2642,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2641, 67, 445, 110, 264])).
% 1.86/2.03 tff(2643,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2644,plain,
% 1.86/2.03 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2643, 2635, 2592])).
% 1.86/2.03 tff(2645,plain,
% 1.86/2.03 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[284, 2644])).
% 1.86/2.03 tff(2646,plain,
% 1.86/2.03 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1783, 2645, 1469, 405, 404])).
% 1.86/2.03 tff(2647,plain,
% 1.86/2.03 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[134, 2646])).
% 1.86/2.03 tff(2648,plain,
% 1.86/2.03 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[518, 2647, 137])).
% 1.86/2.03 tff(2649,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[218, 2648])).
% 1.86/2.03 tff(2650,plain,
% 1.86/2.03 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[225, 67, 136, 2592])).
% 1.86/2.03 tff(2651,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[218, 2650])).
% 1.86/2.03 tff(2652,plain,
% 1.86/2.03 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[161, 136, 2592])).
% 1.86/2.03 tff(2653,plain,
% 1.86/2.03 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[190, 2652])).
% 1.86/2.04 tff(2654,plain,
% 1.86/2.04 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1901, 3, 2653, 2651, 137])).
% 1.86/2.04 tff(2655,plain,
% 1.86/2.04 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[284, 2654])).
% 1.86/2.04 tff(2656,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1519, 336, 2651, 358, 2653])).
% 1.86/2.04 tff(2657,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[641, 2656])).
% 1.86/2.04 tff(2658,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[648, 67, 389, 110, 261])).
% 1.86/2.04 tff(2659,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2660,plain,
% 1.86/2.04 (~r(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2659, 2657, 2592])).
% 1.86/2.04 tff(2661,plain,
% 1.86/2.04 (b(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[376, 2660])).
% 1.86/2.04 tff(2662,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1253, 67, 286, 110, 261])).
% 1.86/2.04 tff(2663,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2664,plain,
% 1.86/2.04 (~r(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2663, 2657, 2592])).
% 1.86/2.04 tff(2665,plain,
% 1.86/2.04 (b(z, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[306, 2664])).
% 1.86/2.04 tff(2666,plain,
% 1.86/2.04 (~b(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1408, 2665, 559, 2661, 479])).
% 1.86/2.04 tff(2667,plain,
% 1.86/2.04 (r(s(s(s(z))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[402, 2666])).
% 1.86/2.04 tff(2668,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2669,plain,
% 1.86/2.04 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2670,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2669])).
% 1.86/2.04 tff(2671,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2670, 2668])).
% 1.86/2.04 tff(2672,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2673,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 1.86/2.04 tff(2674,plain,
% 1.86/2.04 ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2673, 204, 2661, 358, 336])).
% 1.86/2.04 tff(2675,plain,
% 1.86/2.04 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2674, 2665])).
% 1.86/2.04 tff(2676,plain,
% 1.86/2.04 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[431, 2675])).
% 1.86/2.04 tff(2677,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[225, 67, 136, 110])).
% 1.86/2.04 tff(2678,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[218, 2677])).
% 1.86/2.04 tff(2679,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1519, 359, 2678, 361, 191])).
% 1.86/2.04 tff(2680,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[641, 2679])).
% 1.86/2.04 tff(2681,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2682,plain,
% 1.86/2.04 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2683,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2682])).
% 1.86/2.04 tff(2684,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2683, 2681])).
% 1.86/2.04 tff(2685,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2686,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 1.86/2.04 tff(2687,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2686, 67, 308, 110, 2680])).
% 1.86/2.04 tff(2688,plain,
% 1.86/2.04 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[134, 2687])).
% 1.86/2.04 tff(2689,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(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(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2690,plain,
% 1.86/2.04 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2691,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2690])).
% 1.86/2.04 tff(2692,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2691, 2689])).
% 1.86/2.04 tff(2693,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2694,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 1.86/2.04 tff(2695,plain,
% 1.86/2.04 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2694, 204, 444, 566, 2688, 1538])).
% 1.86/2.04 tff(2696,plain,
% 1.86/2.04 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[489, 50, 2695, 249])).
% 1.86/2.04 tff(2697,plain,
% 1.86/2.04 ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[594, 204, 361, 2678, 191])).
% 1.86/2.04 tff(2698,plain,
% 1.86/2.04 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2697, 359])).
% 1.86/2.04 tff(2699,plain,
% 1.86/2.04 (r(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[604, 50, 601, 2698])).
% 1.86/2.04 tff(2700,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2701,plain,
% 1.86/2.04 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2702,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2701])).
% 1.86/2.04 tff(2703,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2702, 2700])).
% 1.86/2.04 tff(2704,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2705,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2704, 2703])).
% 1.86/2.04 tff(2706,plain,
% 1.86/2.04 (~r(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2705, 67, 3, 2699, 2696])).
% 1.86/2.04 tff(2707,plain,
% 1.86/2.04 (b(s(z), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[376, 2706])).
% 1.86/2.04 tff(2708,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2709,plain,
% 1.86/2.04 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2710,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2709])).
% 1.86/2.04 tff(2711,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2710, 2708])).
% 1.86/2.04 tff(2712,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2713,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2712, 2711])).
% 1.86/2.04 tff(2714,plain,
% 1.86/2.04 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2713, 204, 2678, 191, 2688, 1538])).
% 1.86/2.04 tff(2715,plain,
% 1.86/2.04 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[108, 2714])).
% 1.86/2.04 tff(2716,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[730, 656, 2, 444, 566, 378])).
% 1.86/2.04 tff(2717,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2718,plain,
% 1.86/2.04 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2719,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2718])).
% 1.86/2.04 tff(2720,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2719, 2717])).
% 1.86/2.04 tff(2721,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2722,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2721, 2720])).
% 1.86/2.04 tff(2723,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2722, 67, 2, 656, 2716])).
% 1.86/2.04 tff(2724,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2725,plain,
% 1.86/2.04 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2724, 2715, 444, 566, 2])).
% 1.86/2.04 tff(2726,plain,
% 1.86/2.04 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[766, 2725])).
% 1.86/2.04 tff(2727,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2728,plain,
% 1.86/2.05 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2729,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2728])).
% 1.86/2.05 tff(2730,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2729, 2727])).
% 1.86/2.05 tff(2731,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2732,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.86/2.05 tff(2733,plain,
% 1.86/2.05 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2732, 204, 363, 361, 785])).
% 1.86/2.05 tff(2734,plain,
% 1.86/2.05 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2733, 784])).
% 1.86/2.05 tff(2735,plain,
% 1.86/2.05 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[721, 50, 669, 2734])).
% 1.86/2.05 tff(2736,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.86/2.05 tff(2737,plain,
% 1.86/2.05 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[2736])).
% 1.86/2.05 tff(2738,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[761, 2737])).
% 1.86/2.05 tff(2739,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2740,plain,
% 1.86/2.05 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[796, 50, 793, 2739])).
% 1.86/2.05 tff(2741,plain,
% 1.86/2.05 (((~![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(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2742,plain,
% 1.86/2.05 (((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(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(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2743,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))))) | (~r(s(s(s(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(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(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2742])).
% 1.86/2.05 tff(2744,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))))) | (~r(s(s(s(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(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(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2743, 2741])).
% 1.86/2.05 tff(2745,plain,
% 1.86/2.05 ((~![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(s(s(elem!1)))))))) | (~r(s(s(s(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(z)))), s(z))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2746,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 1.86/2.05 tff(2747,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2746, 67, 136, 2740, 2735])).
% 1.86/2.05 tff(2748,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2749,plain,
% 1.86/2.05 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2748, 2726, 361, 136, 359, 2707])).
% 1.86/2.05 tff(2750,plain,
% 1.86/2.05 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[822, 2749])).
% 1.86/2.05 tff(2751,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2752,plain,
% 1.86/2.05 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2753,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2752])).
% 1.86/2.05 tff(2754,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2753, 2751])).
% 1.86/2.05 tff(2755,plain,
% 1.86/2.05 ((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2756,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 1.86/2.05 tff(2757,plain,
% 1.86/2.05 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2756, 67, 308, 2750])).
% 1.86/2.05 tff(2758,plain,
% 1.86/2.05 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[710, 50, 707, 2757])).
% 1.86/2.05 tff(2759,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2760,plain,
% 1.86/2.05 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2761,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2760])).
% 1.86/2.05 tff(2762,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2761, 2759])).
% 1.86/2.05 tff(2763,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2764,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2763, 2762])).
% 1.86/2.05 tff(2765,plain,
% 1.86/2.05 ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2764, 204, 2726, 191, 2688])).
% 1.86/2.05 tff(2766,plain,
% 1.86/2.05 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2765, 2758])).
% 1.86/2.05 tff(2767,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2768,plain,
% 1.86/2.05 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2769,plain,
% 1.86/2.05 (((~![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(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2768])).
% 1.86/2.05 tff(2770,plain,
% 1.86/2.05 (((~![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(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2769, 2767])).
% 1.86/2.05 tff(2771,plain,
% 1.86/2.05 ((~![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(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2772,plain,
% 1.86/2.05 ((~![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(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2771, 2770])).
% 1.86/2.05 tff(2773,plain,
% 1.86/2.05 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2772, 67, 2750, 110, 2680])).
% 1.86/2.05 tff(2774,plain,
% 1.86/2.05 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[850, 50, 2773])).
% 1.86/2.05 tff(2775,plain,
% 1.86/2.05 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2774, 2766])).
% 1.86/2.05 tff(2776,plain,
% 1.86/2.05 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2775])).
% 1.86/2.05 tff(2777,plain,
% 1.86/2.05 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[664, 2776, 121])).
% 1.86/2.05 tff(2778,plain,
% 1.86/2.05 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2777])).
% 1.86/2.05 tff(2779,plain,
% 1.86/2.05 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[875, 2778, 119])).
% 1.86/2.05 tff(2780,plain,
% 1.86/2.05 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2779])).
% 1.86/2.05 tff(2781,plain,
% 1.86/2.05 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[699, 2780, 20])).
% 1.86/2.05 tff(2782,plain,
% 1.86/2.05 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2781])).
% 1.86/2.05 tff(2783,plain,
% 1.86/2.05 (s(s(elem!1)) = s(s(z))),
% 1.86/2.05 inference(transitivity,[status(thm)],[754, 2782, 83])).
% 1.86/2.05 tff(2784,plain,
% 1.86/2.05 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2783])).
% 1.86/2.05 tff(2785,plain,
% 1.86/2.05 (s(elem!1) = s(z)),
% 1.86/2.05 inference(transitivity,[status(thm)],[919, 2784, 78])).
% 1.86/2.05 tff(2786,plain,
% 1.86/2.05 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2785])).
% 1.86/2.05 tff(2787,plain,
% 1.86/2.05 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.86/2.05 inference(symmetry,[status(thm)],[2786])).
% 1.86/2.05 tff(2788,plain,
% 1.86/2.05 (z = elem!1),
% 1.86/2.05 inference(transitivity,[status(thm)],[2194, 2787, 902])).
% 1.86/2.05 tff(2789,plain,
% 1.86/2.05 (elem!1 = z),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2211, 2788])).
% 1.86/2.05 tff(2790,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(z))))), introduced(assumption)).
% 1.86/2.05 tff(2791,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.86/2.05 tff(2792,plain,
% 1.86/2.05 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[684])).
% 1.86/2.05 tff(2793,plain,
% 1.86/2.05 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2792])).
% 1.86/2.05 tff(2794,plain,
% 1.86/2.05 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(commutativity,[status(thm)],[])).
% 1.86/2.05 tff(2795,plain,
% 1.86/2.05 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[2794])).
% 1.86/2.05 tff(2796,plain,
% 1.86/2.05 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2790])).
% 1.86/2.05 tff(2797,plain,
% 1.86/2.05 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[2796])).
% 1.86/2.05 tff(2798,plain,
% 1.86/2.05 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[21, 2797, 698])).
% 1.86/2.05 tff(2799,plain,
% 1.86/2.05 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2798])).
% 1.86/2.05 tff(2800,plain,
% 1.86/2.05 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2799, 2795])).
% 1.86/2.05 tff(2801,assumption,(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.86/2.05 tff(2802,plain,
% 1.86/2.05 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.86/2.05 tff(2803,plain,
% 1.86/2.05 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[699, 2796, 20])).
% 1.86/2.05 tff(2804,plain,
% 1.86/2.05 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2803])).
% 1.86/2.05 tff(2805,plain,
% 1.86/2.05 (s(s(elem!1)) = s(s(z))),
% 1.86/2.05 inference(transitivity,[status(thm)],[754, 2804, 83])).
% 1.86/2.05 tff(2806,plain,
% 1.86/2.05 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2805])).
% 1.86/2.05 tff(2807,plain,
% 1.86/2.05 (s(elem!1) = s(z)),
% 1.86/2.05 inference(transitivity,[status(thm)],[919, 2806, 78])).
% 1.86/2.05 tff(2808,plain,
% 1.86/2.05 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2807])).
% 1.86/2.05 tff(2809,plain,
% 1.86/2.05 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.86/2.05 inference(symmetry,[status(thm)],[2808])).
% 1.86/2.05 tff(2810,plain,
% 1.86/2.05 (z = elem!1),
% 1.86/2.05 inference(transitivity,[status(thm)],[2194, 2809, 902])).
% 1.86/2.05 tff(2811,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.86/2.05 tff(2812,plain,
% 1.86/2.05 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2811])).
% 1.86/2.05 tff(2813,plain,
% 1.86/2.05 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[2812])).
% 1.86/2.05 tff(2814,plain,
% 1.86/2.05 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[754, 2813, 663])).
% 1.86/2.05 tff(2815,plain,
% 1.86/2.05 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2814])).
% 1.86/2.05 tff(2816,plain,
% 1.86/2.05 (s(z) = s(s(s(s(elem!1))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2269, 919, 2815, 687])).
% 1.86/2.05 tff(2817,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[704, 2816])).
% 1.86/2.05 tff(2818,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2819,plain,
% 1.86/2.05 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2818, 2810])).
% 1.86/2.05 tff(2820,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2819, 2802])).
% 1.86/2.05 tff(2821,plain,((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(2822,plain,
% 1.86/2.05 (~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2821, 2790])).
% 1.86/2.05 tff(2823,plain,
% 1.86/2.05 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2822, 2793])).
% 1.86/2.05 tff(2824,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2825,plain,
% 1.86/2.05 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(2826,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2825])).
% 1.86/2.05 tff(2827,plain,
% 1.86/2.05 (((~![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(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[2826, 2824])).
% 1.86/2.05 tff(2828,plain,
% 1.86/2.05 ((~![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(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(2829,plain,
% 1.86/2.05 ((~![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(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 1.86/2.05 tff(2830,plain,
% 1.86/2.05 (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[2829, 67, 824, 2791])).
% 1.86/2.05 tff(2831,plain,
% 1.86/2.05 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[2790])).
% 1.86/2.05 tff(2832,plain,
% 1.86/2.05 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.05 inference(symmetry,[status(thm)],[2831])).
% 1.86/2.06 tff(2833,plain,
% 1.86/2.06 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2810])).
% 1.86/2.06 tff(2834,plain,
% 1.86/2.06 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.06 inference(transitivity,[status(thm)],[2833, 2832])).
% 1.86/2.06 tff(2835,plain,
% 1.86/2.06 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2834])).
% 1.86/2.06 tff(2836,plain,
% 1.86/2.06 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[180, 2835])).
% 1.86/2.06 tff(2837,plain,
% 1.86/2.06 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1084, 2836])).
% 1.86/2.06 tff(2838,plain,
% 1.86/2.06 (elem!1 = z),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2211, 2810])).
% 1.86/2.06 tff(2839,plain,
% 1.86/2.06 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2303])).
% 1.86/2.06 tff(2840,plain,
% 1.86/2.06 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2839, 2086])).
% 1.86/2.06 tff(2841,assumption,(s(s(z)) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.86/2.06 tff(2842,plain,
% 1.86/2.06 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2841, 2840])).
% 1.86/2.06 tff(2843,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1051, 2842])).
% 1.86/2.06 tff(2844,plain,((~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2845,plain,
% 1.86/2.06 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2844, 2838, 2837])).
% 1.86/2.06 tff(2846,plain,
% 1.86/2.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2847,plain,
% 1.86/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2848,plain,
% 1.86/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 1.86/2.06 tff(2849,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2848, 50, 2845, 2830])).
% 1.86/2.06 tff(2850,plain,
% 1.86/2.06 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2756, 67, 308, 824])).
% 1.86/2.06 tff(2851,plain,
% 1.86/2.06 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[710, 50, 2822, 2850])).
% 1.86/2.06 tff(2852,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.86/2.06 tff(2853,plain,
% 1.86/2.06 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2805])).
% 1.86/2.06 tff(2854,plain,
% 1.86/2.06 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[2804])).
% 1.86/2.06 tff(2855,plain,
% 1.86/2.06 (s(s(z)) = s(s(elem!1))),
% 1.86/2.06 inference(transitivity,[status(thm)],[84, 2854, 753])).
% 1.86/2.06 tff(2856,plain,
% 1.86/2.06 (r(s(s(s(s(s(s(elem!1)))))), s(s(z))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2855])).
% 1.86/2.06 tff(2857,plain,
% 1.86/2.06 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2856])).
% 1.86/2.06 tff(2858,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2859,plain,
% 1.86/2.06 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2860,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2859])).
% 1.86/2.06 tff(2861,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2860, 2858])).
% 1.86/2.06 tff(2862,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2863,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 1.86/2.06 tff(2864,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2863, 67, 824, 2791])).
% 1.86/2.06 tff(2865,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2864, 2857])).
% 1.86/2.06 tff(2866,plain,
% 1.86/2.06 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1062, 2865, 2837])).
% 1.86/2.06 tff(2867,plain,
% 1.86/2.06 (b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2866, 2853])).
% 1.86/2.06 tff(2868,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2869,plain,
% 1.86/2.06 (((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), 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(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2870,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2869])).
% 1.86/2.06 tff(2871,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2870, 2868])).
% 1.86/2.06 tff(2872,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2873,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 1.86/2.06 tff(2874,plain,
% 1.86/2.06 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2873, 204, 2867, 2852, 2851, 2849])).
% 1.86/2.06 tff(2875,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), 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))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2876,plain,
% 1.86/2.06 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2877,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2876])).
% 1.86/2.06 tff(2878,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2877, 2875])).
% 1.86/2.06 tff(2879,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2880,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 1.86/2.06 tff(2881,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2880, 67, 308, 824])).
% 1.86/2.06 tff(2882,plain,
% 1.86/2.06 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2434, 50, 2881])).
% 1.86/2.06 tff(2883,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2882, 2874, 2823])).
% 1.86/2.06 tff(2884,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2885,plain,
% 1.86/2.06 (~b(s(s(s(z))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2884, 2791, 308, 824, 2790])).
% 1.86/2.06 tff(2886,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.86/2.06 tff(2887,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2888,plain,
% 1.86/2.06 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2889,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2888])).
% 1.86/2.06 tff(2890,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.86/2.06 tff(2891,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2892,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.86/2.06 tff(2893,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2892, 67, 308, 2791, 2886])).
% 1.86/2.06 tff(2894,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2895,plain,
% 1.86/2.06 (~r(s(s(s(z))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2894, 2791, 308])).
% 1.86/2.06 tff(2896,plain,
% 1.86/2.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2897,plain,
% 1.86/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2898,plain,
% 1.86/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 1.86/2.06 tff(2899,plain,
% 1.86/2.06 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2898, 50])).
% 1.86/2.06 tff(2900,plain,
% 1.86/2.06 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2899, 2124])).
% 1.86/2.06 tff(2901,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2900, 2895, 2885])).
% 1.86/2.06 tff(2902,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2903,plain,
% 1.86/2.06 (~r(s(s(z)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2902, 308, 2750, 2779])).
% 1.86/2.06 tff(2904,plain,
% 1.86/2.06 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2303])).
% 1.86/2.06 tff(2905,plain,
% 1.86/2.06 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 1.86/2.06 inference(symmetry,[status(thm)],[2904])).
% 1.86/2.06 tff(2906,plain,
% 1.86/2.06 (r(s(s(z)), z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[900, 2905])).
% 1.86/2.06 tff(2907,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.86/2.06 tff(2908,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2907, 2906])).
% 1.86/2.06 tff(2909,plain,(r(s(s(z)), z) | (~r(s(s(elem!1)), z)) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(2910,plain,
% 1.86/2.06 (~r(s(s(elem!1)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2909, 2903, 2789])).
% 1.86/2.06 tff(2911,plain,
% 1.86/2.06 (b(s(s(elem!1)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1099, 2910])).
% 1.86/2.06 tff(2912,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2913,plain,
% 1.86/2.06 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(2914,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[2913])).
% 1.86/2.06 tff(2915,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[2914, 2912])).
% 1.86/2.06 tff(2916,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(2917,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2916, 2915])).
% 1.86/2.07 tff(2918,plain,
% 1.86/2.07 (~r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2917, 67, 2699, 2696])).
% 1.86/2.07 tff(2919,plain,
% 1.86/2.07 (b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[306, 2918])).
% 1.86/2.07 tff(2920,plain,
% 1.86/2.07 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[2782])).
% 1.86/2.07 tff(2921,plain,
% 1.86/2.07 (s(s(z)) = s(s(elem!1))),
% 1.86/2.07 inference(transitivity,[status(thm)],[84, 2920, 753])).
% 1.86/2.07 tff(2922,plain,
% 1.86/2.07 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2921])).
% 1.86/2.07 tff(2923,plain,
% 1.86/2.07 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2922, 1123])).
% 1.86/2.07 tff(2924,plain,
% 1.86/2.07 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2923])).
% 1.86/2.07 tff(2925,plain,
% 1.86/2.07 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2122, 2924])).
% 1.86/2.07 tff(2926,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2927,plain,
% 1.86/2.07 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~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(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2928,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2927])).
% 1.86/2.07 tff(2929,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2928, 2926])).
% 1.86/2.07 tff(2930,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2931,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 1.86/2.07 tff(2932,plain,
% 1.86/2.07 ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2931, 204, 363, 1140, 361])).
% 1.86/2.07 tff(2933,plain,
% 1.86/2.07 (~b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2932, 1102])).
% 1.86/2.07 tff(2934,plain,
% 1.86/2.07 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1148, 1102, 361, 359, 1135, 1101])).
% 1.86/2.07 tff(2935,plain,
% 1.86/2.07 (~r(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1111, 2934, 2])).
% 1.86/2.07 tff(2936,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[936, 2935, 2933])).
% 1.86/2.07 tff(2937,plain,((~b(s(s(elem!1)), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(elem!1)), s(s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2938,plain,
% 1.86/2.07 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2937, 2911, 2707, 361, 359, 2925, 2])).
% 1.86/2.07 tff(2939,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2940,plain,
% 1.86/2.07 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2941,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2940])).
% 1.86/2.07 tff(2942,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2941, 2939])).
% 1.86/2.07 tff(2943,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2944,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 1.86/2.07 tff(2945,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2944, 204, 990, 2222, 363, 1102, 362])).
% 1.86/2.07 tff(2946,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2947,plain,
% 1.86/2.07 (~b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2946, 1102, 362, 363, 990])).
% 1.86/2.07 tff(2948,plain,
% 1.86/2.07 (r(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[936, 2947])).
% 1.86/2.07 tff(2949,plain,
% 1.86/2.07 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1121, 2948, 1113])).
% 1.86/2.07 tff(2950,plain,
% 1.86/2.07 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[431, 2949])).
% 1.86/2.07 tff(2951,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2952,plain,
% 1.86/2.07 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2953,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X1, 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(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2952])).
% 1.86/2.07 tff(2954,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), 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(X1, 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(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2953, 2951])).
% 1.86/2.07 tff(2955,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2956,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2955, 2954])).
% 1.86/2.07 tff(2957,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2956, 204, 990, 363, 1102, 2950, 361])).
% 1.86/2.07 tff(2958,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2959,plain,
% 1.86/2.07 (~b(s(s(elem!1)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2958, 2938, 2707, 361, 2919, 2911])).
% 1.86/2.07 tff(2960,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(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(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2961,plain,
% 1.86/2.07 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(2962,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $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(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[2961])).
% 1.86/2.07 tff(2963,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $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(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[2962, 2960])).
% 1.86/2.07 tff(2964,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(2965,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2964, 2963])).
% 1.86/2.07 tff(2966,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2965, 67, 938, 1113, 136])).
% 1.86/2.07 tff(2967,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2968,plain,
% 1.86/2.07 (~r(s(s(elem!1)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2967, 2938, 136])).
% 1.86/2.07 tff(2969,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[952, 2968, 2959])).
% 1.86/2.07 tff(2970,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2971,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2970, 2676, 2667, 358, 336, 136, 2592, 559, 479, 3, 2655])).
% 1.86/2.07 tff(2972,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2973,plain,
% 1.86/2.07 (~r(z, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2972, 136, 137])).
% 1.86/2.07 tff(2974,plain,
% 1.86/2.07 (b(z, s(s(s(z))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[259, 2973])).
% 1.86/2.07 tff(2975,plain,
% 1.86/2.07 (~r(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2464, 308, 137])).
% 1.86/2.07 tff(2976,plain,
% 1.86/2.07 (b(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[335, 2975])).
% 1.86/2.07 tff(2977,plain,
% 1.86/2.07 (~b(z, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1519, 2976, 2651, 1469, 2653])).
% 1.86/2.07 tff(2978,plain,
% 1.86/2.07 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1483, 308, 1469, 2651, 2653])).
% 1.86/2.07 tff(2979,plain,
% 1.86/2.07 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[108, 2978])).
% 1.86/2.07 tff(2980,plain,
% 1.86/2.07 (~r(z, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1594, 2979, 136, 559, 137])).
% 1.86/2.07 tff(2981,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[357, 2980, 2977])).
% 1.86/2.07 tff(2982,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2983,plain,
% 1.86/2.07 (~r(s(s(s(z))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2982, 1469, 137, 136])).
% 1.86/2.07 tff(2984,plain,
% 1.86/2.07 (b(s(s(s(z))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[402, 2983])).
% 1.86/2.07 tff(2985,plain,
% 1.86/2.07 (~b(s(z), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1398, 2984, 559, 479, 2974])).
% 1.86/2.07 tff(2986,plain,
% 1.86/2.07 (r(s(z), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[376, 2985])).
% 1.86/2.07 tff(2987,plain,
% 1.86/2.07 (~r(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[546, 2986, 136])).
% 1.86/2.07 tff(2988,plain,
% 1.86/2.07 (b(s(s(s(s(z)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[335, 2987])).
% 1.86/2.07 tff(2989,plain,
% 1.86/2.07 (~b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1533, 2984, 559, 2974, 479])).
% 1.86/2.07 tff(2990,plain,
% 1.86/2.07 (r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[306, 2989])).
% 1.86/2.07 tff(2991,plain,
% 1.86/2.07 (~r(z, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1503, 2990, 136])).
% 1.86/2.07 tff(2992,plain,
% 1.86/2.07 (b(z, s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[357, 2991])).
% 1.86/2.07 tff(2993,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1519, 2992, 2988, 2651, 1469, 2653])).
% 1.86/2.07 tff(2994,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(2995,plain,
% 1.86/2.07 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2994, 136, 137])).
% 1.86/2.07 tff(2996,plain,
% 1.86/2.07 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[641, 2995])).
% 1.86/2.07 tff(2997,plain,
% 1.86/2.07 (~r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2663, 2996, 2592])).
% 1.86/2.07 tff(2998,plain,
% 1.86/2.07 (b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[306, 2997])).
% 1.86/2.07 tff(2999,plain,
% 1.86/2.07 (~r(s(z), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2659, 2996, 2592])).
% 1.86/2.07 tff(3000,plain,
% 1.86/2.07 (b(s(z), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[376, 2999])).
% 1.86/2.07 tff(3001,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1582, 204, 3000, 2998, 559, 2974, 479])).
% 1.86/2.07 tff(3002,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3003,plain,
% 1.86/2.07 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3002, 137])).
% 1.86/2.07 tff(3004,plain,
% 1.86/2.07 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[55, 3003])).
% 1.86/2.07 tff(3005,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3006,plain,
% 1.86/2.07 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3007,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3006])).
% 1.86/2.07 tff(3008,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[3007, 3005])).
% 1.86/2.07 tff(3009,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3010,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 1.86/2.07 tff(3011,plain,
% 1.86/2.07 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3010, 204, 363, 3004, 2649, 1469])).
% 1.86/2.07 tff(3012,plain,
% 1.86/2.07 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[489, 50, 3011, 249])).
% 1.86/2.07 tff(3013,plain,
% 1.86/2.07 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2027, 204, 405, 404, 1469])).
% 1.86/2.07 tff(3014,plain,
% 1.86/2.07 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3013, 2645])).
% 1.86/2.07 tff(3015,plain,
% 1.86/2.07 (r(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[604, 50, 601, 3014])).
% 1.86/2.07 tff(3016,plain,
% 1.86/2.07 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2034, 3015, 339])).
% 1.86/2.07 tff(3017,plain,
% 1.86/2.07 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[190, 3016])).
% 1.86/2.07 tff(3018,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(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(X1, 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(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3019,plain,
% 1.86/2.07 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(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(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3020,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(X1, 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(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3019])).
% 1.86/2.08 tff(3021,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(X1, 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(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3020, 3018])).
% 1.86/2.08 tff(3022,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3023,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3022, 3021])).
% 1.86/2.08 tff(3024,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3023, 204, 2633, 3004, 3017, 2645])).
% 1.86/2.08 tff(3025,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[108, 3024])).
% 1.86/2.08 tff(3026,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3027,plain,
% 1.86/2.08 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3028,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3027])).
% 1.86/2.08 tff(3029,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3028, 3026])).
% 1.86/2.08 tff(3030,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3031,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 1.86/2.08 tff(3032,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3031, 67, 2635, 3025, 2647, 3012])).
% 1.86/2.08 tff(3033,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3034,plain,
% 1.86/2.08 (~r(z, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3033, 1469, 363, 137, 405, 404])).
% 1.86/2.08 tff(3035,plain,
% 1.86/2.08 (b(z, s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[357, 3034])).
% 1.86/2.08 tff(3036,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3037,plain,
% 1.86/2.08 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3038,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3037])).
% 1.86/2.08 tff(3039,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3038, 3036])).
% 1.86/2.08 tff(3040,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3041,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3040, 3039])).
% 1.86/2.08 tff(3042,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3041, 67, 2, 110, 1])).
% 1.86/2.08 tff(3043,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3044,plain,
% 1.86/2.08 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3043, 1, 2592])).
% 1.86/2.08 tff(3045,plain,
% 1.86/2.08 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[431, 3044])).
% 1.86/2.08 tff(3046,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1685, 3045, 3035, 404, 363])).
% 1.86/2.08 tff(3047,plain,
% 1.86/2.08 (r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[558, 3046])).
% 1.86/2.08 tff(3048,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3049,plain,
% 1.86/2.08 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3050,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3049])).
% 1.86/2.08 tff(3051,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3050, 3048])).
% 1.86/2.08 tff(3052,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3053,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 1.86/2.08 tff(3054,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3053, 67, 3047, 2592, 1, 2598])).
% 1.86/2.08 tff(3055,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3056,plain,
% 1.86/2.08 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3055, 1469, 363, 404, 405, 137])).
% 1.86/2.08 tff(3057,plain,
% 1.86/2.08 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[190, 3056])).
% 1.86/2.08 tff(3058,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3059,plain,
% 1.86/2.08 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3060,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3059])).
% 1.86/2.08 tff(3061,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3060, 3058])).
% 1.86/2.08 tff(3062,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3063,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 1.86/2.08 tff(3064,plain,
% 1.86/2.08 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3063, 204, 363, 3035, 3057, 1469])).
% 1.86/2.08 tff(3065,plain,
% 1.86/2.08 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[489, 50, 3064, 249])).
% 1.86/2.08 tff(3066,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3067,plain,
% 1.86/2.08 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3068,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3067])).
% 1.86/2.08 tff(3069,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3068, 3066])).
% 1.86/2.08 tff(3070,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3071,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 1.86/2.08 tff(3072,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3071, 204, 404, 3035, 3057, 1469])).
% 1.86/2.08 tff(3073,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[134, 3072])).
% 1.86/2.08 tff(3074,plain,
% 1.86/2.08 (~r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1229, 67, 3073, 3065])).
% 1.86/2.08 tff(3075,plain,
% 1.86/2.08 (b(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[558, 3074])).
% 1.86/2.08 tff(3076,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3077,plain,
% 1.86/2.09 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3078,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.09 tff(3079,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3078, 3076])).
% 1.86/2.09 tff(3080,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3081,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3080, 3079])).
% 1.86/2.09 tff(3082,plain,
% 1.86/2.09 (~r(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3081, 67, 3073, 3065])).
% 1.86/2.09 tff(3083,plain,
% 1.86/2.09 (b(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[478, 3082])).
% 1.86/2.09 tff(3084,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1398, 3083, 3075, 363, 404, 405])).
% 1.86/2.09 tff(3085,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3086,plain,
% 1.86/2.09 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3085, 2466, 363, 2596, 137])).
% 1.86/2.09 tff(3087,plain,
% 1.86/2.09 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[641, 3086])).
% 1.86/2.09 tff(3088,plain,
% 1.86/2.09 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1807, 67, 538, 3087])).
% 1.86/2.09 tff(3089,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[190, 3088])).
% 1.86/2.09 tff(3090,plain,
% 1.86/2.09 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1815, 67, 538, 3087])).
% 1.86/2.09 tff(3091,plain,
% 1.86/2.09 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[218, 3090])).
% 1.86/2.09 tff(3092,plain,
% 1.86/2.09 (~r(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2663, 3087, 2592])).
% 1.86/2.09 tff(3093,plain,
% 1.86/2.09 (b(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[306, 3092])).
% 1.86/2.09 tff(3094,plain,
% 1.86/2.09 ((~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2494, 204, 363, 2596, 2466])).
% 1.86/2.09 tff(3095,plain,
% 1.86/2.09 (~b(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3094, 3093])).
% 1.86/2.09 tff(3096,plain,
% 1.86/2.09 (r(s(z), s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[478, 3095])).
% 1.86/2.09 tff(3097,plain,
% 1.86/2.09 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[453, 3096, 137])).
% 1.86/2.09 tff(3098,plain,
% 1.86/2.09 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[431, 3097])).
% 1.86/2.09 tff(3099,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3100,plain,
% 1.86/2.09 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3101,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3100])).
% 1.86/2.09 tff(3102,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3101, 3099])).
% 1.86/2.09 tff(3103,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3104,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 1.86/2.09 tff(3105,plain,
% 1.86/2.09 (~b(z, s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3104, 204, 363, 3093, 3098, 3004])).
% 1.86/2.09 tff(3106,plain,
% 1.86/2.09 (r(z, s(s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[357, 3105])).
% 1.86/2.09 tff(3107,assumption,(~b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 1.86/2.09 tff(3108,plain,
% 1.86/2.09 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[641, 3107])).
% 1.86/2.09 tff(3109,plain,
% 1.86/2.09 (~r(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2663, 3108, 110])).
% 1.86/2.09 tff(3110,plain,
% 1.86/2.09 (b(z, s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[306, 3109])).
% 1.86/2.09 tff(3111,assumption,(b(z, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.09 tff(3112,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3113,plain,
% 1.86/2.09 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3114,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3113])).
% 1.86/2.09 tff(3115,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3114, 3112])).
% 1.86/2.09 tff(3116,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(z))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3117,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 1.86/2.09 tff(3118,plain,
% 1.86/2.09 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3117, 204, 405, 404, 784, 3111])).
% 1.86/2.09 tff(3119,plain,
% 1.86/2.09 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[710, 50, 707, 3118])).
% 1.86/2.09 tff(3120,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3121,plain,
% 1.86/2.09 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(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)))))), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3122,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3121])).
% 1.86/2.09 tff(3123,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3122, 3120])).
% 1.86/2.09 tff(3124,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3125,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3124, 3123])).
% 1.86/2.09 tff(3126,plain,
% 1.86/2.09 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3125, 204, 363, 362, 784])).
% 1.86/2.09 tff(3127,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3126, 676, 3111])).
% 1.86/2.09 tff(3128,plain,((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3129,plain,
% 1.86/2.09 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3128, 3111, 362, 784, 363])).
% 1.86/2.09 tff(3130,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3131,plain,
% 1.86/2.09 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), 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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3132,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3131])).
% 1.86/2.09 tff(3133,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3132, 3130])).
% 1.86/2.09 tff(3134,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3135,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 1.86/2.09 tff(3136,plain,
% 1.86/2.09 (~b(s(s(s(z))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3135, 204, 363, 362, 405, 404])).
% 1.86/2.09 tff(3137,plain,
% 1.86/2.09 (r(s(s(s(z))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[558, 3136])).
% 1.86/2.09 tff(3138,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3139,plain,
% 1.86/2.09 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3140,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3139])).
% 1.86/2.09 tff(3141,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3140, 3138])).
% 1.86/2.09 tff(3142,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3143,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 1.86/2.09 tff(3144,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3143, 67, 3137, 3129, 3119])).
% 1.86/2.09 tff(3145,plain,((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3146,plain,
% 1.86/2.09 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3145, 784, 404, 405, 3110, 363])).
% 1.86/2.09 tff(3147,assumption,(~b(z, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.09 tff(3148,assumption,(z = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.86/2.09 tff(3149,plain,
% 1.86/2.09 (s(s(s(s(s(s(elem!1)))))) = z),
% 1.86/2.09 inference(symmetry,[status(thm)],[3148])).
% 1.86/2.09 tff(3150,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[818, 3149])).
% 1.86/2.09 tff(3151,plain,(~(z = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3152,assumption,(~r(z, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.09 tff(3153,plain,
% 1.86/2.09 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(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(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3154,plain,
% 1.86/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3155,plain,
% 1.86/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3154, 3153])).
% 1.86/2.09 tff(3156,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3155, 50, 3152, 3151, 3147])).
% 1.86/2.09 tff(3157,plain,(b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3158,plain,
% 1.86/2.09 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3157, 3146])).
% 1.86/2.09 tff(3159,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.09 tff(3160,assumption,(r(z, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.09 tff(3161,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3162,plain,
% 1.86/2.09 (((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3163,plain,
% 1.86/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(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(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3162])).
% 1.86/2.10 tff(3164,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(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(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3163, 3161])).
% 1.86/2.10 tff(3165,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3166,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.86/2.10 tff(3167,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3166, 67, 538, 3160, 3159])).
% 1.86/2.10 tff(3168,plain,((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3169,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3168, 3158, 538])).
% 1.86/2.10 tff(3170,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.10 tff(3171,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.10 tff(3172,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[796, 50, 3171, 2739, 3170])).
% 1.86/2.10 tff(3173,plain,(b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3174,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3173, 3169])).
% 1.86/2.10 tff(3175,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.86/2.10 tff(3176,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3177,plain,
% 1.86/2.10 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3178,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3177])).
% 1.86/2.10 tff(3179,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3178, 3176])).
% 1.86/2.10 tff(3180,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3181,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3180, 3179])).
% 1.86/2.10 tff(3182,plain,
% 1.86/2.10 ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3181, 204, 363, 784, 360])).
% 1.86/2.10 tff(3183,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3182, 676, 3175])).
% 1.86/2.10 tff(3184,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3185,plain,
% 1.86/2.10 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3184, 3174, 784, 360, 363])).
% 1.86/2.10 tff(3186,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3187,plain,
% 1.86/2.10 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(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(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3188,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3187])).
% 1.86/2.10 tff(3189,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3188, 3186])).
% 1.86/2.10 tff(3190,plain,
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% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
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% 1.86/2.10 inference(modus_ponens,[status(thm)],[3190, 3189])).
% 1.86/2.10 tff(3192,plain,
% 1.86/2.10 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3191, 67, 110, 3185])).
% 1.86/2.10 tff(3193,plain,
% 1.86/2.10 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1807, 67, 538, 3108])).
% 1.86/2.10 tff(3194,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[190, 3193])).
% 1.86/2.10 tff(3195,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1815, 67, 538, 3108])).
% 1.86/2.10 tff(3196,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[218, 3195])).
% 1.86/2.10 tff(3197,plain,
% 1.86/2.10 (~b(s(z), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2495, 3110])).
% 1.86/2.10 tff(3198,plain,
% 1.86/2.10 (r(s(z), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[478, 3197])).
% 1.86/2.10 tff(3199,plain,
% 1.86/2.10 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2643, 3198, 110])).
% 1.86/2.10 tff(3200,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[284, 3199])).
% 1.86/2.10 tff(3201,plain,
% 1.86/2.10 (~b(s(s(s(z))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3135, 204, 363, 3110, 405, 404])).
% 1.86/2.10 tff(3202,plain,
% 1.86/2.10 (r(s(s(s(z))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[558, 3201])).
% 1.86/2.10 tff(3203,plain,
% 1.86/2.10 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[116, 67, 3202, 110])).
% 1.86/2.10 tff(3204,plain,
% 1.86/2.10 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[134, 3203])).
% 1.86/2.10 tff(3205,plain,
% 1.86/2.10 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2713, 204, 3196, 3194, 3204, 3200])).
% 1.86/2.10 tff(3206,plain,
% 1.86/2.10 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[108, 3205])).
% 1.86/2.10 tff(3207,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3208,plain,
% 1.86/2.10 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3209,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(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(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3208])).
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% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(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(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3209, 3207])).
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% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
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% 1.86/2.10 inference(modus_ponens,[status(thm)],[3211, 3210])).
% 1.86/2.10 tff(3213,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3212, 67, 339, 656, 3160])).
% 1.86/2.10 tff(3214,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3215,plain,
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% 1.86/2.10 tff(3216,plain,
% 1.86/2.10 (b(z, s(s(s(s(s(s(elem!1)))))))),
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% 1.86/2.10 tff(3217,plain,
% 1.86/2.10 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2430, 67, 57, 656, 378])).
% 1.86/2.10 tff(3218,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
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% 1.86/2.10 tff(3219,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3220,plain,
% 1.86/2.10 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(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)))))), s(s(s(z))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3221,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3220])).
% 1.86/2.10 tff(3222,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(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(X1, 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(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3221, 3219])).
% 1.86/2.10 tff(3223,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3224,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3223, 3222])).
% 1.86/2.10 tff(3225,plain,
% 1.86/2.10 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3224, 204, 405, 404, 784])).
% 1.86/2.10 tff(3226,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3225, 3218, 3216])).
% 1.86/2.10 tff(3227,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3228,plain,
% 1.86/2.10 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3227, 784, 404, 405, 3202, 3206, 339])).
% 1.86/2.10 tff(3229,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[766, 3228])).
% 1.86/2.10 tff(3230,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3231,plain,
% 1.86/2.10 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3232,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3231])).
% 1.86/2.11 tff(3233,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3232, 3230])).
% 1.86/2.11 tff(3234,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3235,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3234, 3233])).
% 1.86/2.11 tff(3236,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3235, 204, 3229, 3174, 3196, 3194])).
% 1.86/2.11 tff(3237,plain,
% 1.86/2.11 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2402, 50, 3236])).
% 1.86/2.11 tff(3238,plain,
% 1.86/2.11 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3237, 3192])).
% 1.86/2.11 tff(3239,plain,
% 1.86/2.11 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3238])).
% 1.86/2.11 tff(3240,plain,
% 1.86/2.11 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.11 inference(symmetry,[status(thm)],[3239])).
% 1.86/2.11 tff(3241,plain,
% 1.86/2.11 (b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[784, 3240])).
% 1.86/2.11 tff(3242,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3107, 3241])).
% 1.86/2.11 tff(3243,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | b(s(s(s(s(s(s(z)))))), z) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~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(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3244,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3243, 3086, 2592, 3004, 363, 538, 2466, 2596, 3106])).
% 1.86/2.11 tff(3245,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[822, 3244])).
% 1.86/2.11 tff(3246,plain,
% 1.86/2.11 (((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3247,plain,
% 1.86/2.11 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3248,plain,
% 1.86/2.11 (((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3247])).
% 1.86/2.11 tff(3249,plain,
% 1.86/2.11 (((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3248, 3246])).
% 1.86/2.11 tff(3250,plain,
% 1.86/2.11 ((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3251,plain,
% 1.86/2.11 ((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3250, 3249])).
% 1.86/2.11 tff(3252,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3251, 67, 3245, 538])).
% 1.86/2.11 tff(3253,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3173, 3252])).
% 1.86/2.11 tff(3254,plain,
% 1.86/2.11 (((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3255,plain,
% 1.86/2.11 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3256,plain,
% 1.86/2.11 (((~![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)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3255])).
% 1.86/2.11 tff(3257,plain,
% 1.86/2.11 (((~![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)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3256, 3254])).
% 1.86/2.11 tff(3258,plain,
% 1.86/2.11 ((~![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)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3259,plain,
% 1.86/2.11 ((~![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(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 1.86/2.11 tff(3260,plain,
% 1.86/2.11 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3259, 67, 3245, 538])).
% 1.86/2.11 tff(3261,plain,
% 1.86/2.11 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[766, 3260])).
% 1.86/2.11 tff(3262,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3263,plain,
% 1.86/2.11 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3264,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3263])).
% 1.86/2.11 tff(3265,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3264, 3262])).
% 1.86/2.11 tff(3266,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3267,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3266, 3265])).
% 1.86/2.11 tff(3268,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3267, 204, 3261, 3253, 3091, 3089])).
% 1.86/2.11 tff(3269,plain,
% 1.86/2.11 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2772, 67, 3245, 2592, 3087])).
% 1.86/2.11 tff(3270,plain,
% 1.86/2.11 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[850, 50, 3269])).
% 1.86/2.11 tff(3271,plain,
% 1.86/2.11 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3270, 3268])).
% 1.86/2.11 tff(3272,plain,
% 1.86/2.11 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3271])).
% 1.86/2.11 tff(3273,plain,
% 1.86/2.11 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[664, 3272, 121])).
% 1.86/2.11 tff(3274,plain,
% 1.86/2.11 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3273])).
% 1.86/2.11 tff(3275,plain,
% 1.86/2.11 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[875, 3274, 119])).
% 1.86/2.11 tff(3276,plain,
% 1.86/2.11 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3275])).
% 1.86/2.11 tff(3277,plain,
% 1.86/2.11 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[699, 3276, 20])).
% 1.86/2.11 tff(3278,plain,
% 1.86/2.11 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3277])).
% 1.86/2.11 tff(3279,plain,
% 1.86/2.11 (s(s(elem!1)) = s(s(z))),
% 1.86/2.11 inference(transitivity,[status(thm)],[754, 3278, 83])).
% 1.86/2.11 tff(3280,plain,
% 1.86/2.11 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3279])).
% 1.86/2.11 tff(3281,plain,
% 1.86/2.11 (s(elem!1) = s(z)),
% 1.86/2.11 inference(transitivity,[status(thm)],[919, 3280, 78])).
% 1.86/2.11 tff(3282,plain,
% 1.86/2.11 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3281])).
% 1.86/2.11 tff(3283,plain,
% 1.86/2.11 (elem!1 = z),
% 1.86/2.11 inference(transitivity,[status(thm)],[1009, 3282, 15])).
% 1.86/2.11 tff(3284,plain,
% 1.86/2.11 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3283])).
% 1.86/2.11 tff(3285,plain,
% 1.86/2.11 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.86/2.11 inference(symmetry,[status(thm)],[3284])).
% 1.86/2.11 tff(3286,plain,
% 1.86/2.11 (b(s(z), elem!1)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[363, 3285])).
% 1.86/2.11 tff(3287,plain,
% 1.86/2.11 (~b(s(s(s(z))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3135, 204, 363, 3093, 2596, 2466])).
% 1.86/2.11 tff(3288,plain,
% 1.86/2.11 (r(s(s(s(z))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[558, 3287])).
% 1.86/2.11 tff(3289,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.86/2.11 tff(3290,plain,
% 1.86/2.11 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3289])).
% 1.86/2.11 tff(3291,plain,
% 1.86/2.11 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[664, 3290, 121])).
% 1.86/2.11 tff(3292,plain,
% 1.86/2.11 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3291])).
% 1.86/2.11 tff(3293,plain,
% 1.86/2.11 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[875, 3292, 119])).
% 1.86/2.11 tff(3294,plain,
% 1.86/2.11 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3293])).
% 1.86/2.11 tff(3295,plain,
% 1.86/2.11 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[699, 3294, 20])).
% 1.86/2.11 tff(3296,plain,
% 1.86/2.11 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3295])).
% 1.86/2.11 tff(3297,plain,
% 1.86/2.11 (s(s(elem!1)) = s(s(z))),
% 1.86/2.11 inference(transitivity,[status(thm)],[754, 3296, 83])).
% 1.86/2.11 tff(3298,plain,
% 1.86/2.11 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3297])).
% 1.86/2.11 tff(3299,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.86/2.11 tff(3300,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.86/2.11 tff(3301,plain,
% 1.86/2.11 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3297])).
% 1.86/2.11 tff(3302,plain,
% 1.86/2.11 (b(s(s(z)), s(z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[990, 3301])).
% 1.86/2.11 tff(3303,plain,
% 1.86/2.11 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.11 inference(symmetry,[status(thm)],[3296])).
% 1.86/2.11 tff(3304,plain,
% 1.86/2.11 (s(s(z)) = s(s(elem!1))),
% 1.86/2.11 inference(transitivity,[status(thm)],[84, 3303, 753])).
% 1.86/2.11 tff(3305,plain,
% 1.86/2.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3304])).
% 1.86/2.11 tff(3306,plain,
% 1.86/2.11 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3305, 2223])).
% 1.86/2.11 tff(3307,plain,
% 1.86/2.11 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3306])).
% 1.86/2.11 tff(3308,plain,
% 1.86/2.11 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[2125, 3307])).
% 1.86/2.11 tff(3309,plain,
% 1.86/2.11 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3297])).
% 1.86/2.11 tff(3310,plain,
% 1.86/2.11 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.11 inference(symmetry,[status(thm)],[3309])).
% 1.86/2.11 tff(3311,plain,
% 1.86/2.11 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3297])).
% 1.86/2.11 tff(3312,plain,
% 1.86/2.11 (s(elem!1) = s(z)),
% 1.86/2.11 inference(transitivity,[status(thm)],[919, 3311, 78])).
% 1.86/2.11 tff(3313,plain,
% 1.86/2.11 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3312])).
% 1.86/2.11 tff(3314,plain,
% 1.86/2.11 (elem!1 = z),
% 1.86/2.11 inference(transitivity,[status(thm)],[1009, 3313, 15])).
% 1.86/2.11 tff(3315,plain,
% 1.86/2.11 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3314])).
% 1.86/2.11 tff(3316,plain,
% 1.86/2.11 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.86/2.11 inference(symmetry,[status(thm)],[3315])).
% 1.86/2.11 tff(3317,plain,
% 1.86/2.11 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.86/2.11 inference(transitivity,[status(thm)],[3316, 3310])).
% 1.86/2.11 tff(3318,plain,
% 1.86/2.11 (b(s(s(elem!1)), elem!1)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3300, 3317])).
% 1.86/2.11 tff(3319,plain,
% 1.86/2.11 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3314])).
% 1.86/2.11 tff(3320,plain,
% 1.86/2.11 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.86/2.11 inference(symmetry,[status(thm)],[3319])).
% 1.86/2.11 tff(3321,plain,
% 1.86/2.11 (b(elem!1, s(z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[362, 3320])).
% 1.86/2.11 tff(3322,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3323,plain,
% 1.86/2.11 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3324,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3323])).
% 1.86/2.11 tff(3325,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3324, 3322])).
% 1.86/2.11 tff(3326,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3327,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 1.86/2.11 tff(3328,plain,
% 1.86/2.11 ((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3327, 204])).
% 1.86/2.11 tff(3329,plain,
% 1.86/2.11 (~b(s(z), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3328, 990, 3299, 3321, 3318])).
% 1.86/2.11 tff(3330,plain,
% 1.86/2.11 (r(s(z), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[936, 3329])).
% 1.86/2.11 tff(3331,plain,
% 1.86/2.11 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2135, 3330, 445])).
% 1.86/2.11 tff(3332,assumption,(~r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.86/2.11 tff(3333,assumption,(~b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.86/2.11 tff(3334,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2182, 50, 2179, 3333, 3332])).
% 1.86/2.11 tff(3335,plain,(b(s(s(s(z))), s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3336,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3335, 3331, 3308])).
% 1.86/2.11 tff(3337,plain,
% 1.86/2.11 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[2855])).
% 1.86/2.12 tff(3338,plain,
% 1.86/2.12 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(symmetry,[status(thm)],[3337])).
% 1.86/2.12 tff(3339,plain,
% 1.86/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[2141, 3338])).
% 1.86/2.12 tff(3340,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.86/2.12 tff(3341,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3340, 3339])).
% 1.86/2.12 tff(3342,plain,(b(s(s(s(z))), s(s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3343,plain,
% 1.86/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3342, 3336, 3293])).
% 1.86/2.12 tff(3344,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3345,plain,
% 1.86/2.12 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3346,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3345])).
% 1.86/2.12 tff(3347,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3346, 3344])).
% 1.86/2.12 tff(3348,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3349,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3348, 3347])).
% 1.86/2.12 tff(3350,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3349, 204, 362, 404, 3343, 3302, 3300])).
% 1.86/2.12 tff(3351,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3352,plain,
% 1.86/2.12 (~b(s(s(elem!1)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3351, 3300, 404, 362, 3289, 445, 3299])).
% 1.86/2.12 tff(3353,plain,
% 1.86/2.12 (r(s(s(elem!1)), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[952, 3352])).
% 1.86/2.12 tff(3354,plain,
% 1.86/2.12 (r(s(s(z)), s(z))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3353, 3298])).
% 1.86/2.12 tff(3355,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3356,plain,
% 1.86/2.12 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3357,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3356])).
% 1.86/2.12 tff(3358,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3357, 3355])).
% 1.86/2.12 tff(3359,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3360,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3359, 3358])).
% 1.86/2.12 tff(3361,plain,
% 1.86/2.12 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3360, 67, 110, 3354])).
% 1.86/2.12 tff(3362,plain,
% 1.86/2.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3363,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3364,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3363, 3362])).
% 1.86/2.12 tff(3365,plain,
% 1.86/2.12 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3364, 50])).
% 1.86/2.12 tff(3366,plain,
% 1.86/2.12 (b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3365, 182])).
% 1.86/2.12 tff(3367,plain,
% 1.86/2.12 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3366, 3361])).
% 1.86/2.12 tff(3368,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3369,plain,
% 1.86/2.12 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3370,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3369])).
% 1.86/2.12 tff(3371,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3370, 3368])).
% 1.86/2.12 tff(3372,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3373,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.86/2.12 tff(3374,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3373, 67, 57, 3354])).
% 1.86/2.12 tff(3375,plain,
% 1.86/2.12 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2316, 50])).
% 1.86/2.12 tff(3376,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3375, 2125])).
% 1.86/2.12 tff(3377,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3376, 3374])).
% 1.86/2.12 tff(3378,plain,
% 1.86/2.12 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2643, 445, 110])).
% 1.86/2.12 tff(3379,plain,
% 1.86/2.12 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[284, 3378])).
% 1.86/2.12 tff(3380,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3381,plain,
% 1.86/2.12 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3382,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3381])).
% 1.86/2.12 tff(3383,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3382, 3380])).
% 1.86/2.12 tff(3384,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3385,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.86/2.12 tff(3386,plain,
% 1.86/2.12 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3385, 204, 404, 3300, 3379])).
% 1.86/2.12 tff(3387,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3386, 3377, 3367])).
% 1.86/2.12 tff(3388,plain,((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3389,plain,
% 1.86/2.12 (~b(s(s(z)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3388, 2466, 3288, 2592, 3271, 3093, 3096, 3286])).
% 1.86/2.12 tff(3390,plain,
% 1.86/2.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3391,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3392,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3391, 3390])).
% 1.86/2.12 tff(3393,plain,
% 1.86/2.12 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3392, 50, 97])).
% 1.86/2.12 tff(3394,plain,
% 1.86/2.12 (r(s(s(z)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3393, 3389])).
% 1.86/2.12 tff(3395,plain,
% 1.86/2.12 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.86/2.12 inference(symmetry,[status(thm)],[3282])).
% 1.86/2.12 tff(3396,plain,
% 1.86/2.12 (z = elem!1),
% 1.86/2.12 inference(transitivity,[status(thm)],[2194, 3395, 902])).
% 1.86/2.12 tff(3397,plain,
% 1.86/2.12 (elem!1 = z),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2211, 3396])).
% 1.86/2.12 tff(3398,plain,
% 1.86/2.12 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3275, 3271])).
% 1.86/2.12 tff(3399,plain,
% 1.86/2.12 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3398, 163])).
% 1.86/2.12 tff(3400,plain,
% 1.86/2.12 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.12 inference(symmetry,[status(thm)],[3399])).
% 1.86/2.12 tff(3401,plain,
% 1.86/2.12 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3400])).
% 1.86/2.12 tff(3402,plain,
% 1.86/2.12 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[185, 3401])).
% 1.86/2.12 tff(3403,plain,
% 1.86/2.12 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3271])).
% 1.86/2.12 tff(3404,plain,
% 1.86/2.12 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.86/2.12 inference(symmetry,[status(thm)],[3403])).
% 1.86/2.12 tff(3405,plain,
% 1.86/2.12 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.12 inference(symmetry,[status(thm)],[3278])).
% 1.86/2.12 tff(3406,plain,
% 1.86/2.12 (s(s(z)) = s(s(elem!1))),
% 1.86/2.12 inference(transitivity,[status(thm)],[84, 3405, 753])).
% 1.86/2.12 tff(3407,plain,
% 1.86/2.12 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3406])).
% 1.86/2.12 tff(3408,plain,
% 1.86/2.12 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3407, 3404])).
% 1.86/2.12 tff(3409,plain,
% 1.86/2.12 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3408])).
% 1.86/2.12 tff(3410,plain,
% 1.86/2.12 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[182, 3409])).
% 1.86/2.12 tff(3411,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3412,plain,
% 1.86/2.12 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3413,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3412])).
% 1.86/2.12 tff(3414,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3413, 3411])).
% 1.86/2.12 tff(3415,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3416,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 1.86/2.12 tff(3417,plain,
% 1.86/2.12 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3416, 67, 3394, 538])).
% 1.86/2.12 tff(3418,plain,
% 1.86/2.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3419,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3420,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3419, 3418])).
% 1.86/2.12 tff(3421,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3420, 50, 2122])).
% 1.86/2.12 tff(3422,plain,
% 1.86/2.12 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3421, 3417])).
% 1.86/2.12 tff(3423,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3424,plain,
% 1.86/2.12 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3425,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3424])).
% 1.86/2.12 tff(3426,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3425, 3423])).
% 1.86/2.12 tff(3427,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3428,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3427, 3426])).
% 1.86/2.12 tff(3429,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3428, 67, 3394, 538])).
% 1.86/2.12 tff(3430,plain,
% 1.86/2.12 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.86/2.12 inference(commutativity,[status(thm)],[])).
% 1.86/2.12 tff(3431,plain,
% 1.86/2.12 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.12 inference(symmetry,[status(thm)],[3430])).
% 1.86/2.12 tff(3432,plain,
% 1.86/2.12 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3431])).
% 1.86/2.12 tff(3433,plain,
% 1.86/2.12 (~(s(s(z)) = s(s(s(s(z)))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[2122, 3432])).
% 1.86/2.12 tff(3434,plain,
% 1.86/2.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3435,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3436,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3435, 3434])).
% 1.86/2.13 tff(3437,plain,
% 1.86/2.13 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[3436, 50])).
% 1.86/2.13 tff(3438,plain,
% 1.86/2.13 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[3437, 3433])).
% 1.86/2.13 tff(3439,plain,
% 1.86/2.13 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[3438, 3429])).
% 1.86/2.13 tff(3440,plain,
% 1.86/2.13 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[2302])).
% 1.86/2.13 tff(3441,plain,
% 1.86/2.13 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[3440])).
% 1.86/2.13 tff(3442,plain,
% 1.86/2.13 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.86/2.13 inference(symmetry,[status(thm)],[3441])).
% 1.86/2.13 tff(3443,plain,
% 1.86/2.13 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[3442])).
% 1.86/2.13 tff(3444,plain,
% 1.86/2.13 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(symmetry,[status(thm)],[3443])).
% 1.86/2.13 tff(3445,plain,
% 1.86/2.13 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[3442])).
% 1.86/2.13 tff(3446,plain,
% 1.86/2.13 ((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[3445])).
% 1.86/2.13 tff(3447,plain,
% 1.86/2.13 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[3251, 67, 824, 538])).
% 1.86/2.13 tff(3448,plain,
% 1.86/2.13 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(modus_ponens,[status(thm)],[3447, 3446])).
% 1.86/2.13 tff(3449,plain,
% 1.86/2.13 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[895, 3448, 1335])).
% 1.86/2.13 tff(3450,plain,
% 1.86/2.13 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(modus_ponens,[status(thm)],[3449, 3444])).
% 1.86/2.13 tff(3451,plain,
% 1.86/2.13 (b(s(s(s(s(s(s(elem!1)))))), s(s(z))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[2303])).
% 1.86/2.13 tff(3452,plain,
% 1.86/2.13 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.86/2.13 inference(symmetry,[status(thm)],[3451])).
% 1.86/2.13 tff(3453,plain,
% 1.86/2.13 (r(s(s(s(s(s(s(elem!1)))))), s(s(z))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[2303])).
% 1.86/2.13 tff(3454,plain,
% 1.86/2.13 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.86/2.13 inference(monotonicity,[status(thm)],[3453])).
% 1.86/2.13 tff(3455,plain,
% 1.86/2.13 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.13 inference(modus_ponens,[status(thm)],[2864, 3454])).
% 1.86/2.13 tff(3456,plain,
% 1.86/2.13 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[1062, 3455, 1051])).
% 1.86/2.13 tff(3457,plain,
% 1.86/2.13 (b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.86/2.13 inference(modus_ponens,[status(thm)],[3456, 3452])).
% 1.86/2.13 tff(3458,plain,
% 1.86/2.13 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[2844, 1051, 2300])).
% 1.86/2.13 tff(3459,plain,
% 1.86/2.13 (b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.13 inference(unit_resolution,[status(thm)],[2848, 50, 3458, 2830])).
% 1.86/2.13 tff(3460,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.13 tff(3461,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.86/2.13 tff(3462,plain,
% 1.86/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3463,plain,
% 1.97/2.13 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3464,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[3463])).
% 1.97/2.13 tff(3465,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[3464, 3462])).
% 1.97/2.13 tff(3466,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(3467,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[3466, 3465])).
% 1.97/2.13 tff(3468,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3467, 204, 3461, 3460, 3459, 3457, 3450])).
% 1.97/2.13 tff(3469,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = z)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(3470,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3469, 3439, 3422, 538, 3245, 3410, 3402, 3397, 3394])).
% 1.97/2.13 tff(3471,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(3472,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3471, 363, 137])).
% 1.97/2.13 tff(3473,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[335, 3472])).
% 1.97/2.13 tff(3474,plain,
% 1.97/2.13 (~b(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[371, 361, 360, 363, 359])).
% 1.97/2.13 tff(3475,plain,
% 1.97/2.13 (r(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[306, 3474])).
% 1.97/2.13 tff(3476,plain,
% 1.97/2.13 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1245, 67, 3475, 110])).
% 1.97/2.13 tff(3477,plain,
% 1.97/2.13 (b(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[604, 50, 601, 3476])).
% 1.97/2.13 tff(3478,plain,
% 1.97/2.13 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2663, 3475, 110])).
% 1.97/2.13 tff(3479,plain,
% 1.97/2.13 (b(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[641, 3478])).
% 1.97/2.13 tff(3480,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3481,plain,
% 1.97/2.13 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3482,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[3481])).
% 1.97/2.13 tff(3483,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[3482, 3480])).
% 1.97/2.13 tff(3484,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(3485,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[3484, 3483])).
% 1.97/2.13 tff(3486,plain,
% 1.97/2.13 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3485, 204, 361, 359, 3479])).
% 1.97/2.13 tff(3487,plain,
% 1.97/2.13 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3486, 3477])).
% 1.97/2.13 tff(3488,plain,
% 1.97/2.13 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[190, 3487])).
% 1.97/2.13 tff(3489,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3043, 3488, 110])).
% 1.97/2.13 tff(3490,plain,
% 1.97/2.13 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[431, 3489])).
% 1.97/2.13 tff(3491,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1763, 204, 363, 3490, 361, 360, 359])).
% 1.97/2.13 tff(3492,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(3493,plain,
% 1.97/2.13 (~b(z, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3492, 363, 3004, 3473, 2592])).
% 1.97/2.13 tff(3494,plain,
% 1.97/2.13 (r(z, s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[357, 3493])).
% 1.97/2.13 tff(3495,plain,
% 1.97/2.13 (~r(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[347, 3494, 137])).
% 1.97/2.13 tff(3496,plain,
% 1.97/2.13 (b(z, s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[259, 3495])).
% 1.97/2.13 tff(3497,plain,
% 1.97/2.13 (~b(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2497, 2, 405, 363, 339, 137])).
% 1.97/2.13 tff(3498,plain,
% 1.97/2.13 (r(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[402, 3497])).
% 1.97/2.13 tff(3499,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2464, 3498, 137])).
% 1.97/2.13 tff(3500,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[335, 3499])).
% 1.97/2.13 tff(3501,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1941, 204, 363, 405, 2486, 360, 3500])).
% 1.97/2.13 tff(3502,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(3503,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3502, 3496, 3494, 3004, 137, 363])).
% 1.97/2.13 tff(3504,plain,
% 1.97/2.13 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[431, 3503])).
% 1.97/2.13 tff(3505,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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)) | (~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(X1, 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)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3506,plain,
% 1.97/2.13 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3507,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[3506])).
% 1.97/2.13 tff(3508,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[3507, 3505])).
% 1.97/2.13 tff(3509,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(3510,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 1.97/2.13 tff(3511,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3510, 204, 363, 362, 456, 360, 359])).
% 1.97/2.13 tff(3512,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(3513,plain,
% 1.97/2.13 (~b(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3512, 363, 3504, 3004, 3473])).
% 1.97/2.13 tff(3514,plain,
% 1.97/2.13 (r(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[306, 3513])).
% 1.97/2.13 tff(3515,plain,
% 1.97/2.13 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2663, 3514, 2592])).
% 1.97/2.13 tff(3516,plain,
% 1.97/2.13 (b(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[641, 3515])).
% 1.97/2.13 tff(3517,plain,
% 1.97/2.13 (~b(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3033, 3516, 363, 137, 3494, 3496])).
% 1.97/2.13 tff(3518,plain,
% 1.97/2.13 (r(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[402, 3517])).
% 1.97/2.13 tff(3519,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1479, 3518, 3494])).
% 1.97/2.13 tff(3520,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[108, 3519])).
% 1.97/2.13 tff(3521,plain,
% 1.97/2.13 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[244, 238])).
% 1.97/2.13 tff(3522,plain,
% 1.97/2.13 (~b(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2631, 57, 339, 1469, 3521])).
% 1.97/2.13 tff(3523,plain,
% 1.97/2.13 (r(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[402, 3522])).
% 1.97/2.13 tff(3524,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1479, 3523, 339])).
% 1.97/2.13 tff(3525,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[108, 3524])).
% 1.97/2.13 tff(3526,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[227, 3525, 3521, 57])).
% 1.97/2.13 tff(3527,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[55, 3526])).
% 1.97/2.13 tff(3528,plain,
% 1.97/2.13 (~r(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2003, 3523, 57])).
% 1.97/2.13 tff(3529,plain,
% 1.97/2.13 (b(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[306, 3528])).
% 1.97/2.13 tff(3530,plain,
% 1.97/2.13 (~r(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[397, 3523, 57])).
% 1.97/2.13 tff(3531,plain,
% 1.97/2.13 (b(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[376, 3530])).
% 1.97/2.13 tff(3532,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3510, 204, 3531, 3529, 456, 3527])).
% 1.97/2.13 tff(3533,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[335, 3532])).
% 1.97/2.13 tff(3534,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1479, 308, 339])).
% 1.97/2.13 tff(3535,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[108, 3534])).
% 1.97/2.13 tff(3536,plain,
% 1.97/2.13 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2604, 67, 57, 3521])).
% 1.97/2.13 tff(3537,plain,
% 1.97/2.13 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[282, 50, 3536])).
% 1.97/2.13 tff(3538,plain,
% 1.97/2.13 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3537, 552])).
% 1.97/2.13 tff(3539,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[116, 67, 57, 3521])).
% 1.97/2.13 tff(3540,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[134, 3539])).
% 1.97/2.13 tff(3541,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1612, 67, 308, 538])).
% 1.97/2.13 tff(3542,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[151, 3541])).
% 1.97/2.13 tff(3543,plain,
% 1.97/2.13 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2619, 204, 3542, 3535, 3540, 3538])).
% 1.97/2.13 tff(3544,plain,
% 1.97/2.13 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[190, 3543])).
% 1.97/2.13 tff(3545,plain,
% 1.97/2.13 (~r(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1773, 308, 445])).
% 1.97/2.13 tff(3546,plain,
% 1.97/2.13 (b(s(z), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[376, 3545])).
% 1.97/2.13 tff(3547,plain,
% 1.97/2.13 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1723, 67, 339, 3544])).
% 1.97/2.13 tff(3548,plain,
% 1.97/2.13 (b(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[604, 50, 601, 3547])).
% 1.97/2.13 tff(3549,plain,
% 1.97/2.13 (~r(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2003, 308, 57])).
% 1.97/2.13 tff(3550,plain,
% 1.97/2.13 (b(z, s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[306, 3549])).
% 1.97/2.13 tff(3551,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3552,plain,
% 1.97/2.13 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(3553,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(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(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[3552])).
% 1.97/2.13 tff(3554,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(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(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3553, 3551])).
% 1.97/2.14 tff(3555,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(3556,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[3555, 3554])).
% 1.97/2.14 tff(3557,plain,
% 1.97/2.14 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3556, 204, 3546, 3550, 1469, 3548])).
% 1.97/2.14 tff(3558,plain,
% 1.97/2.14 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[489, 50, 3557, 249])).
% 1.97/2.14 tff(3559,plain,
% 1.97/2.14 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[242, 50, 238, 237])).
% 1.97/2.14 tff(3560,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[161, 3559, 1])).
% 1.97/2.14 tff(3561,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[55, 3560])).
% 1.97/2.14 tff(3562,plain,
% 1.97/2.14 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3043, 3559, 1])).
% 1.97/2.14 tff(3563,plain,
% 1.97/2.14 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[431, 3562])).
% 1.97/2.14 tff(3564,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3565,plain,
% 1.97/2.14 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3566,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3565])).
% 1.97/2.14 tff(3567,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.97/2.14 tff(3568,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(3569,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.97/2.14 tff(3570,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3569, 204, 3563, 3542, 153, 3561])).
% 1.97/2.14 tff(3571,plain,
% 1.97/2.14 (r(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[558, 3570])).
% 1.97/2.14 tff(3572,plain,
% 1.97/2.14 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2604, 67, 3571, 3559])).
% 1.97/2.14 tff(3573,plain,
% 1.97/2.14 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[282, 50, 3572])).
% 1.97/2.14 tff(3574,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3573, 552])).
% 1.97/2.14 tff(3575,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[116, 67, 3571, 3559])).
% 1.97/2.14 tff(3576,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[133, 3575, 129])).
% 1.97/2.14 tff(3577,plain,
% 1.97/2.14 (b(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[604, 50, 601, 1724])).
% 1.97/2.14 tff(3578,assumption,(r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.97/2.14 tff(3579,plain,
% 1.97/2.14 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3297])).
% 1.97/2.14 tff(3580,plain,
% 1.97/2.14 ((elem!1 = s(z)) <=> (z = s(z))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3314])).
% 1.97/2.14 tff(3581,plain,
% 1.97/2.14 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.97/2.14 inference(transitivity,[status(thm)],[3580, 296])).
% 1.97/2.14 tff(3582,plain,
% 1.97/2.14 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.97/2.14 inference(symmetry,[status(thm)],[3581])).
% 1.97/2.14 tff(3583,plain,
% 1.97/2.14 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3582])).
% 1.97/2.14 tff(3584,plain,
% 1.97/2.14 (~(elem!1 = s(z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[300, 3583])).
% 1.97/2.14 tff(3585,plain,
% 1.97/2.14 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1289, 3584])).
% 1.97/2.14 tff(3586,plain,
% 1.97/2.14 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.97/2.14 inference(symmetry,[status(thm)],[1123])).
% 1.97/2.14 tff(3587,plain,
% 1.97/2.14 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3304])).
% 1.97/2.14 tff(3588,plain,
% 1.97/2.14 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3587, 1123])).
% 1.97/2.14 tff(3589,plain,
% 1.97/2.14 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3588, 3586])).
% 1.97/2.14 tff(3590,plain,
% 1.97/2.14 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3589])).
% 1.97/2.14 tff(3591,plain,
% 1.97/2.14 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[2122, 3590])).
% 1.97/2.14 tff(3592,plain,
% 1.97/2.14 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3588])).
% 1.97/2.14 tff(3593,plain,
% 1.97/2.14 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[2122, 3592])).
% 1.97/2.14 tff(3594,plain,
% 1.97/2.14 (((~![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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3595,plain,
% 1.97/2.14 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3596,plain,
% 1.97/2.14 (((~![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(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3595])).
% 1.97/2.14 tff(3597,plain,
% 1.97/2.14 (((~![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(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3596, 3594])).
% 1.97/2.14 tff(3598,plain,
% 1.97/2.14 ((~![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(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(3599,plain,
% 1.97/2.14 ((~![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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[3598, 3597])).
% 1.97/2.14 tff(3600,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3599, 67, 510, 3578])).
% 1.97/2.14 tff(3601,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[55, 3600])).
% 1.97/2.14 tff(3602,plain,
% 1.97/2.14 (((~![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(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3603,plain,
% 1.97/2.14 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3604,plain,
% 1.97/2.14 (((~![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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3603])).
% 1.97/2.14 tff(3605,plain,
% 1.97/2.14 (((~![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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3604, 3602])).
% 1.97/2.14 tff(3606,plain,
% 1.97/2.14 ((~![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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(3607,plain,
% 1.97/2.14 ((~![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(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[3606, 3605])).
% 1.97/2.14 tff(3608,plain,
% 1.97/2.14 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3607, 67, 510, 3578])).
% 1.97/2.14 tff(3609,plain,
% 1.97/2.14 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[431, 3608])).
% 1.97/2.14 tff(3610,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3611,plain,
% 1.97/2.14 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3612,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3611])).
% 1.97/2.14 tff(3613,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(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(X1, 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(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3612, 3610])).
% 1.97/2.14 tff(3614,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(3615,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 1.97/2.14 tff(3616,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3615, 204, 566, 456, 194, 153, 360])).
% 1.97/2.14 tff(3617,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(3618,plain,
% 1.97/2.14 (~b(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3617, 3601, 153, 3542, 3609])).
% 1.97/2.14 tff(3619,plain,
% 1.97/2.14 (r(s(z), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[478, 3618])).
% 1.97/2.14 tff(3620,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3569, 204, 3609, 3542, 153, 3601])).
% 1.97/2.14 tff(3621,plain,
% 1.97/2.14 (r(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[558, 3620])).
% 1.97/2.14 tff(3622,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[116, 67, 3621, 3559])).
% 1.97/2.14 tff(3623,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[133, 3622, 129])).
% 1.97/2.14 tff(3624,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1503, 286, 339])).
% 1.97/2.14 tff(3625,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[55, 3624])).
% 1.97/2.14 tff(3626,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1479, 339, 308])).
% 1.97/2.14 tff(3627,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[108, 3626])).
% 1.97/2.14 tff(3628,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2003, 286, 308])).
% 1.97/2.14 tff(3629,plain,
% 1.97/2.14 (b(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[558, 3628])).
% 1.97/2.14 tff(3630,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3569, 204, 3629, 456, 194, 3627, 3625])).
% 1.97/2.14 tff(3631,plain,((~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(3632,plain,
% 1.97/2.14 (~r(z, s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3631, 3609, 3542, 308, 339])).
% 1.97/2.14 tff(3633,plain,
% 1.97/2.14 (b(z, s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[306, 3632])).
% 1.97/2.14 tff(3634,plain,
% 1.97/2.14 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2604, 67, 3621, 3559])).
% 1.97/2.14 tff(3635,plain,
% 1.97/2.14 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[282, 50, 3634])).
% 1.97/2.14 tff(3636,plain,
% 1.97/2.14 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3635, 552])).
% 1.97/2.14 tff(3637,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3638,plain,
% 1.97/2.14 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(3639,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[3638])).
% 1.97/2.14 tff(3640,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[3639, 3637])).
% 1.97/2.14 tff(3641,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(3642,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 1.97/2.14 tff(3643,plain,
% 1.97/2.14 (~b(z, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3642, 204, 1469, 3623, 3636, 1708])).
% 1.97/2.14 tff(3644,plain,
% 1.97/2.14 (r(z, s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[259, 3643])).
% 1.97/2.14 tff(3645,plain,
% 1.97/2.14 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.97/2.14 inference(symmetry,[status(thm)],[3313])).
% 1.97/2.14 tff(3646,plain,
% 1.97/2.14 (z = elem!1),
% 1.97/2.14 inference(transitivity,[status(thm)],[2194, 3645, 902])).
% 1.97/2.14 tff(3647,plain,
% 1.97/2.14 (elem!1 = z),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2211, 3646])).
% 1.97/2.14 tff(3648,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.97/2.15 tff(3649,plain,
% 1.97/2.15 (s(s(elem!1)) = s(s(s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3648, 2224])).
% 1.97/2.15 tff(3650,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[628, 3649])).
% 1.97/2.15 tff(3651,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(3652,plain,
% 1.97/2.15 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3651, 3585])).
% 1.97/2.15 tff(3653,plain,
% 1.97/2.15 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3297])).
% 1.97/2.15 tff(3654,plain,
% 1.97/2.15 (b(s(s(z)), z)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[1102, 3653])).
% 1.97/2.15 tff(3655,plain,
% 1.97/2.15 (b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3335, 2136, 2179])).
% 1.97/2.15 tff(3656,plain,
% 1.97/2.15 (b(s(s(s(z))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3342, 3655, 2790])).
% 1.97/2.15 tff(3657,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3658,plain,
% 1.97/2.15 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3659,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3658])).
% 1.97/2.15 tff(3660,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[3659, 3657])).
% 1.97/2.15 tff(3661,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(3662,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3661, 3660])).
% 1.97/2.15 tff(3663,plain,
% 1.97/2.15 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3662, 204, 3656, 3300, 1469, 192])).
% 1.97/2.15 tff(3664,plain,
% 1.97/2.15 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3366, 3663])).
% 1.97/2.15 tff(3665,plain,
% 1.97/2.15 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[2303])).
% 1.97/2.15 tff(3666,plain,
% 1.97/2.15 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.97/2.15 inference(symmetry,[status(thm)],[3665])).
% 1.97/2.15 tff(3667,plain,
% 1.97/2.15 (r(s(z), s(s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[907, 3666])).
% 1.97/2.15 tff(3668,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.97/2.15 tff(3669,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3668, 3667])).
% 1.97/2.15 tff(3670,plain,(r(s(z), s(s(z))) | (~r(s(z), s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(3671,plain,
% 1.97/2.15 (r(s(z), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3670, 907, 2300])).
% 1.97/2.15 tff(3672,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3673,plain,
% 1.97/2.15 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3674,plain,
% 1.97/2.15 (((~![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(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3673])).
% 1.97/2.15 tff(3675,plain,
% 1.97/2.15 (((~![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(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[3674, 3672])).
% 1.97/2.15 tff(3676,plain,
% 1.97/2.15 ((~![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(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(3677,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3676, 3675])).
% 1.97/2.15 tff(3678,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3677, 67, 3671, 3664, 3578])).
% 1.97/2.15 tff(3679,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1))) | (~(elem!1 = z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(3680,plain,
% 1.97/2.15 (~r(s(z), s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3679, 3654, 3578, 1469, 192, 3293, 3652, 3647, 445])).
% 1.97/2.15 tff(3681,plain,
% 1.97/2.15 (b(s(z), s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[936, 3680])).
% 1.97/2.15 tff(3682,plain,
% 1.97/2.15 (~b(s(s(elem!1)), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2946, 3681, 363, 362, 1102])).
% 1.97/2.15 tff(3683,plain,
% 1.97/2.15 (r(s(s(elem!1)), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[952, 3682])).
% 1.97/2.15 tff(3684,plain,
% 1.97/2.15 (r(s(s(z)), s(z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3683, 3298])).
% 1.97/2.15 tff(3685,plain,
% 1.97/2.15 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3314])).
% 1.97/2.15 tff(3686,plain,
% 1.97/2.15 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3297])).
% 1.97/2.15 tff(3687,plain,
% 1.97/2.15 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(z)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[3686, 3685])).
% 1.97/2.15 tff(3688,plain,
% 1.97/2.15 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(z)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3297])).
% 1.97/2.15 tff(3689,plain,
% 1.97/2.15 ((elem!1 = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 1.97/2.15 inference(symmetry,[status(thm)],[3688])).
% 1.97/2.15 tff(3690,plain,
% 1.97/2.15 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.97/2.15 inference(commutativity,[status(thm)],[])).
% 1.97/2.15 tff(3691,plain,
% 1.97/2.15 ((elem!1 = s(s(z))) <=> (z = s(s(z)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3314])).
% 1.97/2.15 tff(3692,plain,
% 1.97/2.15 ((elem!1 = s(s(z))) <=> (s(s(z)) = z)),
% 1.97/2.15 inference(transitivity,[status(thm)],[3691, 3690])).
% 1.97/2.15 tff(3693,plain,
% 1.97/2.15 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 1.97/2.15 inference(symmetry,[status(thm)],[3692])).
% 1.97/2.15 tff(3694,plain,
% 1.97/2.15 ((s(s(z)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.97/2.15 inference(transitivity,[status(thm)],[3693, 3689])).
% 1.97/2.15 tff(3695,plain,
% 1.97/2.15 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3694])).
% 1.97/2.15 tff(3696,plain,
% 1.97/2.15 (~(elem!1 = s(s(elem!1)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[97, 3695])).
% 1.97/2.15 tff(3697,plain,
% 1.97/2.15 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.97/2.15 inference(transitivity,[status(thm)],[3653, 3316, 3310])).
% 1.97/2.15 tff(3698,plain,
% 1.97/2.15 (b(s(s(elem!1)), elem!1)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[1102, 3697])).
% 1.97/2.15 tff(3699,plain,
% 1.97/2.15 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[2207])).
% 1.97/2.15 tff(3700,plain,
% 1.97/2.15 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.97/2.15 inference(symmetry,[status(thm)],[3699])).
% 1.97/2.15 tff(3701,plain,
% 1.97/2.15 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3700])).
% 1.97/2.15 tff(3702,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.97/2.15 tff(3703,plain,
% 1.97/2.15 (~b(z, s(z))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3702, 3701])).
% 1.97/2.15 tff(3704,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[362, 3703])).
% 1.97/2.15 tff(3705,plain,((~(z = elem!1)) | (~b(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(3706,plain,
% 1.97/2.15 (b(elem!1, s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3705, 362, 3646])).
% 1.97/2.15 tff(3707,plain,
% 1.97/2.15 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3314])).
% 1.97/2.15 tff(3708,plain,
% 1.97/2.15 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.97/2.15 inference(symmetry,[status(thm)],[3707])).
% 1.97/2.15 tff(3709,plain,
% 1.97/2.15 (b(s(z), elem!1)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[363, 3708])).
% 1.97/2.15 tff(3710,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3711,plain,
% 1.97/2.15 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3712,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3711])).
% 1.97/2.15 tff(3713,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[3712, 3710])).
% 1.97/2.15 tff(3714,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(3715,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3714, 3713])).
% 1.97/2.15 tff(3716,plain,
% 1.97/2.15 ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3715, 204])).
% 1.97/2.15 tff(3717,plain,
% 1.97/2.15 (~b(elem!1, s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3716, 3681, 3709, 3706, 3698])).
% 1.97/2.15 tff(3718,plain,
% 1.97/2.15 (r(elem!1, s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2351, 3717, 3696])).
% 1.97/2.15 tff(3719,plain,
% 1.97/2.15 (r(z, s(s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3718, 3687])).
% 1.97/2.15 tff(3720,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.97/2.15 tff(3721,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3722,plain,
% 1.97/2.15 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3723,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3722])).
% 1.97/2.15 tff(3724,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[3723, 3721])).
% 1.97/2.15 tff(3725,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(3726,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3725, 3724])).
% 1.97/2.15 tff(3727,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3726, 204, 2222, 3720, 363, 1102, 362])).
% 1.97/2.15 tff(3728,plain,((~b(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(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(3729,plain,
% 1.97/2.15 (~b(z, s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3728, 3681, 362, 1102, 363])).
% 1.97/2.15 tff(3730,plain,
% 1.97/2.15 (r(z, s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[2160, 3729])).
% 1.97/2.15 tff(3731,plain,
% 1.97/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3732,plain,
% 1.97/2.15 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(3733,plain,
% 1.97/2.15 (((~![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(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), 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(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3732])).
% 1.97/2.15 tff(3734,plain,
% 1.97/2.15 (((~![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(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), 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(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[3733, 3731])).
% 1.97/2.15 tff(3735,plain,
% 1.97/2.15 ((~![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(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(3736,plain,
% 1.97/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[3735, 3734])).
% 1.97/2.15 tff(3737,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3736, 67, 2142, 339, 1103])).
% 1.97/2.15 tff(3738,plain,((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(3739,plain,
% 1.97/2.15 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[3738, 3730, 339])).
% 1.97/2.15 tff(3740,plain,
% 1.97/2.15 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3295])).
% 1.97/2.15 tff(3741,plain,
% 1.97/2.15 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.97/2.15 inference(symmetry,[status(thm)],[3740])).
% 1.97/2.15 tff(3742,plain,
% 1.97/2.15 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[3314])).
% 1.97/2.16 tff(3743,plain,
% 1.97/2.16 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.97/2.16 inference(symmetry,[status(thm)],[3742])).
% 1.97/2.16 tff(3744,plain,
% 1.97/2.16 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3743, 3741])).
% 1.97/2.16 tff(3745,plain,
% 1.97/2.16 (r(elem!1, s(s(s(elem!1))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3, 3744])).
% 1.97/2.16 tff(3746,plain,
% 1.97/2.16 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[2290])).
% 1.97/2.16 tff(3747,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.16 inference(symmetry,[status(thm)],[3746])).
% 1.97/2.16 tff(3748,plain,
% 1.97/2.16 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3747])).
% 1.97/2.16 tff(3749,plain,
% 1.97/2.16 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3333, 3748])).
% 1.97/2.16 tff(3750,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.97/2.16 tff(3751,plain,
% 1.97/2.16 (s(s(s(z))) = s(s(elem!1))),
% 1.97/2.16 inference(transitivity,[status(thm)],[2271, 3750])).
% 1.97/2.16 tff(3752,plain,
% 1.97/2.16 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.97/2.16 inference(commutativity,[status(thm)],[])).
% 1.97/2.16 tff(3753,plain,
% 1.97/2.16 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[2207])).
% 1.97/2.16 tff(3754,plain,
% 1.97/2.16 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3753, 3752])).
% 1.97/2.16 tff(3755,plain,
% 1.97/2.16 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3754])).
% 1.97/2.16 tff(3756,plain,
% 1.97/2.16 (~(elem!1 = s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[300, 3755])).
% 1.97/2.16 tff(3757,plain,
% 1.97/2.16 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1289, 3756])).
% 1.97/2.16 tff(3758,plain,
% 1.97/2.16 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3651, 3757])).
% 1.97/2.16 tff(3759,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3758, 3751])).
% 1.97/2.16 tff(3760,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(3761,plain,
% 1.97/2.16 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3760, 2207])).
% 1.97/2.16 tff(3762,plain,
% 1.97/2.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3763,plain,
% 1.97/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3764,plain,
% 1.97/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3763, 3762])).
% 1.97/2.16 tff(3765,plain,
% 1.97/2.16 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3764, 50, 3761, 3749])).
% 1.97/2.16 tff(3766,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.97/2.16 tff(3767,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3768,plain,
% 1.97/2.16 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3769,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3768])).
% 1.97/2.16 tff(3770,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3769, 3767])).
% 1.97/2.16 tff(3771,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3772,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3771, 3770])).
% 1.97/2.16 tff(3773,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3772, 67, 2365, 3766, 3765])).
% 1.97/2.16 tff(3774,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | b(s(s(s(z))), s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(3775,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3774, 3718, 3646, 3745])).
% 1.97/2.16 tff(3776,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.97/2.16 tff(3777,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(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(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3778,plain,
% 1.97/2.16 (((~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(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3779,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3778])).
% 1.97/2.16 tff(3780,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3779, 3777])).
% 1.97/2.16 tff(3781,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3782,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 1.97/2.16 tff(3783,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3782, 67, 2142, 3, 3776])).
% 1.97/2.16 tff(3784,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(3785,plain,
% 1.97/2.16 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3784, 3730, 3])).
% 1.97/2.16 tff(3786,plain,
% 1.97/2.16 (b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1167, 3785, 3585])).
% 1.97/2.16 tff(3787,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3788,plain,
% 1.97/2.16 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3789,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3788])).
% 1.97/2.16 tff(3790,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3789, 3787])).
% 1.97/2.16 tff(3791,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3792,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3791, 3790])).
% 1.97/2.16 tff(3793,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3792, 204, 1140, 2323, 2141, 194, 1134])).
% 1.97/2.16 tff(3794,plain,((s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(3795,plain,
% 1.97/2.16 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3794, 3786, 3593, 3775, 3739, 194])).
% 1.97/2.16 tff(3796,plain,
% 1.97/2.16 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3795, 3579])).
% 1.97/2.16 tff(3797,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3798,plain,
% 1.97/2.16 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3799,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3798])).
% 1.97/2.16 tff(3800,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3799, 3797])).
% 1.97/2.16 tff(3801,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3802,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 1.97/2.16 tff(3803,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3802, 67, 339, 3796, 3719, 3684])).
% 1.97/2.16 tff(3804,plain,((~b(s(s(elem!1)), z)) | (~r(z, s(s(s(s(z)))))) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(3805,plain,
% 1.97/2.16 (~b(s(s(elem!1)), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3804, 3644, 3289, 3542, 339, 3633, 363, 3578, 1469, 3623, 3619])).
% 1.97/2.16 tff(3806,plain,
% 1.97/2.16 (r(s(s(elem!1)), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1099, 3805])).
% 1.97/2.16 tff(3807,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3808,plain,
% 1.97/2.16 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3809,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3808])).
% 1.97/2.16 tff(3810,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3809, 3807])).
% 1.97/2.16 tff(3811,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3812,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3811, 3810])).
% 1.97/2.16 tff(3813,plain,
% 1.97/2.16 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3812, 67, 900, 538])).
% 1.97/2.16 tff(3814,assumption,(~(s(s(s(s(z)))) = s(s(elem!1)))), introduced(assumption)).
% 1.97/2.16 tff(3815,plain,
% 1.97/2.16 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1132, 50, 3814, 3813])).
% 1.97/2.16 tff(3816,plain,
% 1.97/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(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(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3817,plain,
% 1.97/2.16 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3818,plain,
% 1.97/2.16 (((~![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(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(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(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3817])).
% 1.97/2.16 tff(3819,plain,
% 1.97/2.16 (((~![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(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(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(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3818, 3816])).
% 1.97/2.16 tff(3820,plain,
% 1.97/2.16 ((~![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(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3821,plain,
% 1.97/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 1.97/2.16 tff(3822,plain,
% 1.97/2.16 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3821, 67, 900, 538])).
% 1.97/2.16 tff(3823,plain,
% 1.97/2.16 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[1139, 3822, 1101])).
% 1.97/2.16 tff(3824,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3825,plain,
% 1.97/2.16 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(3826,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[3825])).
% 1.97/2.16 tff(3827,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[3826, 3824])).
% 1.97/2.16 tff(3828,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(3829,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[3828, 3827])).
% 1.97/2.16 tff(3830,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[3829, 204, 990, 3823, 456, 360, 3815])).
% 1.97/2.17 tff(3831,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(3832,plain,
% 1.97/2.17 (~b(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3831, 3806, 3609, 538, 3601, 3593, 3591])).
% 1.97/2.17 tff(3833,plain,
% 1.97/2.17 (r(s(s(elem!1)), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[952, 3832])).
% 1.97/2.17 tff(3834,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3812, 67, 900, 538, 1103])).
% 1.97/2.17 tff(3835,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(3836,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3835, 3806, 538])).
% 1.97/2.17 tff(3837,plain,
% 1.97/2.17 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3651, 628])).
% 1.97/2.17 tff(3838,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3839,plain,
% 1.97/2.17 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3840,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[3839])).
% 1.97/2.17 tff(3841,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[3840, 3838])).
% 1.97/2.17 tff(3842,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(3843,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[3842, 3841])).
% 1.97/2.17 tff(3844,plain,
% 1.97/2.17 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3843, 67, 938, 900, 308])).
% 1.97/2.17 tff(3845,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(elem!1)))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3335, 3844, 3837])).
% 1.97/2.17 tff(3846,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(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(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3847,plain,
% 1.97/2.17 (((~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(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3848,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(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(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[3847])).
% 1.97/2.17 tff(3849,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(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(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[3848, 3846])).
% 1.97/2.17 tff(3850,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(3851,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[3850, 3849])).
% 1.97/2.17 tff(3852,plain,
% 1.97/2.17 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3851, 67, 900, 308])).
% 1.97/2.17 tff(3853,plain,
% 1.97/2.17 (b(s(s(elem!1)), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1167, 3852, 628])).
% 1.97/2.17 tff(3854,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3794, 3542, 3853, 1101, 1135, 1129, 3845])).
% 1.97/2.17 tff(3855,plain,((~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(s(s(z)))), s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(3856,plain,
% 1.97/2.17 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3855, 3836, 308, 3593, 3806, 3833, 3585, 538])).
% 1.97/2.17 tff(3857,plain,
% 1.97/2.17 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[3856, 3579])).
% 1.97/2.17 tff(3858,plain,
% 1.97/2.17 (r(s(s(z)), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2909, 3806, 3647])).
% 1.97/2.17 tff(3859,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3428, 67, 3858, 538, 3857])).
% 1.97/2.17 tff(3860,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(s(z)))))), s(z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(3861,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3860, 238, 3289, 308, 339, 363, 3578, 1469, 3577, 538, 153])).
% 1.97/2.17 tff(3862,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[217, 3861, 184])).
% 1.97/2.17 tff(3863,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3864,plain,
% 1.97/2.17 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3865,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[3864])).
% 1.97/2.17 tff(3866,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[3865, 3863])).
% 1.97/2.17 tff(3867,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(3868,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 1.97/2.17 tff(3869,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3868, 204, 3542, 153, 3862, 3576, 3574])).
% 1.97/2.17 tff(3870,plain,(b(s(s(s(s(s(s(z)))))), s(z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(3871,plain,
% 1.97/2.17 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3870, 3558, 238, 538, 308, 339, 3546, 3544, 1469, 3535])).
% 1.97/2.17 tff(3872,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[161, 3544, 3521])).
% 1.97/2.17 tff(3873,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[55, 3872])).
% 1.97/2.17 tff(3874,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2434, 50, 706, 2881])).
% 1.97/2.17 tff(3875,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[796, 50, 2739, 3447])).
% 1.97/2.17 tff(3876,plain,
% 1.97/2.17 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3259, 67, 824, 538])).
% 1.97/2.17 tff(3877,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[766, 3876])).
% 1.97/2.17 tff(3878,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3879,plain,
% 1.97/2.17 (((~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(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3880,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[3879])).
% 1.97/2.17 tff(3881,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[3880, 3878])).
% 1.97/2.17 tff(3882,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(3883,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[3882, 3881])).
% 1.97/2.17 tff(3884,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3883, 204, 3877, 3875, 3542, 153, 3874])).
% 1.97/2.17 tff(3885,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(3886,plain,
% 1.97/2.17 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3885, 3535, 538, 308])).
% 1.97/2.17 tff(3887,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[822, 3886])).
% 1.97/2.17 tff(3888,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3889,plain,
% 1.97/2.17 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(3890,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[3889])).
% 1.97/2.17 tff(3891,plain,
% 1.97/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[3890, 3888])).
% 1.97/2.17 tff(3892,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(3893,plain,
% 1.97/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[3892, 3891])).
% 1.97/2.18 tff(3894,plain,
% 1.97/2.18 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3893, 67, 656, 110, 1])).
% 1.97/2.18 tff(3895,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.97/2.18 tff(3896,plain,
% 1.97/2.18 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[850, 50, 3895, 3894])).
% 1.97/2.18 tff(3897,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3898,plain,
% 1.97/2.18 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3899,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[3898])).
% 1.97/2.18 tff(3900,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[3899, 3897])).
% 1.97/2.18 tff(3901,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(3902,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[3901, 3900])).
% 1.97/2.18 tff(3903,plain,
% 1.97/2.18 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3902, 204, 784, 1469, 3577])).
% 1.97/2.18 tff(3904,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3903, 3896, 3216])).
% 1.97/2.18 tff(3905,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(3906,plain,
% 1.97/2.18 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3905, 3871, 339, 1469, 3521, 3544, 3887])).
% 1.97/2.18 tff(3907,plain,
% 1.97/2.18 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[766, 3906])).
% 1.97/2.18 tff(3908,plain,
% 1.97/2.18 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3883, 204, 785, 194, 153])).
% 1.97/2.18 tff(3909,plain,
% 1.97/2.18 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3908, 3175])).
% 1.97/2.18 tff(3910,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2434, 50, 706, 3909])).
% 1.97/2.18 tff(3911,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3912,plain,
% 1.97/2.18 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3913,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[3912])).
% 1.97/2.18 tff(3914,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[3913, 3911])).
% 1.97/2.18 tff(3915,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(3916,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[3915, 3914])).
% 1.97/2.18 tff(3917,plain,
% 1.97/2.18 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3916, 204, 456, 785, 3175, 360])).
% 1.97/2.18 tff(3918,plain,
% 1.97/2.18 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[721, 50, 669, 3917])).
% 1.97/2.18 tff(3919,plain,
% 1.97/2.18 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3182, 3175])).
% 1.97/2.18 tff(3920,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[675, 50, 671, 3919])).
% 1.97/2.18 tff(3921,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(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(z))))) | (~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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3922,plain,
% 1.97/2.18 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(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)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3923,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(z), 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(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)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[3922])).
% 1.97/2.18 tff(3924,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(z), 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(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)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[3923, 3921])).
% 1.97/2.18 tff(3925,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(3926,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[3925, 3924])).
% 1.97/2.18 tff(3927,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3926, 67, 445, 3920, 3918, 3910])).
% 1.97/2.18 tff(3928,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(3929,plain,
% 1.97/2.18 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3928, 3907, 445, 3542, 3535, 3546, 3887, 3873, 456])).
% 1.97/2.18 tff(3930,plain,
% 1.97/2.18 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[796, 50, 3929, 2739])).
% 1.97/2.18 tff(3931,plain,
% 1.97/2.18 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3168, 3930, 538])).
% 1.97/2.18 tff(3932,plain,
% 1.97/2.18 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3155, 50, 3931, 3151])).
% 1.97/2.18 tff(3933,plain,
% 1.97/2.18 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3902, 204, 3887, 1469, 3548])).
% 1.97/2.18 tff(3934,plain,
% 1.97/2.18 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3933, 3932])).
% 1.97/2.18 tff(3935,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[850, 50, 3934, 3871])).
% 1.97/2.18 tff(3936,plain,
% 1.97/2.18 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3868, 204, 3542, 3535, 3540, 3538])).
% 1.97/2.18 tff(3937,plain,
% 1.97/2.18 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[218, 3936])).
% 1.97/2.18 tff(3938,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3128, 3932, 3550, 3887, 3546])).
% 1.97/2.18 tff(3939,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3940,plain,
% 1.97/2.18 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3941,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[3940])).
% 1.97/2.18 tff(3942,plain,
% 1.97/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[3941, 3939])).
% 1.97/2.18 tff(3943,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(3944,plain,
% 1.97/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[3943, 3942])).
% 1.97/2.18 tff(3945,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3944, 67, 3938, 3937, 3930, 3935])).
% 1.97/2.18 tff(3946,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(3947,plain,
% 1.97/2.18 (~r(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3946, 3533, 3523, 1469, 456, 339, 238, 57])).
% 1.97/2.18 tff(3948,plain,
% 1.97/2.18 (b(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[478, 3947])).
% 1.97/2.18 tff(3949,plain,
% 1.97/2.18 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3617, 3948, 3527, 3525, 456])).
% 1.97/2.18 tff(3950,plain,
% 1.97/2.18 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[151, 3949])).
% 1.97/2.18 tff(3951,plain,
% 1.97/2.18 (~r(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[347, 3950, 339])).
% 1.97/2.18 tff(3952,plain,
% 1.97/2.18 (b(z, s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[259, 3951])).
% 1.97/2.18 tff(3953,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1592, 204, 3529, 3952, 3948, 456, 3525])).
% 1.97/2.18 tff(3954,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | b(s(s(s(s(s(s(z)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(3955,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3954, 3516, 2591, 3494, 3504])).
% 1.97/2.18 tff(3956,plain,
% 1.97/2.18 (b(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[558, 3955])).
% 1.97/2.18 tff(3957,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3958,plain,
% 1.97/2.18 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(3959,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[3958])).
% 1.97/2.18 tff(3960,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[3959, 3957])).
% 1.97/2.18 tff(3961,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(3962,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 1.97/2.18 tff(3963,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3962, 204, 363, 3956, 3520, 3004, 3473])).
% 1.97/2.18 tff(3964,plain,((~b(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(3965,plain,
% 1.97/2.18 (~b(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3964, 137])).
% 1.97/2.18 tff(3966,plain,
% 1.97/2.18 (r(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[376, 3965])).
% 1.97/2.18 tff(3967,plain,
% 1.97/2.18 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2659, 3966, 2592])).
% 1.97/2.18 tff(3968,plain,
% 1.97/2.18 (b(s(s(s(s(s(s(z)))))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[641, 3967])).
% 1.97/2.18 tff(3969,plain,
% 1.97/2.18 (~r(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1773, 308, 3966])).
% 1.97/2.18 tff(3970,plain,
% 1.97/2.18 (b(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[478, 3969])).
% 1.97/2.18 tff(3971,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[397, 308, 3966])).
% 1.97/2.18 tff(3972,plain,
% 1.97/2.18 (b(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[558, 3971])).
% 1.97/2.18 tff(3973,plain,
% 1.97/2.18 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[710, 50, 707, 2850])).
% 1.97/2.18 tff(3974,plain,
% 1.97/2.18 (~r(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1773, 308, 389])).
% 1.97/2.18 tff(3975,plain,
% 1.97/2.18 (b(s(z), s(s(s(z))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[478, 3974])).
% 1.97/2.18 tff(3976,plain,
% 1.97/2.18 (~r(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[397, 308, 389])).
% 1.97/2.18 tff(3977,plain,
% 1.97/2.18 (b(s(s(s(z))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[558, 3976])).
% 1.97/2.18 tff(3978,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[728, 204, 3977, 3975, 832, 3973, 2398])).
% 1.97/2.18 tff(3979,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(3980,plain,
% 1.97/2.18 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3979, 308, 3966])).
% 1.97/2.18 tff(3981,plain,
% 1.97/2.18 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[822, 3980])).
% 1.97/2.19 tff(3982,plain,
% 1.97/2.19 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[536, 339, 389])).
% 1.97/2.19 tff(3983,plain,
% 1.97/2.19 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[431, 3982])).
% 1.97/2.19 tff(3984,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(3985,plain,
% 1.97/2.19 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(3986,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[3985])).
% 1.97/2.19 tff(3987,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[3986, 3984])).
% 1.97/2.19 tff(3988,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(3989,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[3988, 3987])).
% 1.97/2.19 tff(3990,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3989, 204, 3977, 3975, 3983, 3627, 360])).
% 1.97/2.19 tff(3991,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(3992,plain,
% 1.97/2.19 (~r(z, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3991, 308, 3004, 3966])).
% 1.97/2.19 tff(3993,plain,
% 1.97/2.19 (b(z, s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[357, 3992])).
% 1.97/2.19 tff(3994,plain,
% 1.97/2.19 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3043, 2, 2592])).
% 1.97/2.19 tff(3995,plain,
% 1.97/2.19 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[190, 3994])).
% 1.97/2.19 tff(3996,plain,
% 1.97/2.19 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1519, 3995, 359, 361, 3968])).
% 1.97/2.19 tff(3997,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[218, 3996])).
% 1.97/2.19 tff(3998,plain,
% 1.97/2.19 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2474, 3997, 137])).
% 1.97/2.19 tff(3999,plain,
% 1.97/2.19 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[284, 3998])).
% 1.97/2.19 tff(4000,plain,
% 1.97/2.19 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3023, 204, 444, 3004, 3995, 3999])).
% 1.97/2.19 tff(4001,plain,
% 1.97/2.19 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[108, 4000])).
% 1.97/2.19 tff(4002,plain,
% 1.97/2.19 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2724, 4001, 444, 566, 2])).
% 1.97/2.19 tff(4003,plain,
% 1.97/2.19 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[766, 4002])).
% 1.97/2.19 tff(4004,plain,
% 1.97/2.19 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3485, 204, 361, 359, 3968])).
% 1.97/2.19 tff(4005,plain,
% 1.97/2.19 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4004, 3995])).
% 1.97/2.19 tff(4006,plain,
% 1.97/2.19 (r(z, s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[604, 50, 601, 4005])).
% 1.97/2.19 tff(4007,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1245, 67, 286, 110, 2032])).
% 1.97/2.19 tff(4008,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(4009,plain,
% 1.97/2.19 (~r(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4008, 4006, 2592])).
% 1.97/2.19 tff(4010,plain,
% 1.97/2.19 (b(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[306, 4009])).
% 1.97/2.19 tff(4011,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4012,plain,
% 1.97/2.19 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4013,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[4012])).
% 1.97/2.19 tff(4014,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[4013, 4011])).
% 1.97/2.19 tff(4015,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(4016,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 1.97/2.19 tff(4017,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4016, 204, 4010, 361, 4003, 784, 3004])).
% 1.97/2.19 tff(4018,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(4019,plain,
% 1.97/2.19 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4018, 3993, 3981, 3972, 3970, 137, 2976])).
% 1.97/2.19 tff(4020,plain,
% 1.97/2.19 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[431, 4019])).
% 1.97/2.19 tff(4021,plain,
% 1.97/2.19 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3989, 204, 3972, 3970, 4020, 3004])).
% 1.97/2.19 tff(4022,plain,
% 1.97/2.19 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[108, 4021])).
% 1.97/2.19 tff(4023,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4024,plain,
% 1.97/2.19 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4025,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[4024])).
% 1.97/2.19 tff(4026,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[4025, 4023])).
% 1.97/2.19 tff(4027,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(4028,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[4027, 4026])).
% 1.97/2.19 tff(4029,plain,
% 1.97/2.19 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4028, 204, 456, 784, 359])).
% 1.97/2.19 tff(4030,plain,
% 1.97/2.19 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4029, 785])).
% 1.97/2.19 tff(4031,plain,
% 1.97/2.19 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[721, 50, 669, 4030])).
% 1.97/2.19 tff(4032,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4033,plain,
% 1.97/2.19 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4034,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[4033])).
% 1.97/2.19 tff(4035,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[4034, 4032])).
% 1.97/2.19 tff(4036,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(4037,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 1.97/2.19 tff(4038,plain,
% 1.97/2.19 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4037, 204, 361, 784, 359])).
% 1.97/2.19 tff(4039,plain,
% 1.97/2.19 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4038, 785])).
% 1.97/2.19 tff(4040,plain,
% 1.97/2.19 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3157, 4039])).
% 1.97/2.19 tff(4041,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(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), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4042,plain,
% 1.97/2.19 (((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(4043,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(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(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[4042])).
% 1.97/2.19 tff(4044,plain,
% 1.97/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(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(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[4043, 4041])).
% 1.97/2.19 tff(4045,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), z)))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(4046,plain,
% 1.97/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 1.97/2.19 tff(4047,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4046, 67, 389, 4040, 4031])).
% 1.97/2.19 tff(4048,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(4049,plain,
% 1.97/2.19 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4048, 4020, 3966, 3981, 2976, 3993])).
% 1.97/2.19 tff(4050,plain,
% 1.97/2.20 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[766, 4049])).
% 1.97/2.20 tff(4051,plain,
% 1.97/2.20 (((~![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(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(4052,plain,
% 1.97/2.20 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(4053,plain,
% 1.97/2.20 (((~![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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[4052])).
% 1.97/2.20 tff(4054,plain,
% 1.97/2.20 (((~![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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(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(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.97/2.20 inference(transitivity,[status(thm)],[4053, 4051])).
% 1.97/2.20 tff(4055,plain,
% 1.97/2.20 ((~![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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(4056,plain,
% 1.97/2.20 ((~![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(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[4055, 4054])).
% 1.97/2.20 tff(4057,plain,
% 1.97/2.20 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[4056, 67, 4050, 4022])).
% 1.97/2.20 tff(4058,plain,
% 1.97/2.20 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[2434, 50, 706, 4057])).
% 1.97/2.20 tff(4059,plain,
% 1.97/2.20 (~b(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[438, 204, 4020, 3993, 3004, 2976])).
% 2.04/2.20 tff(4060,plain,
% 2.04/2.20 (r(z, s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[306, 4059])).
% 2.04/2.20 tff(4061,plain,
% 2.04/2.20 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4008, 4060, 2592])).
% 2.04/2.20 tff(4062,plain,
% 2.04/2.20 (b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[604, 50, 601, 4061])).
% 2.04/2.20 tff(4063,plain,
% 2.04/2.20 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3485, 204, 3993, 2976, 3968])).
% 2.04/2.20 tff(4064,plain,
% 2.04/2.20 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4063, 4062])).
% 2.04/2.20 tff(4065,plain,
% 2.04/2.20 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[190, 4064])).
% 2.04/2.20 tff(4066,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[507, 4065, 4022])).
% 2.04/2.20 tff(4067,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[134, 4066])).
% 2.04/2.20 tff(4068,plain,
% 2.04/2.20 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 2.04/2.20 inference(commutativity,[status(thm)],[])).
% 2.04/2.20 tff(4069,plain,
% 2.04/2.20 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 2.04/2.20 inference(symmetry,[status(thm)],[4068])).
% 2.04/2.20 tff(4070,plain,
% 2.04/2.20 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3485, 204, 358, 2976, 3968, 1708])).
% 2.04/2.20 tff(4071,plain,
% 2.04/2.20 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[190, 4070])).
% 2.04/2.20 tff(4072,plain,
% 2.04/2.20 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3043, 4071, 2592])).
% 2.04/2.20 tff(4073,plain,
% 2.04/2.20 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[431, 4072])).
% 2.04/2.20 tff(4074,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3989, 204, 3972, 3970, 4073, 3004])).
% 2.04/2.20 tff(4075,plain,
% 2.04/2.20 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[108, 4074])).
% 2.04/2.20 tff(4076,plain,
% 2.04/2.20 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4048, 4073, 3966, 3981, 2976, 358])).
% 2.04/2.20 tff(4077,plain,
% 2.04/2.20 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[766, 4076])).
% 2.04/2.20 tff(4078,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[682, 67, 4077, 4075])).
% 2.04/2.20 tff(4079,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[710, 50, 707, 4078])).
% 2.04/2.20 tff(4080,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4081,plain,
% 2.04/2.20 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4082,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4081])).
% 2.04/2.20 tff(4083,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4082, 4080])).
% 2.04/2.20 tff(4084,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4085,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4084, 4083])).
% 2.04/2.20 tff(4086,plain,
% 2.04/2.20 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4085, 204, 2976, 3968, 1708])).
% 2.04/2.20 tff(4087,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4086, 358])).
% 2.04/2.20 tff(4088,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[218, 4087])).
% 2.04/2.20 tff(4089,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[518, 4088, 137])).
% 2.04/2.20 tff(4090,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[134, 4089])).
% 2.04/2.20 tff(4091,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4092,plain,
% 2.04/2.20 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4093,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4092])).
% 2.04/2.20 tff(4094,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4093, 4091])).
% 2.04/2.20 tff(4095,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4096,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4095, 4094])).
% 2.04/2.20 tff(4097,plain,
% 2.04/2.20 ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4096, 204, 3981, 3968, 4090])).
% 2.04/2.20 tff(4098,plain,
% 2.04/2.20 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4097, 4079])).
% 2.04/2.20 tff(4099,plain,
% 2.04/2.20 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3893, 67, 4077, 2592, 4071])).
% 2.04/2.20 tff(4100,plain,
% 2.04/2.20 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[850, 50, 4099])).
% 2.04/2.20 tff(4101,plain,
% 2.04/2.20 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4100, 4098])).
% 2.04/2.20 tff(4102,plain,
% 2.04/2.20 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4101])).
% 2.04/2.20 tff(4103,plain,
% 2.04/2.20 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[664, 4102, 121])).
% 2.04/2.20 tff(4104,plain,
% 2.04/2.20 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4103])).
% 2.04/2.20 tff(4105,plain,
% 2.04/2.20 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[875, 4104, 119])).
% 2.04/2.20 tff(4106,plain,
% 2.04/2.20 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4105])).
% 2.04/2.20 tff(4107,plain,
% 2.04/2.20 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[699, 4106, 20])).
% 2.04/2.20 tff(4108,plain,
% 2.04/2.20 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4107])).
% 2.04/2.20 tff(4109,plain,
% 2.04/2.20 (s(s(elem!1)) = s(s(z))),
% 2.04/2.20 inference(transitivity,[status(thm)],[754, 4108, 83])).
% 2.04/2.20 tff(4110,plain,
% 2.04/2.20 ((s(s(elem!1)) = s(z)) <=> (s(s(z)) = s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4109])).
% 2.04/2.20 tff(4111,plain,
% 2.04/2.20 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(z)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4110, 4069])).
% 2.04/2.20 tff(4112,plain,
% 2.04/2.20 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4111])).
% 2.04/2.20 tff(4113,plain,
% 2.04/2.20 (~(s(z) = s(s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[924, 4112])).
% 2.04/2.20 tff(4114,plain,
% 2.04/2.20 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 2.04/2.20 inference(commutativity,[status(thm)],[])).
% 2.04/2.20 tff(4115,plain,
% 2.04/2.20 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[4114])).
% 2.04/2.20 tff(4116,plain,
% 2.04/2.20 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4115])).
% 2.04/2.20 tff(4117,plain,
% 2.04/2.20 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[182, 4116])).
% 2.04/2.20 tff(4118,plain,
% 2.04/2.20 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4107])).
% 2.04/2.20 tff(4119,plain,
% 2.04/2.20 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[4118])).
% 2.04/2.20 tff(4120,plain,
% 2.04/2.20 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4109])).
% 2.04/2.20 tff(4121,plain,
% 2.04/2.20 (s(elem!1) = s(z)),
% 2.04/2.20 inference(transitivity,[status(thm)],[919, 4120, 78])).
% 2.04/2.20 tff(4122,plain,
% 2.04/2.20 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4121])).
% 2.04/2.20 tff(4123,plain,
% 2.04/2.20 (elem!1 = z),
% 2.04/2.20 inference(transitivity,[status(thm)],[1009, 4122, 15])).
% 2.04/2.20 tff(4124,plain,
% 2.04/2.20 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4123])).
% 2.04/2.20 tff(4125,plain,
% 2.04/2.20 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[4124])).
% 2.04/2.20 tff(4126,plain,
% 2.04/2.20 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4125, 4119])).
% 2.04/2.20 tff(4127,plain,
% 2.04/2.20 (r(elem!1, s(s(s(elem!1))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[3, 4126])).
% 2.04/2.20 tff(4128,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(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4129,plain,
% 2.04/2.20 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4130,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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4129])).
% 2.04/2.20 tff(4131,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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4130, 4128])).
% 2.04/2.20 tff(4132,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(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4133,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 2.04/2.20 tff(4134,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4133, 67, 3, 2791, 2296])).
% 2.04/2.20 tff(4135,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(4136,plain,
% 2.04/2.20 (~r(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4135, 2791, 3])).
% 2.04/2.20 tff(4137,plain,
% 2.04/2.20 (b(s(s(z)), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3376, 4136])).
% 2.04/2.20 tff(4138,assumption,(~(s(z) = s(s(z)))), introduced(assumption)).
% 2.04/2.20 tff(4139,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 2.04/2.20 tff(4140,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(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4141,plain,
% 2.04/2.20 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4142,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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4141])).
% 2.04/2.20 tff(4143,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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4142, 4140])).
% 2.04/2.20 tff(4144,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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4145,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4144, 4143])).
% 2.04/2.20 tff(4146,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4145, 67, 389, 2791, 4139])).
% 2.04/2.20 tff(4147,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(4148,plain,
% 2.04/2.20 (~r(s(z), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4147, 2791, 389])).
% 2.04/2.20 tff(4149,plain,
% 2.04/2.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4150,plain,
% 2.04/2.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4151,plain,
% 2.04/2.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4150, 4149])).
% 2.04/2.20 tff(4152,plain,
% 2.04/2.20 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4151, 50])).
% 2.04/2.20 tff(4153,plain,
% 2.04/2.20 (b(s(z), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4152, 4148, 4138])).
% 2.04/2.20 tff(4154,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2900, 2895])).
% 2.04/2.21 tff(4155,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4156,plain,
% 2.04/2.21 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4157,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4156])).
% 2.04/2.21 tff(4158,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4157, 4155])).
% 2.04/2.21 tff(4159,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4160,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4159, 4158])).
% 2.04/2.21 tff(4161,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4160, 204, 3977, 3975, 4154, 4153, 4137])).
% 2.04/2.21 tff(4162,plain,((~r(s(s(z)), z)) | (s(z) = s(s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(4163,plain,
% 2.04/2.21 (~r(s(s(z)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4162, 4113, 3966, 3, 308])).
% 2.04/2.21 tff(4164,plain,
% 2.04/2.21 (b(s(s(z)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3393, 4163])).
% 2.04/2.21 tff(4165,plain,
% 2.04/2.21 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2900, 3340])).
% 2.04/2.21 tff(4166,plain,
% 2.04/2.21 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[3314])).
% 2.04/2.21 tff(4167,plain,
% 2.04/2.21 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[3297])).
% 2.04/2.21 tff(4168,plain,
% 2.04/2.21 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4167, 4166])).
% 2.04/2.21 tff(4169,plain,
% 2.04/2.21 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3342, 3340, 3293])).
% 2.04/2.21 tff(4170,plain,
% 2.04/2.21 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3774, 4169, 3646, 3766])).
% 2.04/2.21 tff(4171,plain,
% 2.04/2.21 (b(elem!1, s(s(elem!1)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2351, 4170, 3696])).
% 2.04/2.21 tff(4172,plain,
% 2.04/2.21 (b(z, s(s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4171, 4168])).
% 2.04/2.21 tff(4173,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4174,plain,
% 2.04/2.21 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4175,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4174])).
% 2.04/2.21 tff(4176,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4175, 4173])).
% 2.04/2.21 tff(4177,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4178,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 2.04/2.21 tff(4179,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4178, 204, 361, 359, 4172, 3300])).
% 2.04/2.21 tff(4180,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3421, 4179])).
% 2.04/2.21 tff(4181,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(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4182,plain,
% 2.04/2.21 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4183,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(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4182])).
% 2.04/2.21 tff(4184,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(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4183, 4181])).
% 2.04/2.21 tff(4185,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(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4186,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 2.04/2.21 tff(4187,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4186, 67, 4180, 378, 4165])).
% 2.04/2.21 tff(4188,plain,(b(s(s(s(z))), s(s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(4189,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4188, 4075, 358, 2976, 4164, 4101, 4127])).
% 2.04/2.21 tff(4190,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4191,plain,
% 2.04/2.21 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4192,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4191])).
% 2.04/2.21 tff(4193,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4192, 4190])).
% 2.04/2.21 tff(4194,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4195,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4194, 4193])).
% 2.04/2.21 tff(4196,plain,
% 2.04/2.21 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4195, 204, 4164, 3968, 4090])).
% 2.04/2.21 tff(4197,plain,
% 2.04/2.21 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4196, 4189])).
% 2.04/2.21 tff(4198,plain,
% 2.04/2.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4199,plain,
% 2.04/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4200,plain,
% 2.04/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 2.04/2.21 tff(4201,plain,
% 2.04/2.21 ((s(s(z)) = s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4200, 50, 4197])).
% 2.04/2.21 tff(4202,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4201, 4117])).
% 2.04/2.21 tff(4203,plain,
% 2.04/2.21 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2474, 4088, 137])).
% 2.04/2.21 tff(4204,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[284, 4203])).
% 2.04/2.21 tff(4205,plain,
% 2.04/2.21 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2694, 204, 3972, 3970, 4090, 4204])).
% 2.04/2.21 tff(4206,plain,
% 2.04/2.21 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[489, 50, 4205, 249])).
% 2.04/2.21 tff(4207,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(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4208,plain,
% 2.04/2.21 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4209,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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4208])).
% 2.04/2.21 tff(4210,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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4209, 4207])).
% 2.04/2.21 tff(4211,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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4212,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(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 2.04/2.21 tff(4213,plain,
% 2.04/2.21 (~r(s(z), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4212, 67, 4206, 4202])).
% 2.04/2.21 tff(4214,plain,
% 2.04/2.21 (b(s(z), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4152, 4213, 4113])).
% 2.04/2.21 tff(4215,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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4216,plain,
% 2.04/2.21 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4217,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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4216])).
% 2.04/2.21 tff(4218,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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4217, 4215])).
% 2.04/2.22 tff(4219,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(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4220,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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4219, 4218])).
% 2.04/2.22 tff(4221,plain,
% 2.04/2.22 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4220, 67, 137, 4088, 4202])).
% 2.04/2.22 tff(4222,plain,
% 2.04/2.22 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3438, 4221])).
% 2.04/2.22 tff(4223,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4224,plain,
% 2.04/2.22 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4225,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4224])).
% 2.04/2.22 tff(4226,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4225, 4223])).
% 2.04/2.22 tff(4227,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4228,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4227, 4226])).
% 2.04/2.22 tff(4229,plain,
% 2.04/2.22 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4228, 204, 4073, 2976, 4164])).
% 2.04/2.22 tff(4230,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4229, 4222, 4214])).
% 2.04/2.22 tff(4231,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4232,plain,
% 2.04/2.22 (~r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4231, 4062, 308, 137])).
% 2.04/2.22 tff(4233,plain,
% 2.04/2.22 (b(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[259, 4232])).
% 2.04/2.22 tff(4234,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4235,plain,
% 2.04/2.22 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4236,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(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(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4235])).
% 2.04/2.22 tff(4237,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(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(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4236, 4234])).
% 2.04/2.22 tff(4238,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4239,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 2.04/2.22 tff(4240,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4239, 204, 4233, 3981, 4067, 4062, 4058])).
% 2.04/2.22 tff(4241,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4242,plain,
% 2.04/2.22 (~r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4241, 137])).
% 2.04/2.22 tff(4243,plain,
% 2.04/2.22 (b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[402, 4242])).
% 2.04/2.22 tff(4244,plain,
% 2.04/2.22 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2604, 67, 57, 2592])).
% 2.04/2.22 tff(4245,plain,
% 2.04/2.22 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[284, 4244])).
% 2.04/2.22 tff(4246,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[116, 67, 57, 2592])).
% 2.04/2.22 tff(4247,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[134, 4246])).
% 2.04/2.22 tff(4248,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1783, 4247, 4245, 4243, 3968, 442])).
% 2.04/2.22 tff(4249,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4250,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4249, 137])).
% 2.04/2.22 tff(4251,plain,
% 2.04/2.22 (b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[558, 4250])).
% 2.04/2.22 tff(4252,plain,
% 2.04/2.22 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3013, 1538])).
% 2.04/2.22 tff(4253,plain,
% 2.04/2.22 (r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[604, 50, 601, 4252])).
% 2.04/2.22 tff(4254,plain,
% 2.04/2.22 (~r(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4008, 4253, 110])).
% 2.04/2.22 tff(4255,plain,
% 2.04/2.22 (b(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[306, 4254])).
% 2.04/2.22 tff(4256,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))))), z)) | (~b(s(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(X1, 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(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4257,plain,
% 2.04/2.22 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4258,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(X1, 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(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4257])).
% 2.04/2.22 tff(4259,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(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(X1, 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(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4258, 4256])).
% 2.04/2.22 tff(4260,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4261,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4260, 4259])).
% 2.04/2.22 tff(4262,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4261, 204, 4255, 444, 404, 1469, 1538])).
% 2.04/2.22 tff(4263,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4264,plain,
% 2.04/2.22 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4263, 1574, 4243, 3968, 2592, 4251])).
% 2.04/2.22 tff(4265,plain,
% 2.04/2.22 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[284, 4264])).
% 2.04/2.22 tff(4266,plain,
% 2.04/2.22 (~r(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2643, 4265, 2592])).
% 2.04/2.22 tff(4267,plain,
% 2.04/2.22 (b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[478, 4266])).
% 2.04/2.22 tff(4268,plain,
% 2.04/2.22 (~b(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1533, 4267, 4243, 4251, 1574])).
% 2.04/2.22 tff(4269,plain,
% 2.04/2.22 (r(z, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[306, 4268])).
% 2.04/2.22 tff(4270,plain,
% 2.04/2.22 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[536, 339, 3966])).
% 2.04/2.22 tff(4271,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[431, 4270])).
% 2.04/2.22 tff(4272,plain,
% 2.04/2.22 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3989, 204, 4251, 4271, 3004])).
% 2.04/2.22 tff(4273,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4272, 4267])).
% 2.04/2.22 tff(4274,plain,
% 2.04/2.22 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[108, 4273])).
% 2.04/2.22 tff(4275,plain,
% 2.04/2.22 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4056, 67, 656, 378])).
% 2.04/2.22 tff(4276,plain,
% 2.04/2.22 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2434, 50, 706, 4275])).
% 2.04/2.22 tff(4277,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(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4278,plain,
% 2.04/2.22 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4279,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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4278])).
% 2.04/2.22 tff(4280,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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4279, 4277])).
% 2.04/2.22 tff(4281,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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4282,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4281, 4280])).
% 2.04/2.22 tff(4283,plain,
% 2.04/2.22 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4282, 67, 286, 339, 656])).
% 2.04/2.22 tff(4284,plain,
% 2.04/2.22 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[822, 4283])).
% 2.04/2.22 tff(4285,plain,
% 2.04/2.22 (b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[402, 1912])).
% 2.04/2.22 tff(4286,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3224, 204, 1924, 4285, 4284, 3216, 4276])).
% 2.04/2.22 tff(4287,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4288,plain,
% 2.04/2.22 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4287, 4274, 339, 4269])).
% 2.04/2.22 tff(4289,plain,
% 2.04/2.22 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[766, 4288])).
% 2.04/2.22 tff(4290,plain,
% 2.04/2.22 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4008, 4269, 2592])).
% 2.04/2.22 tff(4291,plain,
% 2.04/2.22 (b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[604, 50, 601, 4290])).
% 2.04/2.22 tff(4292,plain,
% 2.04/2.22 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1699, 4265, 137])).
% 2.04/2.22 tff(4293,plain,
% 2.04/2.22 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[190, 4292])).
% 2.04/2.22 tff(4294,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2474, 4265, 137])).
% 2.04/2.22 tff(4295,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[218, 4294])).
% 2.04/2.22 tff(4296,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4297,plain,
% 2.04/2.22 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4298,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(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(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4297])).
% 2.04/2.22 tff(4299,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(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(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4298, 4296])).
% 2.04/2.22 tff(4300,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4301,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4300, 4299])).
% 2.04/2.22 tff(4302,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4301, 204, 4295, 4293, 3968, 4291])).
% 2.04/2.22 tff(4303,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[335, 4302])).
% 2.04/2.22 tff(4304,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3173, 3447])).
% 2.04/2.22 tff(4305,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4306,plain,
% 2.04/2.22 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4307,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4306])).
% 2.04/2.23 tff(4308,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4307, 4305])).
% 2.04/2.23 tff(4309,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(4310,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4309, 4308])).
% 2.04/2.23 tff(4311,plain,
% 2.04/2.23 ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4310, 204, 456, 785, 360])).
% 2.04/2.23 tff(4312,plain,
% 2.04/2.23 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4311, 4304])).
% 2.04/2.23 tff(4313,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[675, 50, 2397, 671, 4312])).
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% 2.04/2.23 inference(rewrite,[status(thm)],[])).
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% 2.04/2.23 inference(monotonicity,[status(thm)],[4338])).
% 2.04/2.23 tff(4340,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4339, 4337])).
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% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
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% 2.04/2.23 inference(modus_ponens,[status(thm)],[4341, 4340])).
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% 2.04/2.23 inference(unit_resolution,[status(thm)],[4342, 204, 785, 4327, 4325])).
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% 2.04/2.23 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4343, 4333])).
% 2.04/2.23 tff(4345,plain,
% 2.04/2.23 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
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% 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(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(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(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4347,plain,
% 2.04/2.23 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4348,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(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4347])).
% 2.04/2.23 tff(4349,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(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4348, 4346])).
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% 2.04/2.23 tff(4351,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4350, 4349])).
% 2.04/2.23 tff(4352,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4351, 67, 137, 3159, 4345, 4336])).
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% 2.04/2.23 tff(4354,plain,
% 2.04/2.23 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
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% 2.04/2.23 tff(4355,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4354])).
% 2.04/2.23 tff(4356,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(symmetry,[status(thm)],[4355])).
% 2.04/2.23 tff(4357,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4329, 4356])).
% 2.04/2.23 tff(4358,plain,
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% 2.04/2.23 inference(unit_resolution,[status(thm)],[3171, 4357])).
% 2.04/2.23 tff(4359,plain,(b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(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(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4360,plain,
% 2.04/2.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4359, 1574, 137, 4316, 4289])).
% 2.04/2.23 tff(4361,plain,
% 2.04/2.23 ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4310, 204, 4271, 4289, 3004])).
% 2.04/2.23 tff(4362,plain,
% 2.04/2.23 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4361, 4360])).
% 2.04/2.23 tff(4363,assumption,(~b(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 2.04/2.23 tff(4364,plain,
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% 2.04/2.23 inference(unit_resolution,[status(thm)],[675, 50, 672, 671, 4363])).
% 2.04/2.23 tff(4365,plain,(b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4366,plain,
% 2.04/2.23 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4365, 4362])).
% 2.04/2.23 tff(4367,plain,
% 2.04/2.23 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3191, 67, 2592, 4366])).
% 2.04/2.23 tff(4368,plain,
% 2.04/2.23 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3235, 204, 4289, 4360, 4295, 4293])).
% 2.04/2.23 tff(4369,plain,
% 2.04/2.23 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2402, 50, 4368])).
% 2.04/2.23 tff(4370,plain,
% 2.04/2.23 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4369, 4367])).
% 2.04/2.23 tff(4371,plain,
% 2.04/2.23 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4370])).
% 2.04/2.23 tff(4372,plain,
% 2.04/2.23 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[175, 4371, 663])).
% 2.04/2.23 tff(4373,plain,
% 2.04/2.23 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4372])).
% 2.04/2.23 tff(4374,plain,
% 2.04/2.23 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[170, 4373, 687])).
% 2.04/2.23 tff(4375,plain,
% 2.04/2.23 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4374])).
% 2.04/2.23 tff(4376,plain,
% 2.04/2.23 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[21, 4375, 698])).
% 2.04/2.23 tff(4377,plain,
% 2.04/2.23 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4376])).
% 2.04/2.23 tff(4378,plain,
% 2.04/2.23 (s(s(z)) = s(s(elem!1))),
% 2.04/2.23 inference(transitivity,[status(thm)],[84, 4377, 753])).
% 2.04/2.23 tff(4379,plain,
% 2.04/2.23 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4374, 4378])).
% 2.04/2.23 tff(4380,plain,
% 2.04/2.23 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4379])).
% 2.04/2.23 tff(4381,plain,
% 2.04/2.23 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[2122, 4380])).
% 2.04/2.23 tff(4382,plain,
% 2.04/2.23 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4374, 4376])).
% 2.04/2.23 tff(4383,plain,
% 2.04/2.23 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[137, 4382])).
% 2.04/2.23 tff(4384,plain,
% 2.04/2.23 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4378])).
% 2.04/2.23 tff(4385,plain,
% 2.04/2.23 (s(z) = s(elem!1)),
% 2.04/2.23 inference(transitivity,[status(thm)],[126, 4384, 904])).
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% 2.04/2.23 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4385])).
% 2.04/2.23 tff(4387,plain,
% 2.04/2.23 (z = elem!1),
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% 2.04/2.23 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.04/2.23 inference(symmetry,[status(thm)],[4375])).
% 2.04/2.23 tff(4389,plain,
% 2.04/2.23 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[699, 4388, 20])).
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% 2.04/2.23 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4389])).
% 2.04/2.23 tff(4391,plain,
% 2.04/2.23 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4378, 4376])).
% 2.04/2.23 tff(4392,plain,
% 2.04/2.23 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4391, 2108])).
% 2.04/2.23 tff(4393,plain,
% 2.04/2.23 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4392, 4390])).
% 2.04/2.23 tff(4394,plain,
% 2.04/2.23 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4393])).
% 2.04/2.23 tff(4395,plain,
% 2.04/2.23 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[2125, 4394])).
% 2.04/2.23 tff(4396,plain,
% 2.04/2.23 (elem!1 = z),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2211, 4387])).
% 2.04/2.23 tff(4397,plain,
% 2.04/2.23 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4385])).
% 2.04/2.23 tff(4398,plain,
% 2.04/2.23 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4376])).
% 2.04/2.23 tff(4399,plain,
% 2.04/2.23 (b(s(z), s(s(s(elem!1))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4267, 4398])).
% 2.04/2.23 tff(4400,plain,
% 2.04/2.23 (b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4399, 4397])).
% 2.04/2.23 tff(4401,plain,
% 2.04/2.23 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4374])).
% 2.04/2.23 tff(4402,plain,
% 2.04/2.23 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4401, 2214])).
% 2.04/2.23 tff(4403,plain,
% 2.04/2.23 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.04/2.23 inference(symmetry,[status(thm)],[4402])).
% 2.04/2.23 tff(4404,plain,
% 2.04/2.23 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4379, 4403])).
% 2.04/2.23 tff(4405,plain,
% 2.04/2.23 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4404])).
% 2.04/2.23 tff(4406,plain,
% 2.04/2.23 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[2122, 4405])).
% 2.04/2.23 tff(4407,plain,
% 2.04/2.23 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1887, 286, 339])).
% 2.04/2.23 tff(4408,plain,
% 2.04/2.23 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[431, 4407])).
% 2.04/2.23 tff(4409,plain,
% 2.04/2.23 (~b(s(s(elem!1)), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[3831, 3625, 900, 538, 1128, 1101, 4408])).
% 2.04/2.23 tff(4410,plain,
% 2.04/2.23 (r(s(s(elem!1)), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[952, 4409])).
% 2.04/2.23 tff(4411,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(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))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4412,plain,
% 2.04/2.23 (((~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))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4413,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(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)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4412])).
% 2.04/2.23 tff(4414,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(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))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4413, 4411])).
% 2.04/2.23 tff(4415,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(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(4416,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4415, 4414])).
% 2.04/2.23 tff(4417,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4416, 67, 4410, 900, 286])).
% 2.04/2.23 tff(4418,plain,((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4419,plain,
% 2.04/2.23 (~r(s(s(elem!1)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4418, 4406, 4269, 4303, 339])).
% 2.04/2.23 tff(4420,plain,
% 2.04/2.23 (b(s(s(elem!1)), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1099, 4419])).
% 2.04/2.23 tff(4421,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4370])).
% 2.04/2.23 tff(4422,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.23 inference(symmetry,[status(thm)],[4421])).
% 2.04/2.23 tff(4423,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4387])).
% 2.04/2.23 tff(4424,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.23 inference(transitivity,[status(thm)],[4423, 4422])).
% 2.04/2.23 tff(4425,plain,
% 2.04/2.23 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4316, 4424])).
% 2.04/2.23 tff(4426,plain,
% 2.04/2.23 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4376])).
% 2.04/2.23 tff(4427,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(symmetry,[status(thm)],[4426])).
% 2.04/2.23 tff(4428,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4387])).
% 2.04/2.23 tff(4429,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), elem!1)),
% 2.04/2.23 inference(transitivity,[status(thm)],[4428, 4427])).
% 2.04/2.23 tff(4430,plain,
% 2.04/2.23 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4376])).
% 2.04/2.23 tff(4431,plain,
% 2.04/2.23 (b(s(s(s(elem!1))), z)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4243, 4430])).
% 2.04/2.23 tff(4432,plain,
% 2.04/2.24 (b(s(s(s(z))), elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4431, 4429])).
% 2.04/2.24 tff(4433,plain,
% 2.04/2.24 (b(z, s(s(s(s(s(s(elem!1))))))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4387])).
% 2.04/2.24 tff(4434,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(z, s(z))) | (~r(z, 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(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4435,plain,
% 2.04/2.24 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4436,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(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), 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(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4435])).
% 2.04/2.24 tff(4437,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(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), 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(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4436, 4434])).
% 2.04/2.24 tff(4438,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(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4439,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(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4438, 4437])).
% 2.04/2.24 tff(4440,plain,
% 2.04/2.24 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4439, 67, 4269, 4366])).
% 2.04/2.24 tff(4441,plain,
% 2.04/2.24 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3157, 4440])).
% 2.04/2.24 tff(4442,plain,
% 2.04/2.24 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4441, 4433])).
% 2.04/2.24 tff(4443,plain,
% 2.04/2.24 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4431, 4428])).
% 2.04/2.24 tff(4444,assumption,(b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 2.04/2.24 tff(4445,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 2.04/2.24 tff(4446,plain,
% 2.04/2.24 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[2092])).
% 2.04/2.24 tff(4447,plain,
% 2.04/2.24 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[4446])).
% 2.04/2.24 tff(4448,plain,
% 2.04/2.24 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[2337, 4447])).
% 2.04/2.24 tff(4449,plain,
% 2.04/2.24 (b(elem!1, s(s(s(z))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[2339, 4448])).
% 2.04/2.24 tff(4450,assumption,(b(elem!1, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.04/2.24 tff(4451,plain,
% 2.04/2.24 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4287, 378, 339, 286])).
% 2.04/2.24 tff(4452,plain,
% 2.04/2.24 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[766, 4451])).
% 2.04/2.24 tff(4453,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.04/2.24 tff(4454,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.24 tff(4455,plain,
% 2.04/2.24 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.04/2.24 inference(symmetry,[status(thm)],[2191])).
% 2.04/2.24 tff(4456,plain,
% 2.04/2.24 (s(elem!1) = s(z)),
% 2.04/2.24 inference(transitivity,[status(thm)],[919, 4455, 78])).
% 2.04/2.24 tff(4457,plain,
% 2.04/2.24 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4456])).
% 2.04/2.24 tff(4458,plain,
% 2.04/2.24 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.04/2.24 inference(symmetry,[status(thm)],[4457])).
% 2.04/2.24 tff(4459,plain,
% 2.04/2.24 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[2222, 4458])).
% 2.04/2.24 tff(4460,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4461,plain,
% 2.04/2.24 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4462,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4461])).
% 2.04/2.24 tff(4463,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4462, 4460])).
% 2.04/2.24 tff(4464,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4465,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4464, 4463])).
% 2.04/2.24 tff(4466,plain,
% 2.04/2.24 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4465, 204, 2336, 4454, 4453])).
% 2.04/2.24 tff(4467,plain,
% 2.04/2.24 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4466, 4459])).
% 2.04/2.24 tff(4468,plain,
% 2.04/2.24 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2327, 4467, 2195])).
% 2.04/2.24 tff(4469,plain,
% 2.04/2.24 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2319, 4468, 2212, 2126])).
% 2.04/2.24 tff(4470,plain,
% 2.04/2.24 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2298, 4469, 2195])).
% 2.04/2.24 tff(4471,plain,
% 2.04/2.24 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2286, 4470, 2188, 2195])).
% 2.04/2.24 tff(4472,plain,
% 2.04/2.24 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1139, 4471, 2221])).
% 2.04/2.24 tff(4473,plain,
% 2.04/2.24 (~b(s(s(elem!1)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2266, 4472, 360, 2222, 456])).
% 2.04/2.24 tff(4474,assumption,(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.04/2.24 tff(4475,plain,
% 2.04/2.24 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 2.04/2.24 inference(symmetry,[status(thm)],[4474])).
% 2.04/2.24 tff(4476,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1051, 4475])).
% 2.04/2.24 tff(4477,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4478,plain,
% 2.04/2.24 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4477, 1051])).
% 2.04/2.24 tff(4479,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.04/2.24 tff(4480,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4481,plain,
% 2.04/2.24 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(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(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4482,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4481])).
% 2.04/2.24 tff(4483,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4482, 4480])).
% 2.04/2.24 tff(4484,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4485,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4484, 4483])).
% 2.04/2.24 tff(4486,plain,
% 2.04/2.24 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4485, 204, 2258, 785, 360, 676])).
% 2.04/2.24 tff(4487,plain,
% 2.04/2.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4488,plain,
% 2.04/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4489,plain,
% 2.04/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4488, 4487])).
% 2.04/2.24 tff(4490,plain,
% 2.04/2.24 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4489, 50, 4479, 4486])).
% 2.04/2.24 tff(4491,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(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(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4492,plain,
% 2.04/2.24 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(z))) | (~b(s(s(s(z))), s(s(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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4493,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4492])).
% 2.04/2.24 tff(4494,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4493, 4491])).
% 2.04/2.24 tff(4495,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4496,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4495, 4494])).
% 2.04/2.24 tff(4497,plain,
% 2.04/2.24 ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4496, 204, 444, 456, 785])).
% 2.04/2.24 tff(4498,plain,
% 2.04/2.24 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4497, 676])).
% 2.04/2.24 tff(4499,plain,
% 2.04/2.24 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[710, 50, 707, 4498])).
% 2.04/2.24 tff(4500,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(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4501,plain,
% 2.04/2.24 (((~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4502,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(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4501])).
% 2.04/2.24 tff(4503,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(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4502, 4500])).
% 2.04/2.24 tff(4504,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(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4505,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4504, 4503])).
% 2.04/2.24 tff(4506,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4505, 67, 2127, 4499, 4490])).
% 2.04/2.24 tff(4507,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | r(s(s(s(s(s(s(elem!1)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4508,plain,
% 2.04/2.24 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4507, 672, 4479, 2258, 360, 444, 456, 2127])).
% 2.04/2.24 tff(4509,plain,
% 2.04/2.24 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[766, 4508])).
% 2.04/2.24 tff(4510,plain,
% 2.04/2.24 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3214, 4509, 339])).
% 2.04/2.24 tff(4511,plain,
% 2.04/2.24 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3155, 50, 4510, 3151])).
% 2.04/2.24 tff(4512,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(z))), s(s(elem!1)))) | (~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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4513,plain,
% 2.04/2.25 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4514,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(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), 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(s(elem!1)))) | (~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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4513])).
% 2.04/2.25 tff(4515,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(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), 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(s(elem!1)))) | (~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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4514, 4512])).
% 2.04/2.25 tff(4516,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(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4517,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(elem!1)))) | (~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(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4516, 4515])).
% 2.04/2.25 tff(4518,plain,
% 2.04/2.25 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4517, 67, 4509, 2127, 378])).
% 2.04/2.25 tff(4519,plain,
% 2.04/2.25 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2434, 50, 706, 4518])).
% 2.04/2.25 tff(4520,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), 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(X1, 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(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4521,plain,
% 2.04/2.25 (((~b(s(s(s(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(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4522,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(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(X1, 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(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4521])).
% 2.04/2.25 tff(4523,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(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(X1, 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(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4522, 4520])).
% 2.04/2.25 tff(4524,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4525,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4524, 4523])).
% 2.04/2.25 tff(4526,plain,
% 2.04/2.25 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4525, 204, 444, 405, 676])).
% 2.04/2.25 tff(4527,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4526, 4519, 4511])).
% 2.04/2.25 tff(4528,plain,(r(s(s(s(s(s(s(elem!1)))))), s(z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(4529,plain,
% 2.04/2.25 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4528, 4478, 405, 2127, 378, 339, 444, 2258, 360, 456])).
% 2.04/2.25 tff(4530,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(elem!1)), s(z))) | (~r(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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4531,plain,
% 2.04/2.25 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4532,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(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4531])).
% 2.04/2.25 tff(4533,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(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4532, 4530])).
% 2.04/2.25 tff(4534,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(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4535,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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4534, 4533])).
% 2.04/2.25 tff(4536,plain,
% 2.04/2.25 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4535, 67, 938, 4529])).
% 2.04/2.25 tff(4537,plain,
% 2.04/2.25 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4489, 50, 4478, 4536])).
% 2.04/2.25 tff(4538,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(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), 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(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4539,plain,
% 2.04/2.25 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4540,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(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4539])).
% 2.04/2.25 tff(4541,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(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4540, 4538])).
% 2.04/2.25 tff(4542,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(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4543,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(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4542, 4541])).
% 2.04/2.25 tff(4544,plain,
% 2.04/2.25 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4543, 67, 286, 4529])).
% 2.04/2.25 tff(4545,plain,
% 2.04/2.25 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[822, 4544])).
% 2.04/2.25 tff(4546,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(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(elem!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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4547,plain,
% 2.04/2.25 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~r(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(elem!1)))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4548,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(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4547])).
% 2.04/2.25 tff(4549,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(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(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(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4548, 4546])).
% 2.04/2.25 tff(4550,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(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4551,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(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(elem!1))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4550, 4549])).
% 2.04/2.25 tff(4552,plain,
% 2.04/2.25 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4551, 67, 938, 4529])).
% 2.04/2.25 tff(4553,plain,
% 2.04/2.25 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1062, 4552, 1051])).
% 2.04/2.25 tff(4554,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4555,plain,
% 2.04/2.25 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4556,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4555])).
% 2.04/2.25 tff(4557,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4556, 4554])).
% 2.04/2.25 tff(4558,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4559,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4558, 4557])).
% 2.04/2.25 tff(4560,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4559, 204, 2246, 1102, 4553, 4545, 4537])).
% 2.04/2.25 tff(4561,plain,((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(4562,plain,
% 2.04/2.25 (~r(s(s(elem!1)), s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4561, 4472, 339, 405, 286, 2354, 378, 1102, 444, 2127, 360, 456])).
% 2.04/2.25 tff(4563,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[952, 4562, 4473])).
% 2.04/2.25 tff(4564,plain,((~b(s(z), s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(4565,plain,
% 2.04/2.25 (~b(s(z), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4564, 2127, 405, 286, 378, 1102, 444, 339, 360, 456, 4454, 4453, 2083])).
% 2.04/2.25 tff(4566,plain,
% 2.04/2.25 (r(s(z), s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[936, 4565])).
% 2.04/2.25 tff(4567,plain,
% 2.04/2.25 (~r(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2150, 4566, 286])).
% 2.04/2.25 tff(4568,plain,
% 2.04/2.25 (b(z, s(s(elem!1)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2160, 4567])).
% 2.04/2.25 tff(4569,plain,
% 2.04/2.25 (s(s(elem!1)) = s(s(z))),
% 2.04/2.25 inference(symmetry,[status(thm)],[2270])).
% 2.04/2.25 tff(4570,plain,
% 2.04/2.25 (r(s(s(s(s(s(s(z)))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4569])).
% 2.04/2.25 tff(4571,plain,
% 2.04/2.25 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.04/2.25 inference(symmetry,[status(thm)],[4570])).
% 2.04/2.25 tff(4572,plain,
% 2.04/2.25 (elem!1 = z),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[2211, 2207])).
% 2.04/2.25 tff(4573,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(z)))))), introduced(assumption)).
% 2.04/2.25 tff(4574,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4573, 3441])).
% 2.04/2.25 tff(4575,plain,((~(elem!1 = z)) | (s(s(s(s(elem!1)))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(4576,plain,
% 2.04/2.25 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4575, 4572])).
% 2.04/2.25 tff(4577,plain,
% 2.04/2.25 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4576])).
% 2.04/2.25 tff(4578,plain,
% 2.04/2.25 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4577])).
% 2.04/2.25 tff(4579,plain,
% 2.04/2.25 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4578, 4569])).
% 2.04/2.25 tff(4580,plain,
% 2.04/2.25 (b(z, s(s(s(s(s(s(elem!1))))))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[2207])).
% 2.04/2.25 tff(4581,plain,
% 2.04/2.25 (b(elem!1, s(s(s(s(s(s(elem!1))))))) <=> b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(symmetry,[status(thm)],[4580])).
% 2.04/2.25 tff(4582,plain,
% 2.04/2.25 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4450, 4581])).
% 2.04/2.25 tff(4583,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4584,plain,
% 2.04/2.25 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4585,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4584])).
% 2.04/2.25 tff(4586,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[4585, 4583])).
% 2.04/2.26 tff(4587,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(4588,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4587, 4586])).
% 2.04/2.26 tff(4589,plain,
% 2.04/2.26 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4588, 204, 3720, 2258, 785])).
% 2.04/2.26 tff(4590,plain,
% 2.04/2.26 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4589, 4582])).
% 2.04/2.26 tff(4591,plain,
% 2.04/2.26 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1062, 4590, 1051])).
% 2.04/2.26 tff(4592,plain,
% 2.04/2.26 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4591, 4579])).
% 2.04/2.26 tff(4593,plain,
% 2.04/2.26 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4592, 4571])).
% 2.04/2.26 tff(4594,plain,
% 2.04/2.26 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2790])).
% 2.04/2.26 tff(4595,plain,
% 2.04/2.26 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4594])).
% 2.04/2.26 tff(4596,plain,
% 2.04/2.26 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[4595])).
% 2.04/2.26 tff(4597,plain,
% 2.04/2.26 (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[122, 4596])).
% 2.04/2.26 tff(4598,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2822, 4597])).
% 2.04/2.26 tff(4599,plain,((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) | (~(s(s(s(s(elem!1)))) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(4600,plain,
% 2.04/2.26 (~(s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4599, 4576])).
% 2.04/2.26 tff(4601,plain,
% 2.04/2.26 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[4578])).
% 2.04/2.26 tff(4602,plain,
% 2.04/2.26 (b(elem!1, s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4601])).
% 2.04/2.26 tff(4603,plain,
% 2.04/2.26 (b(elem!1, s(s(s(s(s(s(elem!1))))))) <=> b(elem!1, s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[4602])).
% 2.04/2.26 tff(4604,plain,
% 2.04/2.26 (b(elem!1, s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4450, 4603])).
% 2.04/2.26 tff(4605,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.04/2.26 tff(4606,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4607,plain,
% 2.04/2.26 (((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4608,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4607])).
% 2.04/2.26 tff(4609,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[4608, 4606])).
% 2.04/2.26 tff(4610,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(4611,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4610, 4609])).
% 2.04/2.26 tff(4612,plain,
% 2.04/2.26 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4611, 204, 4605, 4445, 4604, 4444])).
% 2.04/2.26 tff(4613,plain,
% 2.04/2.26 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[133, 4612, 4600])).
% 2.04/2.26 tff(4614,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(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4615,plain,
% 2.04/2.26 (((~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4616,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(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4615])).
% 2.04/2.26 tff(4617,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(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[4616, 4614])).
% 2.04/2.26 tff(4618,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(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(4619,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 2.04/2.26 tff(4620,plain,
% 2.04/2.26 (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4619, 67, 2127, 4613])).
% 2.04/2.26 tff(4621,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4620, 4593])).
% 2.04/2.26 tff(4622,plain,((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~(z = elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (s(s(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(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(4623,plain,
% 2.04/2.26 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4622, 4568, 4452, 2354, 4450, 2195, 2127, 4449, 4445, 4444])).
% 2.04/2.26 tff(4624,plain,
% 2.04/2.26 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1139, 4623, 2221])).
% 2.04/2.26 tff(4625,plain,
% 2.04/2.26 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2286, 4624, 2188, 2195])).
% 2.04/2.26 tff(4626,plain,
% 2.04/2.26 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2192])).
% 2.04/2.26 tff(4627,plain,
% 2.04/2.26 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 2.04/2.26 inference(symmetry,[status(thm)],[4626])).
% 2.04/2.26 tff(4628,plain,
% 2.04/2.26 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2195])).
% 2.04/2.26 tff(4629,plain,
% 2.04/2.26 (r(z, s(elem!1)) <=> r(elem!1, s(z))),
% 2.04/2.26 inference(transitivity,[status(thm)],[4628, 4627])).
% 2.04/2.26 tff(4630,plain,
% 2.04/2.26 (r(z, s(z)) <=> r(z, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[2192])).
% 2.04/2.26 tff(4631,plain,
% 2.04/2.26 (r(z, s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[286, 4630])).
% 2.04/2.26 tff(4632,plain,
% 2.04/2.26 (r(elem!1, s(z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4631, 4629])).
% 2.04/2.26 tff(4633,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(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4634,plain,
% 2.04/2.26 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4635,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(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4634])).
% 2.04/2.26 tff(4636,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(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[4635, 4633])).
% 2.04/2.26 tff(4637,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(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(4638,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4637, 4636])).
% 2.04/2.26 tff(4639,plain,
% 2.04/2.26 ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4638, 67])).
% 2.04/2.26 tff(4640,plain,
% 2.04/2.26 (~r(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4639, 4566, 4632])).
% 2.04/2.26 tff(4641,plain,
% 2.04/2.26 (b(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2351, 4640, 2204])).
% 2.04/2.26 tff(4642,plain,
% 2.04/2.26 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2346, 204, 2340, 2336, 4453])).
% 2.04/2.26 tff(4643,plain,
% 2.04/2.26 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4642, 4641])).
% 2.04/2.26 tff(4644,plain,
% 2.04/2.26 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2327, 4643, 2195])).
% 2.04/2.26 tff(4645,plain,
% 2.04/2.26 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2319, 4644, 2212, 2126])).
% 2.04/2.26 tff(4646,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2298, 4645, 4625, 2195])).
% 2.04/2.26 tff(4647,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(4648,plain,
% 2.04/2.26 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4647, 4443, 4442, 4432, 4425, 4269, 1574, 4274, 4420, 4251, 339, 3004, 4271, 4400, 4370])).
% 2.04/2.26 tff(4649,plain,
% 2.04/2.26 (b(s(s(s(z))), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3335, 4648, 4395])).
% 2.04/2.26 tff(4650,plain,
% 2.04/2.26 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4387])).
% 2.04/2.26 tff(4651,plain,
% 2.04/2.26 (b(s(s(elem!1)), elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4420, 4650])).
% 2.04/2.26 tff(4652,plain,
% 2.04/2.26 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4385])).
% 2.04/2.26 tff(4653,plain,
% 2.04/2.26 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 2.04/2.26 inference(symmetry,[status(thm)],[4652])).
% 2.04/2.26 tff(4654,plain,
% 2.04/2.26 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4387])).
% 2.04/2.26 tff(4655,plain,
% 2.04/2.26 (r(z, s(elem!1)) <=> r(elem!1, s(z))),
% 2.04/2.26 inference(transitivity,[status(thm)],[4654, 4653])).
% 2.04/2.26 tff(4656,plain,
% 2.04/2.26 (r(z, s(z)) <=> r(z, s(elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4385])).
% 2.04/2.26 tff(4657,plain,
% 2.04/2.26 (r(z, s(elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4269, 4656])).
% 2.04/2.26 tff(4658,plain,
% 2.04/2.26 (r(elem!1, s(z))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4657, 4655])).
% 2.04/2.26 tff(4659,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 2.04/2.26 tff(4660,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.04/2.26 tff(4661,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4662,plain,
% 2.04/2.26 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~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(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4663,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4662])).
% 2.04/2.26 tff(4664,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[4663, 4661])).
% 2.04/2.26 tff(4665,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(4666,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4665, 4664])).
% 2.04/2.26 tff(4667,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4666, 204, 4660, 1065, 4445, 2323, 2141])).
% 2.04/2.26 tff(4668,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(4669,plain,
% 2.04/2.26 (~b(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4668, 2323, 4445, 2141, 1065])).
% 2.04/2.26 tff(4670,plain,
% 2.04/2.26 (r(elem!1, s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2351, 4669, 2204])).
% 2.04/2.26 tff(4671,plain,
% 2.04/2.26 (~r(s(z), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4639, 4670, 4659])).
% 2.04/2.26 tff(4672,plain,
% 2.04/2.26 (b(s(z), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[936, 4671])).
% 2.04/2.26 tff(4673,plain,
% 2.04/2.26 (b(s(elem!1), s(s(elem!1)))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[4672, 4458])).
% 2.04/2.26 tff(4674,plain,
% 2.04/2.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2327, 2323, 2195])).
% 2.04/2.26 tff(4675,plain,
% 2.04/2.26 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4465, 204, 1065, 4454, 4453])).
% 2.04/2.26 tff(4676,plain,
% 2.04/2.26 (~b(s(elem!1), s(s(elem!1)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4675, 4674])).
% 2.04/2.26 tff(4677,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4676, 4673])).
% 2.04/2.26 tff(4678,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(4679,plain,
% 2.04/2.26 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4678, 4370, 4658, 4651, 4400, 4443, 4432, 4649])).
% 2.04/2.26 tff(4680,plain,
% 2.04/2.26 (r(s(s(z)), s(s(s(z))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2319, 4679, 4396, 4395])).
% 2.04/2.26 tff(4681,plain,
% 2.04/2.26 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2298, 4680, 4387])).
% 2.04/2.26 tff(4682,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.26 tff(4683,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 2.04/2.26 tff(4684,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4685,plain,
% 2.04/2.26 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(4686,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[4685])).
% 2.04/2.26 tff(4687,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4686, 4684])).
% 2.04/2.27 tff(4688,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(4689,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4688, 4687])).
% 2.04/2.27 tff(4690,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4689, 67, 4683, 2277, 4682])).
% 2.04/2.27 tff(4691,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(4692,plain,
% 2.04/2.27 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4691, 4681, 4383])).
% 2.04/2.27 tff(4693,plain,
% 2.04/2.27 (((~![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))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4694,plain,
% 2.04/2.27 ((~![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))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(4695,plain,
% 2.04/2.27 ((~![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)))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4694, 4693])).
% 2.04/2.27 tff(4696,plain,
% 2.04/2.27 ((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)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4695, 50])).
% 2.04/2.27 tff(4697,plain,
% 2.04/2.27 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4696, 4692, 4381])).
% 2.04/2.27 tff(4698,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4316, 4423])).
% 2.04/2.27 tff(4699,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4374])).
% 2.04/2.27 tff(4700,plain,
% 2.04/2.27 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4360, 4699])).
% 2.04/2.27 tff(4701,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4702,plain,
% 2.04/2.27 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4703,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4702])).
% 2.04/2.27 tff(4704,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4703, 4701])).
% 2.04/2.27 tff(4705,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(4706,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4705, 4704])).
% 2.04/2.27 tff(4707,plain,
% 2.04/2.27 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4706, 204, 4651, 4700, 4698])).
% 2.04/2.27 tff(4708,plain,
% 2.04/2.27 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4707, 4697])).
% 2.04/2.27 tff(4709,plain,
% 2.04/2.27 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[2086])).
% 2.04/2.27 tff(4710,plain,
% 2.04/2.27 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4378])).
% 2.04/2.27 tff(4711,plain,
% 2.04/2.27 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4710, 2086])).
% 2.04/2.27 tff(4712,plain,
% 2.04/2.27 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4711, 4709])).
% 2.04/2.27 tff(4713,plain,
% 2.04/2.27 ((~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4712])).
% 2.04/2.27 tff(4714,plain,
% 2.04/2.27 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4370])).
% 2.04/2.27 tff(4715,plain,
% 2.04/2.27 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4714, 2099])).
% 2.04/2.27 tff(4716,plain,
% 2.04/2.27 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4715])).
% 2.04/2.27 tff(4717,plain,
% 2.04/2.27 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[182, 4716])).
% 2.04/2.27 tff(4718,plain,
% 2.04/2.27 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4717, 4713])).
% 2.04/2.27 tff(4719,plain,
% 2.04/2.27 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4489, 50, 4718, 4708])).
% 2.04/2.27 tff(4720,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4370, 4376])).
% 2.04/2.27 tff(4721,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4265, 4720])).
% 2.04/2.27 tff(4722,plain,
% 2.04/2.27 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.04/2.27 inference(symmetry,[status(thm)],[4384])).
% 2.04/2.27 tff(4723,plain,
% 2.04/2.27 (s(elem!1) = s(z)),
% 2.04/2.27 inference(transitivity,[status(thm)],[919, 4722, 78])).
% 2.04/2.27 tff(4724,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4723])).
% 2.04/2.27 tff(4725,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 2.04/2.27 inference(symmetry,[status(thm)],[4724])).
% 2.04/2.27 tff(4726,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4366, 4725])).
% 2.04/2.27 tff(4727,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4728,plain,
% 2.04/2.27 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4729,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(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4728])).
% 2.04/2.27 tff(4730,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(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4729, 4727])).
% 2.04/2.27 tff(4731,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(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(4732,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4731, 4730])).
% 2.04/2.27 tff(4733,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4732, 67, 4681, 4726, 4721, 4719])).
% 2.04/2.27 tff(4734,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(4735,plain,
% 2.04/2.27 (~r(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4734, 137])).
% 2.04/2.27 tff(4736,plain,
% 2.04/2.27 (b(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[357, 4735])).
% 2.04/2.27 tff(4737,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2594, 3, 137])).
% 2.04/2.27 tff(4738,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[335, 4737])).
% 2.04/2.27 tff(4739,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1519, 4, 4736, 359, 3968])).
% 2.04/2.27 tff(4740,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[218, 4739])).
% 2.04/2.27 tff(4741,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[518, 4740, 137])).
% 2.04/2.27 tff(4742,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[134, 4741])).
% 2.04/2.27 tff(4743,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3071, 204, 4243, 4736, 4, 3968, 4742])).
% 2.04/2.27 tff(4744,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(4745,plain,
% 2.04/2.27 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4744, 4738, 137])).
% 2.04/2.27 tff(4746,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[190, 4745])).
% 2.04/2.27 tff(4747,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3043, 4746, 2592])).
% 2.04/2.27 tff(4748,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[431, 4747])).
% 2.04/2.27 tff(4749,plain,
% 2.04/2.27 (~b(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1237, 204, 4251, 4243, 4748, 4736])).
% 2.04/2.27 tff(4750,plain,
% 2.04/2.27 (r(z, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[306, 4749])).
% 2.04/2.27 tff(4751,plain,
% 2.04/2.27 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4008, 4750, 2592])).
% 2.04/2.27 tff(4752,plain,
% 2.04/2.27 (b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[604, 50, 601, 4751])).
% 2.04/2.27 tff(4753,plain,
% 2.04/2.27 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1699, 4746, 137])).
% 2.04/2.27 tff(4754,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[284, 4753])).
% 2.04/2.27 tff(4755,plain,
% 2.04/2.27 (~r(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1831, 3, 3966])).
% 2.04/2.27 tff(4756,plain,
% 2.04/2.27 (b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[478, 4755])).
% 2.04/2.27 tff(4757,plain,
% 2.04/2.27 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3989, 204, 4251, 4756, 4748, 3004])).
% 2.04/2.27 tff(4758,plain,
% 2.04/2.27 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[108, 4757])).
% 2.04/2.27 tff(4759,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[507, 4758, 4746])).
% 2.04/2.27 tff(4760,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[134, 4759])).
% 2.04/2.27 tff(4761,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2629, 204, 4243, 3968, 4760, 4754, 4752])).
% 2.04/2.27 tff(4762,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(4763,plain,
% 2.04/2.27 (~r(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4762, 137])).
% 2.04/2.27 tff(4764,plain,
% 2.04/2.27 (b(z, s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[259, 4763])).
% 2.04/2.27 tff(4765,plain,
% 2.04/2.27 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4263, 4764, 4243, 3968, 2592, 4251])).
% 2.04/2.27 tff(4766,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[284, 4765])).
% 2.04/2.27 tff(4767,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2474, 4766, 137])).
% 2.04/2.27 tff(4768,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[218, 4767])).
% 2.04/2.27 tff(4769,plain,
% 2.04/2.27 ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1746, 204, 4251, 4736, 3004])).
% 2.04/2.27 tff(4770,plain,
% 2.04/2.27 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4769, 4764])).
% 2.04/2.27 tff(4771,plain,
% 2.04/2.27 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[108, 4770])).
% 2.04/2.27 tff(4772,plain,
% 2.04/2.27 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1699, 4766, 137])).
% 2.04/2.27 tff(4773,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[190, 4772])).
% 2.04/2.27 tff(4774,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4744, 4773, 137])).
% 2.04/2.27 tff(4775,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[335, 4774])).
% 2.04/2.27 tff(4776,plain,
% 2.04/2.27 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1263, 4775, 3004, 3966, 4736, 4771, 4768])).
% 2.04/2.27 tff(4777,plain,
% 2.04/2.27 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[134, 4776])).
% 2.04/2.27 tff(4778,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3071, 204, 4243, 4736, 4773, 3968, 4777])).
% 2.04/2.27 tff(4779,plain,(~r(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(4780,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[151, 4779])).
% 2.04/2.27 tff(4781,plain,
% 2.04/2.27 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2619, 204, 4780, 263, 324, 316])).
% 2.04/2.27 tff(4782,plain,
% 2.04/2.27 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[190, 4781])).
% 2.04/2.27 tff(4783,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1807, 67, 538, 1, 261])).
% 2.04/2.27 tff(4784,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(4785,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4784, 4782, 261])).
% 2.04/2.27 tff(4786,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[335, 4785])).
% 2.04/2.27 tff(4787,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2452, 67, 339, 1, 261])).
% 2.04/2.27 tff(4788,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(4789,plain,
% 2.04/2.27 (~r(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4788, 4782, 261])).
% 2.04/2.27 tff(4790,plain,
% 2.04/2.27 (b(z, s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[357, 4789])).
% 2.04/2.27 tff(4791,plain,
% 2.04/2.27 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[227, 263, 136, 57])).
% 2.04/2.27 tff(4792,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[244, 4791])).
% 2.04/2.27 tff(4793,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1640, 67, 2, 4782])).
% 2.04/2.27 tff(4794,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[489, 50, 4793, 249])).
% 2.04/2.27 tff(4795,plain,
% 2.04/2.27 (~b(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2588, 204, 324, 4794, 4792, 316])).
% 2.04/2.27 tff(4796,plain,
% 2.04/2.27 (r(s(z), s(s(s(z))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[478, 4795])).
% 2.04/2.27 tff(4797,plain,
% 2.04/2.27 (~r(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[397, 308, 57])).
% 2.04/2.27 tff(4798,plain,
% 2.04/2.27 (b(s(z), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[376, 4797])).
% 2.04/2.27 tff(4799,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(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4800,plain,
% 2.04/2.27 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4801,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(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(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), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4800])).
% 2.04/2.27 tff(4802,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(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(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), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4801, 4799])).
% 2.04/2.27 tff(4803,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(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(4804,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(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4803, 4802])).
% 2.04/2.27 tff(4805,plain,
% 2.04/2.27 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4804, 67, 445, 2, 656])).
% 2.04/2.27 tff(4806,plain,
% 2.04/2.27 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4365, 4805])).
% 2.04/2.27 tff(4807,plain,
% 2.04/2.27 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1640, 67, 2, 1])).
% 2.04/2.27 tff(4808,plain,
% 2.04/2.27 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[489, 50, 4807, 249])).
% 2.04/2.27 tff(4809,plain,
% 2.04/2.27 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2410, 204, 4808, 443, 4806, 722])).
% 2.04/2.27 tff(4810,plain,
% 2.04/2.27 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2422, 67, 656, 1])).
% 2.04/2.27 tff(4811,plain,
% 2.04/2.27 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2402, 50, 4810])).
% 2.04/2.27 tff(4812,plain,
% 2.04/2.27 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4811, 4809])).
% 2.04/2.27 tff(4813,plain,
% 2.04/2.27 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4812])).
% 2.04/2.27 tff(4814,plain,
% 2.04/2.27 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[175, 4813, 663])).
% 2.04/2.27 tff(4815,plain,
% 2.04/2.27 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4814])).
% 2.04/2.27 tff(4816,plain,
% 2.04/2.27 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[170, 4815, 687])).
% 2.04/2.27 tff(4817,plain,
% 2.04/2.27 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4816])).
% 2.04/2.27 tff(4818,plain,
% 2.04/2.27 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[21, 4817, 698])).
% 2.04/2.27 tff(4819,plain,
% 2.04/2.27 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4818])).
% 2.04/2.27 tff(4820,plain,
% 2.04/2.27 (s(s(z)) = s(s(elem!1))),
% 2.04/2.27 inference(transitivity,[status(thm)],[84, 4819, 753])).
% 2.04/2.27 tff(4821,plain,
% 2.04/2.27 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4820])).
% 2.04/2.27 tff(4822,plain,
% 2.04/2.27 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4821, 2086])).
% 2.04/2.27 tff(4823,plain,
% 2.04/2.27 ((~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4822])).
% 2.04/2.27 tff(4824,plain,
% 2.04/2.27 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4812])).
% 2.04/2.27 tff(4825,plain,
% 2.04/2.27 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4824, 2099])).
% 2.04/2.27 tff(4826,plain,
% 2.04/2.27 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4825])).
% 2.04/2.27 tff(4827,plain,
% 2.04/2.27 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[182, 4826])).
% 2.04/2.27 tff(4828,plain,
% 2.04/2.27 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[4827, 4823])).
% 2.04/2.27 tff(4829,plain,
% 2.04/2.27 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4816])).
% 2.04/2.27 tff(4830,plain,
% 2.04/2.27 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4829, 2214])).
% 2.04/2.27 tff(4831,plain,
% 2.04/2.27 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[4830])).
% 2.04/2.27 tff(4832,plain,
% 2.04/2.27 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4816, 4820])).
% 2.04/2.27 tff(4833,plain,
% 2.04/2.27 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[4832, 4831])).
% 2.04/2.27 tff(4834,plain,
% 2.04/2.27 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[4833])).
% 2.04/2.27 tff(4835,plain,
% 2.04/2.27 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[2122, 4834])).
% 2.04/2.27 tff(4836,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4837,plain,
% 2.04/2.27 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(4838,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(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(X1, 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(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4837])).
% 2.04/2.28 tff(4839,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(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(X1, 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(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[4838, 4836])).
% 2.04/2.28 tff(4840,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(4841,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4840, 4839])).
% 2.04/2.28 tff(4842,plain,
% 2.04/2.28 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4841, 204, 363, 362, 4808, 443])).
% 2.04/2.28 tff(4843,plain,
% 2.04/2.28 (r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[604, 50, 601, 4842])).
% 2.04/2.28 tff(4844,plain,
% 2.04/2.28 (~r(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2034, 4843, 1])).
% 2.04/2.28 tff(4845,plain,
% 2.04/2.28 (b(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[357, 4844])).
% 2.04/2.28 tff(4846,plain,
% 2.04/2.28 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4820])).
% 2.04/2.28 tff(4847,plain,
% 2.04/2.28 (s(z) = s(elem!1)),
% 2.04/2.28 inference(transitivity,[status(thm)],[126, 4846, 904])).
% 2.04/2.28 tff(4848,plain,
% 2.04/2.28 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4847])).
% 2.04/2.28 tff(4849,plain,
% 2.04/2.28 (z = elem!1),
% 2.04/2.28 inference(transitivity,[status(thm)],[2194, 4848, 902])).
% 2.04/2.28 tff(4850,plain,
% 2.04/2.28 (elem!1 = z),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2211, 4849])).
% 2.04/2.28 tff(4851,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(z), s(s(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(X1, 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(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4852,plain,
% 2.04/2.28 (((~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(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4853,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(X1, 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(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4852])).
% 2.04/2.28 tff(4854,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(X1, 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(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[4853, 4851])).
% 2.04/2.28 tff(4855,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(4856,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4855, 4854])).
% 2.04/2.28 tff(4857,plain,
% 2.04/2.28 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4856, 204, 363, 362, 4806, 722])).
% 2.04/2.28 tff(4858,plain,
% 2.04/2.28 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[822, 4857])).
% 2.04/2.28 tff(4859,plain,
% 2.04/2.28 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[4815])).
% 2.04/2.28 tff(4860,plain,
% 2.04/2.28 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[875, 4859, 119])).
% 2.04/2.28 tff(4861,plain,
% 2.04/2.28 (~r(s(s(z)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2902, 4860, 308, 4858])).
% 2.04/2.28 tff(4862,plain,
% 2.04/2.28 (~r(s(s(elem!1)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2909, 4861, 4850])).
% 2.04/2.28 tff(4863,plain,
% 2.04/2.28 (b(s(s(elem!1)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1099, 4862])).
% 2.04/2.28 tff(4864,plain,
% 2.04/2.28 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2937, 4863, 363, 4845, 359, 4835, 2])).
% 2.04/2.28 tff(4865,plain,
% 2.04/2.28 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2722, 67, 2, 656])).
% 2.04/2.28 tff(4866,plain,
% 2.04/2.28 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[675, 50, 4865, 671])).
% 2.04/2.28 tff(4867,plain,
% 2.04/2.28 (((~![X0: $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(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(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(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4868,plain,
% 2.04/2.28 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4869,plain,
% 2.04/2.28 (((~![X0: $i, 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(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(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(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4868])).
% 2.04/2.28 tff(4870,plain,
% 2.04/2.28 (((~![X0: $i, 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(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(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(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[4869, 4867])).
% 2.04/2.28 tff(4871,plain,
% 2.04/2.28 ((~![X0: $i, 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(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(4872,plain,
% 2.04/2.28 ((~![X0: $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(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4871, 4870])).
% 2.04/2.28 tff(4873,plain,
% 2.04/2.28 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4872, 67, 1113, 656])).
% 2.04/2.28 tff(4874,plain,
% 2.04/2.28 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4489, 50, 4478, 4873])).
% 2.04/2.28 tff(4875,plain,
% 2.04/2.28 (((~![X0: $i, 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(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(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(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4876,plain,
% 2.04/2.28 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4877,plain,
% 2.04/2.28 (((~![X0: $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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(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(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4876])).
% 2.04/2.28 tff(4878,plain,
% 2.04/2.28 (((~![X0: $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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(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(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[4877, 4875])).
% 2.04/2.28 tff(4879,plain,
% 2.04/2.28 ((~![X0: $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(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(4880,plain,
% 2.04/2.28 ((~![X0: $i, 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(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4879, 4878])).
% 2.04/2.28 tff(4881,plain,
% 2.04/2.28 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4880, 67, 1113, 656])).
% 2.04/2.28 tff(4882,plain,
% 2.04/2.28 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1062, 4881, 1051])).
% 2.04/2.28 tff(4883,plain,
% 2.04/2.28 (~r(s(z), s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1121, 1113, 2])).
% 2.04/2.28 tff(4884,plain,
% 2.04/2.28 (b(s(z), s(s(elem!1)))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[936, 4883])).
% 2.04/2.28 tff(4885,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4886,plain,
% 2.04/2.28 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4887,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4886])).
% 2.04/2.28 tff(4888,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[4887, 4885])).
% 2.04/2.28 tff(4889,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(4890,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[4889, 4888])).
% 2.04/2.28 tff(4891,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4890, 204, 990, 4884, 4882, 4874, 4866])).
% 2.04/2.28 tff(4892,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(4893,plain,
% 2.04/2.28 (~b(s(s(elem!1)), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4892, 4864, 2, 656, 4828])).
% 2.04/2.28 tff(4894,plain,
% 2.04/2.28 (~r(s(s(elem!1)), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2967, 4864, 136])).
% 2.04/2.28 tff(4895,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[952, 4894, 4893])).
% 2.04/2.28 tff(4896,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(4897,plain,
% 2.04/2.28 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4896, 2, 136, 4798, 4786, 308, 362, 4792, 4796, 4782])).
% 2.04/2.28 tff(4898,plain,
% 2.04/2.28 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[766, 4897])).
% 2.04/2.28 tff(4899,plain,
% 2.04/2.28 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4841, 204, 4798, 362, 4794, 4792])).
% 2.04/2.28 tff(4900,plain,
% 2.04/2.28 (r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[604, 50, 601, 4899])).
% 2.04/2.28 tff(4901,plain,
% 2.04/2.28 (~r(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2034, 4900, 4782])).
% 2.04/2.28 tff(4902,plain,
% 2.04/2.28 (b(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[357, 4901])).
% 2.04/2.28 tff(4903,plain,
% 2.04/2.28 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2748, 4898, 136, 4902, 4786, 4798])).
% 2.04/2.28 tff(4904,plain,
% 2.04/2.28 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[822, 4903])).
% 2.04/2.28 tff(4905,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), 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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4906,plain,
% 2.04/2.28 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(4907,plain,
% 2.04/2.28 (((~![X0: $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(s(elem!1)))))), z)) | (~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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[4906])).
% 2.04/2.29 tff(4908,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(s(s(s(s(s(s(elem!1)))))), z)) | (~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))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[4907, 4905])).
% 2.04/2.29 tff(4909,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(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(4910,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(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[4909, 4908])).
% 2.04/2.29 tff(4911,plain,
% 2.04/2.29 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4910, 67, 57, 308, 824])).
% 2.04/2.29 tff(4912,plain,
% 2.04/2.29 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2434, 50, 706, 4911])).
% 2.04/2.29 tff(4913,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4914,plain,
% 2.04/2.29 (((~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(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4915,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[4914])).
% 2.04/2.29 tff(4916,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[4915, 4913])).
% 2.04/2.29 tff(4917,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(4918,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[4917, 4916])).
% 2.04/2.29 tff(4919,plain,
% 2.04/2.29 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4918, 204, 785, 153])).
% 2.04/2.29 tff(4920,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4919, 4912, 2403, 1538])).
% 2.04/2.29 tff(4921,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(4922,plain,
% 2.04/2.29 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4921, 4904, 263, 261, 4898, 57, 308, 316])).
% 2.04/2.29 tff(4923,plain,
% 2.04/2.29 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[4922])).
% 2.04/2.29 tff(4924,plain,
% 2.04/2.29 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[4923])).
% 2.04/2.29 tff(4925,plain,
% 2.04/2.29 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[4898, 4924])).
% 2.04/2.29 tff(4926,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4781, 4925])).
% 2.04/2.29 tff(4927,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(4928,plain,
% 2.04/2.29 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4927, 308, 57, 261, 136, 362])).
% 2.04/2.29 tff(4929,plain,
% 2.04/2.29 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[431, 4928])).
% 2.04/2.29 tff(4930,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2673, 204, 4798, 362, 4929, 4790, 4786])).
% 2.04/2.29 tff(4931,plain,((~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(4932,plain,
% 2.04/2.29 (~r(s(s(s(z))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4931, 261, 307, 57, 136])).
% 2.04/2.29 tff(4933,plain,
% 2.04/2.29 (b(s(s(s(z))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[402, 4932])).
% 2.04/2.29 tff(4934,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4935,plain,
% 2.04/2.29 (((~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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4936,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[4935])).
% 2.04/2.29 tff(4937,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[4936, 4934])).
% 2.04/2.29 tff(4938,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(4939,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[4938, 4937])).
% 2.04/2.29 tff(4940,plain,
% 2.04/2.29 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4939, 204, 4780, 153, 4, 1538])).
% 2.04/2.29 tff(4941,plain,
% 2.04/2.29 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[218, 4940])).
% 2.04/2.29 tff(4942,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1815, 67, 538, 261, 510])).
% 2.04/2.29 tff(4943,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(4944,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4943, 4941, 261])).
% 2.04/2.29 tff(4945,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[335, 4944])).
% 2.04/2.29 tff(4946,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4947,plain,
% 2.04/2.29 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4948,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[4947])).
% 2.04/2.29 tff(4949,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[4948, 4946])).
% 2.04/2.29 tff(4950,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(4951,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[4950, 4949])).
% 2.04/2.29 tff(4952,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4951, 204, 404, 4780, 4945, 4, 1538])).
% 2.04/2.29 tff(4953,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(4954,plain,
% 2.04/2.29 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4953, 4933, 285, 261, 263])).
% 2.04/2.29 tff(4955,plain,
% 2.04/2.29 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[190, 4954])).
% 2.04/2.29 tff(4956,plain,
% 2.04/2.29 (~r(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4784, 4955, 261])).
% 2.04/2.29 tff(4957,plain,
% 2.04/2.29 (b(s(s(s(s(z)))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[335, 4956])).
% 2.04/2.29 tff(4958,plain,
% 2.04/2.29 (~r(z, s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4788, 4955, 261])).
% 2.04/2.29 tff(4959,plain,
% 2.04/2.29 (b(z, s(s(s(s(z)))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[357, 4958])).
% 2.04/2.29 tff(4960,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4961,plain,
% 2.04/2.29 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(4962,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[4961])).
% 2.04/2.29 tff(4963,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[4962, 4960])).
% 2.04/2.29 tff(4964,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(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))))))),
% 2.04/2.30 inference(quant_inst,[status(thm)],[])).
% 2.04/2.30 tff(4965,plain,
% 2.04/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.30 inference(modus_ponens,[status(thm)],[4964, 4963])).
% 2.04/2.30 tff(4966,plain,
% 2.04/2.30 ($false),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[4965, 204, 4933, 4959, 4780, 263, 4957])).
% 2.04/2.30 tff(4967,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.30 tff(4968,plain,
% 2.04/2.30 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[4967, 260, 57, 56])).
% 2.04/2.30 tff(4969,plain,
% 2.04/2.30 (b(s(s(s(s(s(s(z)))))), z)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[641, 4968])).
% 2.04/2.30 tff(4970,plain,
% 2.04/2.30 (~r(z, s(z))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[294, 260, 57])).
% 2.04/2.30 tff(4971,plain,
% 2.04/2.30 (b(z, s(z))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[306, 4970])).
% 2.04/2.30 tff(4972,plain,
% 2.04/2.30 (~r(s(z), z)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[546, 538, 56])).
% 2.04/2.30 tff(4973,plain,
% 2.04/2.30 (b(s(z), z)),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[376, 4972])).
% 2.04/2.30 tff(4974,plain,
% 2.04/2.30 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[1993, 4973, 443, 362, 1469])).
% 2.04/2.30 tff(4975,plain,
% 2.04/2.30 (r(z, s(s(s(s(s(s(z)))))))),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[604, 50, 601, 4974])).
% 2.04/2.30 tff(4976,plain,
% 2.04/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.04/2.30 inference(rewrite,[status(thm)],[])).
% 2.04/2.30 tff(4977,plain,
% 2.04/2.30 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.04/2.30 inference(rewrite,[status(thm)],[])).
% 2.04/2.30 tff(4978,plain,
% 2.04/2.30 (((~![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(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 2.04/2.30 inference(monotonicity,[status(thm)],[4977])).
% 2.04/2.30 tff(4979,plain,
% 2.04/2.30 (((~![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(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.04/2.30 inference(transitivity,[status(thm)],[4978, 4976])).
% 2.04/2.30 tff(4980,plain,
% 2.04/2.30 ((~![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(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.04/2.30 inference(quant_inst,[status(thm)],[])).
% 2.04/2.30 tff(4981,plain,
% 2.04/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 2.04/2.30 inference(modus_ponens,[status(thm)],[4980, 4979])).
% 2.04/2.30 tff(4982,plain,
% 2.04/2.30 ($false),
% 2.04/2.30 inference(unit_resolution,[status(thm)],[4981, 67, 3, 2032, 264])).
% 2.04/2.30 tff(4983,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(4984,plain,
% 2.14/2.30 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4983, 4975, 260])).
% 2.14/2.30 tff(4985,plain,
% 2.14/2.30 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[284, 4984])).
% 2.14/2.30 tff(4986,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[619, 67, 3, 499, 2032])).
% 2.14/2.30 tff(4987,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(4988,plain,
% 2.14/2.30 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4987, 4975, 260])).
% 2.14/2.30 tff(4989,plain,
% 2.14/2.30 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[134, 4988])).
% 2.14/2.30 tff(4990,plain,
% 2.14/2.30 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2619, 204, 4780, 153, 4985])).
% 2.14/2.30 tff(4991,plain,
% 2.14/2.30 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[4990, 4989])).
% 2.14/2.30 tff(4992,plain,
% 2.14/2.30 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[190, 4991])).
% 2.14/2.30 tff(4993,plain,
% 2.14/2.30 (~r(z, s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2034, 4992, 4975])).
% 2.14/2.30 tff(4994,plain,
% 2.14/2.30 (b(z, s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[357, 4993])).
% 2.14/2.30 tff(4995,plain,
% 2.14/2.30 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1289, 1287])).
% 2.14/2.30 tff(4996,plain,
% 2.14/2.30 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1139, 1135, 1101])).
% 2.14/2.30 tff(4997,plain,
% 2.14/2.30 (~r(s(s(elem!1)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[946, 938, 389])).
% 2.14/2.30 tff(4998,plain,
% 2.14/2.30 (b(s(s(elem!1)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1099, 4997])).
% 2.14/2.30 tff(4999,plain,
% 2.14/2.30 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1148, 4998, 361, 548, 1101, 1135])).
% 2.14/2.30 tff(5000,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5001,plain,
% 2.14/2.30 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5002,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5001])).
% 2.14/2.30 tff(5003,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5002, 5000])).
% 2.14/2.30 tff(5004,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5005,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5004, 5003])).
% 2.14/2.30 tff(5006,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5005, 67, 938, 136, 4999])).
% 2.14/2.30 tff(5007,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(5008,plain,
% 2.14/2.30 (~r(s(s(elem!1)), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5007, 1135, 361, 1101, 136, 389])).
% 2.14/2.30 tff(5009,plain,
% 2.14/2.30 (b(s(s(elem!1)), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[952, 5008])).
% 2.14/2.30 tff(5010,plain,
% 2.14/2.30 (~r(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1773, 389, 308])).
% 2.14/2.30 tff(5011,plain,
% 2.14/2.30 (b(s(z), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[478, 5010])).
% 2.14/2.30 tff(5012,plain,
% 2.14/2.30 (~r(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[397, 389, 308])).
% 2.14/2.30 tff(5013,plain,
% 2.14/2.30 (b(s(s(s(z))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[558, 5012])).
% 2.14/2.30 tff(5014,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5015,plain,
% 2.14/2.30 (((~b(s(s(s(z))), 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))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5016,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), 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)))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5015])).
% 2.14/2.30 tff(5017,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5016, 5014])).
% 2.14/2.30 tff(5018,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(z), s(s(elem!1)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5019,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5018, 5017])).
% 2.14/2.30 tff(5020,plain,
% 2.14/2.30 ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5019, 204, 990, 5013, 5011])).
% 2.14/2.30 tff(5021,plain,
% 2.14/2.30 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5020, 937])).
% 2.14/2.30 tff(5022,plain,
% 2.14/2.30 (r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1167, 5021, 628])).
% 2.14/2.30 tff(5023,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3851, 67, 900, 308, 5022])).
% 2.14/2.30 tff(5024,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(5025,plain,
% 2.14/2.30 (~r(s(s(elem!1)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5024, 5009, 628, 308, 389])).
% 2.14/2.30 tff(5026,plain,
% 2.14/2.30 (b(s(s(elem!1)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1099, 5025])).
% 2.14/2.30 tff(5027,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5028,plain,
% 2.14/2.30 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5029,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5028])).
% 2.14/2.30 tff(5030,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5029, 5027])).
% 2.14/2.30 tff(5031,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5032,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5031, 5030])).
% 2.14/2.30 tff(5033,plain,
% 2.14/2.30 (~b(z, s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5032, 204, 5026, 4996, 361, 548])).
% 2.14/2.30 tff(5034,plain,
% 2.14/2.30 (r(z, s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2160, 5033])).
% 2.14/2.30 tff(5035,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5036,plain,
% 2.14/2.30 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5037,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), 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(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5036])).
% 2.14/2.30 tff(5038,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), 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(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5037, 5035])).
% 2.14/2.30 tff(5039,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(s(z))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5040,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5039, 5038])).
% 2.14/2.30 tff(5041,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5040, 67, 2142, 3, 2127])).
% 2.14/2.30 tff(5042,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(5043,plain,
% 2.14/2.30 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5042, 5034, 3])).
% 2.14/2.30 tff(5044,plain,
% 2.14/2.30 (b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3335, 5043, 3837])).
% 2.14/2.30 tff(5045,plain,
% 2.14/2.30 (~b(s(s(elem!1)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1148, 1129, 361, 359, 1101, 1135])).
% 2.14/2.30 tff(5046,plain,
% 2.14/2.30 (r(s(s(elem!1)), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1099, 5045])).
% 2.14/2.30 tff(5047,plain,
% 2.14/2.30 (~r(s(z), s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[915, 5046, 389])).
% 2.14/2.30 tff(5048,plain,
% 2.14/2.30 (b(s(z), s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[936, 5047])).
% 2.14/2.30 tff(5049,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5050,plain,
% 2.14/2.30 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5051,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5050])).
% 2.14/2.30 tff(5052,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5051, 5049])).
% 2.14/2.30 tff(5053,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5054,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5053, 5052])).
% 2.14/2.30 tff(5055,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5054, 204, 3720, 1140, 361, 359, 1134])).
% 2.14/2.30 tff(5056,plain,((s(s(elem!1)) = s(s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(5057,plain,
% 2.14/2.30 (~b(z, s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5056, 1129, 361, 1101, 359, 1135])).
% 2.14/2.30 tff(5058,plain,
% 2.14/2.30 (r(z, s(s(elem!1)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[2160, 5057])).
% 2.14/2.30 tff(5059,plain,
% 2.14/2.30 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[3784, 5058, 3])).
% 2.14/2.30 tff(5060,plain,
% 2.14/2.30 (b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1167, 5059, 628])).
% 2.14/2.30 tff(5061,plain,
% 2.14/2.30 ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5019, 204, 990, 444, 566])).
% 2.14/2.30 tff(5062,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5061, 5060, 5048])).
% 2.14/2.30 tff(5063,plain,(r(s(s(s(s(z)))), s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(elem!1)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5064,plain,
% 2.14/2.31 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5063, 5009, 5013, 5011, 628, 3, 389, 361, 1101, 548, 1135])).
% 2.14/2.31 tff(5065,plain,
% 2.14/2.31 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3784, 5034, 3])).
% 2.14/2.31 tff(5066,plain,
% 2.14/2.31 (b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1167, 5065, 628])).
% 2.14/2.31 tff(5067,plain,
% 2.14/2.31 ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5019, 204, 5009, 5013, 5011])).
% 2.14/2.31 tff(5068,plain,
% 2.14/2.31 (~b(s(z), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5067, 5066])).
% 2.14/2.31 tff(5069,plain,
% 2.14/2.31 (r(s(z), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[936, 5068])).
% 2.14/2.31 tff(5070,plain,
% 2.14/2.31 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1111, 5069, 5064])).
% 2.14/2.31 tff(5071,plain,
% 2.14/2.31 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[431, 5070])).
% 2.14/2.31 tff(5072,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5073,plain,
% 2.14/2.31 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5074,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5073])).
% 2.14/2.31 tff(5075,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5074, 5072])).
% 2.14/2.31 tff(5076,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5077,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5076, 5075])).
% 2.14/2.31 tff(5078,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5077, 204, 5009, 5013, 4996, 5071, 5044])).
% 2.14/2.31 tff(5079,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5080,plain,
% 2.14/2.31 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5079, 1101, 3, 361, 308, 389, 628, 136])).
% 2.14/2.31 tff(5081,plain,
% 2.14/2.31 (~r(s(s(elem!1)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2967, 5080, 136])).
% 2.14/2.31 tff(5082,plain,
% 2.14/2.31 (b(s(s(elem!1)), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[952, 5081])).
% 2.14/2.31 tff(5083,plain,
% 2.14/2.31 (~r(s(s(elem!1)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5024, 5082, 628, 308, 389])).
% 2.14/2.31 tff(5084,plain,
% 2.14/2.31 (b(s(s(elem!1)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1099, 5083])).
% 2.14/2.31 tff(5085,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5086,plain,
% 2.14/2.31 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5087,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5086])).
% 2.14/2.31 tff(5088,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5087, 5085])).
% 2.14/2.31 tff(5089,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5090,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5089, 5088])).
% 2.14/2.31 tff(5091,plain,
% 2.14/2.31 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5090, 204, 5082, 5084, 362, 548])).
% 2.14/2.31 tff(5092,plain,
% 2.14/2.31 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1132, 50, 1128, 5091])).
% 2.14/2.31 tff(5093,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5094,plain,
% 2.14/2.31 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5095,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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)))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5094])).
% 2.14/2.31 tff(5096,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5095, 5093])).
% 2.14/2.31 tff(5097,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5098,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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)))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5097, 5096])).
% 2.14/2.31 tff(5099,plain,
% 2.14/2.31 ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5098, 204, 990, 1102, 362, 444, 566])).
% 2.14/2.31 tff(5100,plain,
% 2.14/2.31 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5099, 2222])).
% 2.14/2.31 tff(5101,plain,
% 2.14/2.31 (r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1167, 5100, 628])).
% 2.14/2.31 tff(5102,plain,
% 2.14/2.31 (~r(z, s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3784, 5101, 3])).
% 2.14/2.31 tff(5103,plain,
% 2.14/2.31 (b(z, s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2160, 5102])).
% 2.14/2.31 tff(5104,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5105,plain,
% 2.14/2.31 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5106,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5105])).
% 2.14/2.31 tff(5107,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5106, 5104])).
% 2.14/2.31 tff(5108,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5109,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5108, 5107])).
% 2.14/2.31 tff(5110,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5109, 204, 990, 2222, 5103, 1102, 362])).
% 2.14/2.31 tff(5111,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5112,plain,
% 2.14/2.31 (~b(s(z), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5111, 5082, 5084, 362, 3, 628, 5013, 5011])).
% 2.14/2.31 tff(5113,plain,
% 2.14/2.31 (r(s(z), s(s(elem!1)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[936, 5112])).
% 2.14/2.31 tff(5114,plain,
% 2.14/2.31 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1111, 5113, 5092])).
% 2.14/2.31 tff(5115,plain,
% 2.14/2.31 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[431, 5114])).
% 2.14/2.31 tff(5116,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5117,plain,
% 2.14/2.31 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5118,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5117])).
% 2.14/2.31 tff(5119,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5118, 5116])).
% 2.14/2.31 tff(5120,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5121,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5120, 5119])).
% 2.14/2.31 tff(5122,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5121, 204, 5082, 5084, 362, 5115, 361])).
% 2.14/2.31 tff(5123,plain,((s(s(elem!1)) = s(s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5124,plain,
% 2.14/2.31 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5123, 389, 361, 3, 4995, 308, 362, 56])).
% 2.14/2.32 tff(5125,plain,
% 2.14/2.32 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5124])).
% 2.14/2.32 tff(5126,plain,
% 2.14/2.32 (s(elem!1) = s(s(s(z)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[919, 5125, 20])).
% 2.14/2.32 tff(5127,plain,
% 2.14/2.32 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5126])).
% 2.14/2.32 tff(5128,plain,
% 2.14/2.32 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[5127])).
% 2.14/2.32 tff(5129,plain,
% 2.14/2.32 (s(s(z)) = elem!1),
% 2.14/2.32 inference(transitivity,[status(thm)],[84, 5128, 902])).
% 2.14/2.32 tff(5130,plain,
% 2.14/2.32 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5129])).
% 2.14/2.32 tff(5131,plain,
% 2.14/2.32 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.14/2.32 inference(symmetry,[status(thm)],[5130])).
% 2.14/2.32 tff(5132,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.32 tff(5133,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.14/2.32 inference(symmetry,[status(thm)],[5132])).
% 2.14/2.32 tff(5134,plain,
% 2.14/2.32 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5133])).
% 2.14/2.32 tff(5135,plain,
% 2.14/2.32 (~b(s(s(elem!1)), s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5, 5134])).
% 2.14/2.32 tff(5136,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[990, 5135])).
% 2.14/2.32 tff(5137,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5138,plain,
% 2.14/2.32 (~b(s(s(elem!1)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5137, 5124, 5])).
% 2.14/2.32 tff(5139,plain,
% 2.14/2.32 (r(s(s(elem!1)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[952, 5138])).
% 2.14/2.32 tff(5140,plain,
% 2.14/2.32 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2967, 5139, 56])).
% 2.14/2.32 tff(5141,plain,
% 2.14/2.32 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[2272])).
% 2.14/2.32 tff(5142,plain,
% 2.14/2.32 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5141, 2214])).
% 2.14/2.32 tff(5143,plain,
% 2.14/2.32 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[853, 5142])).
% 2.14/2.32 tff(5144,plain,
% 2.14/2.32 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.14/2.32 inference(monotonicity,[status(thm)],[2207])).
% 2.14/2.32 tff(5145,plain,
% 2.14/2.32 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5144, 2200])).
% 2.14/2.32 tff(5146,plain,
% 2.14/2.32 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5145])).
% 2.14/2.32 tff(5147,plain,
% 2.14/2.32 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[757, 5146])).
% 2.14/2.32 tff(5148,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 2.14/2.32 tff(5149,plain,
% 2.14/2.32 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5148])).
% 2.14/2.32 tff(5150,plain,
% 2.14/2.32 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[5149])).
% 2.14/2.32 tff(5151,plain,
% 2.14/2.32 (s(elem!1) = s(s(s(elem!1)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[919, 5150, 698])).
% 2.14/2.32 tff(5152,plain,
% 2.14/2.32 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5151])).
% 2.14/2.32 tff(5153,plain,
% 2.14/2.32 (elem!1 = s(s(elem!1))),
% 2.14/2.32 inference(transitivity,[status(thm)],[1009, 5152, 753])).
% 2.14/2.32 tff(5154,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 2.14/2.32 tff(5155,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5154, 5153])).
% 2.14/2.32 tff(5156,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5157,plain,
% 2.14/2.32 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5156, 5147])).
% 2.14/2.32 tff(5158,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5157, 5143])).
% 2.14/2.32 tff(5159,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5160,plain,
% 2.14/2.32 (~(z = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5159, 5124])).
% 2.14/2.32 tff(5161,plain,
% 2.14/2.32 (z = elem!1),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[2300, 2205])).
% 2.14/2.32 tff(5162,assumption,(~(z = elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5163,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5162, 5161])).
% 2.14/2.32 tff(5164,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5165,plain,
% 2.14/2.32 (~(elem!1 = z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5164, 5160])).
% 2.14/2.32 tff(5166,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[546, 389, 56])).
% 2.14/2.32 tff(5167,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[335, 5166])).
% 2.14/2.32 tff(5168,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5124])).
% 2.14/2.32 tff(5169,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(s(s(z))))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.32 inference(symmetry,[status(thm)],[5168])).
% 2.14/2.32 tff(5170,plain,
% 2.14/2.32 ((~r(s(s(s(s(z)))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5169])).
% 2.14/2.32 tff(5171,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5172,plain,
% 2.14/2.32 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5173,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5172])).
% 2.14/2.32 tff(5174,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5173, 5171])).
% 2.14/2.32 tff(5175,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z)))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5176,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5175, 5174])).
% 2.14/2.32 tff(5177,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5176, 67, 56])).
% 2.14/2.32 tff(5178,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5177, 5170])).
% 2.14/2.32 tff(5179,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 2.14/2.32 tff(5180,plain,
% 2.14/2.32 (r(s(s(elem!1)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[952, 5179])).
% 2.14/2.32 tff(5181,plain,
% 2.14/2.32 (((~![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))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5182,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5183,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5182, 5181])).
% 2.14/2.32 tff(5184,plain,
% 2.14/2.32 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5183, 50])).
% 2.14/2.32 tff(5185,plain,
% 2.14/2.32 (r(elem!1, z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5184, 2209, 1014])).
% 2.14/2.32 tff(5186,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, 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(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5187,plain,
% 2.14/2.32 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5188,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), 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(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5187])).
% 2.14/2.32 tff(5189,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), 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(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5188, 5186])).
% 2.14/2.32 tff(5190,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5191,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5190, 5189])).
% 2.14/2.32 tff(5192,plain,
% 2.14/2.32 ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5191, 67])).
% 2.14/2.32 tff(5193,plain,
% 2.14/2.32 (~r(elem!1, s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5192, 5185, 389])).
% 2.14/2.32 tff(5194,plain,
% 2.14/2.32 (((~![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)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5195,plain,
% 2.14/2.32 ((~![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)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5196,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5195, 5194])).
% 2.14/2.32 tff(5197,plain,
% 2.14/2.32 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5196, 50])).
% 2.14/2.32 tff(5198,plain,
% 2.14/2.32 (b(elem!1, s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5197, 5193, 1287])).
% 2.14/2.32 tff(5199,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 2.14/2.32 tff(5200,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5199])).
% 2.14/2.32 tff(5201,plain,
% 2.14/2.32 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.14/2.32 inference(symmetry,[status(thm)],[5200])).
% 2.14/2.32 tff(5202,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 2.14/2.32 tff(5203,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(z))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5202, 5201])).
% 2.14/2.32 tff(5204,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5179, 5203])).
% 2.14/2.32 tff(5205,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5206,plain,
% 2.14/2.32 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5205, 5198, 5179])).
% 2.14/2.32 tff(5207,plain,
% 2.14/2.32 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 2.14/2.32 inference(symmetry,[status(thm)],[2200])).
% 2.14/2.32 tff(5208,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 2.14/2.32 tff(5209,plain,
% 2.14/2.32 (s(s(elem!1)) = elem!1),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5208, 5207])).
% 2.14/2.32 tff(5210,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5211,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5210, 5209])).
% 2.14/2.32 tff(5212,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5213,plain,
% 2.14/2.32 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5212, 5206])).
% 2.14/2.32 tff(5214,plain,
% 2.14/2.32 (~r(z, s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2244, 938, 2142])).
% 2.14/2.32 tff(5215,plain,
% 2.14/2.32 (b(z, s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[306, 5214])).
% 2.14/2.32 tff(5216,plain,
% 2.14/2.32 (~r(s(s(elem!1)), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[946, 389, 938])).
% 2.14/2.32 tff(5217,plain,
% 2.14/2.32 (b(s(s(elem!1)), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1099, 5216])).
% 2.14/2.32 tff(5218,plain,
% 2.14/2.32 (~b(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1533, 404, 444, 362, 566])).
% 2.14/2.32 tff(5219,plain,
% 2.14/2.32 (r(z, s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[259, 5218])).
% 2.14/2.32 tff(5220,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5221,plain,
% 2.14/2.32 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~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(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5222,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5221])).
% 2.14/2.32 tff(5223,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5222, 5220])).
% 2.14/2.32 tff(5224,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5225,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5224, 5223])).
% 2.14/2.32 tff(5226,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5225, 204, 1102, 362, 444, 404, 2323])).
% 2.14/2.32 tff(5227,plain,((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5228,plain,
% 2.14/2.32 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5227, 404, 444, 362, 1102])).
% 2.14/2.32 tff(5229,plain,
% 2.14/2.32 (r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1167, 5228, 628])).
% 2.14/2.32 tff(5230,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3784, 5229, 5219, 2142])).
% 2.14/2.32 tff(5231,plain,((~b(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5232,plain,
% 2.14/2.32 (~b(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5231, 5217, 628, 444, 5215, 2142, 566])).
% 2.14/2.32 tff(5233,plain,
% 2.14/2.32 (r(s(s(s(z))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[402, 5232])).
% 2.14/2.32 tff(5234,plain,
% 2.14/2.32 (~(z = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2211, 2209])).
% 2.14/2.32 tff(5235,plain,
% 2.14/2.32 (s(s(s(z))) = s(s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[1324])).
% 2.14/2.32 tff(5236,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2179, 5235])).
% 2.14/2.32 tff(5237,plain,((~(elem!1 = s(z))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5238,plain,
% 2.14/2.32 (~(elem!1 = s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5237, 3837])).
% 2.14/2.32 tff(5239,plain,
% 2.14/2.32 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3784, 260, 2142])).
% 2.14/2.32 tff(5240,plain,
% 2.14/2.32 (b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[1167, 5239, 628])).
% 2.14/2.32 tff(5241,plain,
% 2.14/2.32 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5042, 260, 2142])).
% 2.14/2.32 tff(5242,plain,
% 2.14/2.32 (b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3335, 5241, 3837])).
% 2.14/2.32 tff(5243,assumption,(b(z, elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5244,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5245,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5246,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5247,plain,
% 2.14/2.32 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5248,plain,
% 2.14/2.32 (((~![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(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5247])).
% 2.14/2.32 tff(5249,plain,
% 2.14/2.32 (((~![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(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5248, 5246])).
% 2.14/2.32 tff(5250,plain,
% 2.14/2.32 ((~![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(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5251,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5250, 5249])).
% 2.14/2.32 tff(5252,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5251, 67, 938, 4659, 5245])).
% 2.14/2.32 tff(5253,plain,((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5254,plain,
% 2.14/2.32 (~r(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5253, 4659, 938])).
% 2.14/2.32 tff(5255,plain,
% 2.14/2.32 (~r(elem!1, z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5192, 4659, 389])).
% 2.14/2.32 tff(5256,plain,
% 2.14/2.32 (b(elem!1, z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5184, 5255, 2209])).
% 2.14/2.32 tff(5257,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5258,plain,
% 2.14/2.32 (elem!1 = s(s(elem!1))),
% 2.14/2.32 inference(symmetry,[status(thm)],[5199])).
% 2.14/2.32 tff(5259,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5154, 5258])).
% 2.14/2.32 tff(5260,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5261,plain,
% 2.14/2.32 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5260, 5154])).
% 2.14/2.32 tff(5262,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5263,plain,
% 2.14/2.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5264,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5265,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5264, 5263])).
% 2.14/2.32 tff(5266,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5265, 50, 5257, 5262, 5210])).
% 2.14/2.32 tff(5267,plain,(r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5268,plain,
% 2.14/2.32 (b(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5267, 5261, 5257])).
% 2.14/2.32 tff(5269,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.14/2.32 tff(5270,plain,
% 2.14/2.32 (b(elem!1, s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2351, 5154, 5269])).
% 2.14/2.32 tff(5271,plain,
% 2.14/2.32 (b(s(s(elem!1)), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5267, 5210, 5257])).
% 2.14/2.32 tff(5272,plain,
% 2.14/2.32 (~b(elem!1, s(s(elem!1)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[4668, 5271, 4445, 2323, 2141])).
% 2.14/2.32 tff(5273,plain,
% 2.14/2.32 (elem!1 = s(s(elem!1))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[2351, 5272, 5269])).
% 2.14/2.32 tff(5274,plain,
% 2.14/2.32 (s(s(elem!1)) = elem!1),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5273, 5207])).
% 2.14/2.32 tff(5275,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5210, 5274])).
% 2.14/2.32 tff(5276,plain,((s(s(elem!1)) = elem!1) | r(elem!1, s(s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5277,plain,
% 2.14/2.32 (~b(s(s(s(z))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5276, 5261, 2323, 2141, 5269, 5257])).
% 2.14/2.32 tff(5278,plain,
% 2.14/2.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5279,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5280,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5279, 5278])).
% 2.14/2.32 tff(5281,plain,
% 2.14/2.32 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5280, 50])).
% 2.14/2.32 tff(5282,plain,
% 2.14/2.32 (r(s(s(s(z))), elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5281, 5277, 5244])).
% 2.14/2.32 tff(5283,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5284,assumption,(r(z, elem!1)), introduced(assumption)).
% 2.14/2.32 tff(5285,plain,
% 2.14/2.32 (((~![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(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5286,plain,
% 2.14/2.32 (((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5287,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), 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, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5286])).
% 2.14/2.32 tff(5288,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), 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, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5287, 5285])).
% 2.14/2.32 tff(5289,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5290,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5289, 5288])).
% 2.14/2.32 tff(5291,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5290, 67, 5284, 5283, 3])).
% 2.14/2.32 tff(5292,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5293,plain,
% 2.14/2.32 (~r(z, elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5292, 5282, 3])).
% 2.14/2.32 tff(5294,plain,
% 2.14/2.32 (((~![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))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5295,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5296,plain,
% 2.14/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 2.14/2.32 tff(5297,plain,
% 2.14/2.32 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5296, 50])).
% 2.14/2.32 tff(5298,plain,
% 2.14/2.32 (b(z, elem!1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5297, 5293, 5162])).
% 2.14/2.32 tff(5299,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5300,plain,
% 2.14/2.33 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5301,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5300])).
% 2.14/2.33 tff(5302,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5301, 5299])).
% 2.14/2.33 tff(5303,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5304,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5303, 5302])).
% 2.14/2.33 tff(5305,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5304, 204, 5298, 1026, 5270, 1102, 5268])).
% 2.14/2.33 tff(5306,plain,((elem!1 = s(s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (z = elem!1) | (~r(z, s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | r(elem!1, s(s(elem!1))) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5307,plain,
% 2.14/2.33 (r(elem!1, s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5306, 5256, 5154, 5234, 5217, 3, 2323, 2141, 5244, 5254])).
% 2.14/2.33 tff(5308,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5309,plain,
% 2.14/2.33 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5310,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5309])).
% 2.14/2.33 tff(5311,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5310, 5308])).
% 2.14/2.33 tff(5312,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5313,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5312, 5311])).
% 2.14/2.33 tff(5314,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5313, 67, 938, 5307, 4659])).
% 2.14/2.33 tff(5315,plain,((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (s(s(s(z))) = elem!1) | (elem!1 = z) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5316,plain,
% 2.14/2.33 (~r(elem!1, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5315, 5244, 5154, 3, 2323, 2141, 938, 2209, 389])).
% 2.14/2.33 tff(5317,plain,
% 2.14/2.33 (b(elem!1, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5197, 5316, 1287])).
% 2.14/2.33 tff(5318,assumption,(s(z) = elem!1), introduced(assumption)).
% 2.14/2.33 tff(5319,plain,
% 2.14/2.33 (elem!1 = s(z)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5318, 3752])).
% 2.14/2.33 tff(5320,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[1287, 5319])).
% 2.14/2.33 tff(5321,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5322,plain,
% 2.14/2.33 (~(s(z) = elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5321, 1287])).
% 2.14/2.33 tff(5323,plain,
% 2.14/2.33 (b(s(s(elem!1)), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5267, 5257, 5210])).
% 2.14/2.33 tff(5324,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5325,plain,
% 2.14/2.33 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5326,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5325])).
% 2.14/2.33 tff(5327,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5326, 5324])).
% 2.14/2.33 tff(5328,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5329,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 2.14/2.33 tff(5330,plain,
% 2.14/2.33 ((~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5329, 204, 1102, 362, 5202])).
% 2.14/2.33 tff(5331,plain,
% 2.14/2.33 (~b(elem!1, z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5330, 5323])).
% 2.14/2.33 tff(5332,plain,
% 2.14/2.33 (r(elem!1, z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5184, 5331, 2209])).
% 2.14/2.33 tff(5333,assumption,(r(elem!1, z)), introduced(assumption)).
% 2.14/2.33 tff(5334,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5335,plain,
% 2.14/2.33 (((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5336,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5335])).
% 2.14/2.33 tff(5337,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5336, 5334])).
% 2.14/2.33 tff(5338,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5339,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 2.14/2.33 tff(5340,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5339, 67, 5333, 5283, 308])).
% 2.14/2.33 tff(5341,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5342,plain,
% 2.14/2.33 (~r(s(s(s(z))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5341, 5332, 308])).
% 2.14/2.33 tff(5343,plain,
% 2.14/2.33 (b(s(s(s(z))), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5281, 5342, 5244])).
% 2.14/2.33 tff(5344,plain,
% 2.14/2.33 (r(elem!1, s(s(elem!1)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5276, 5343, 5210, 2141, 2323, 5257])).
% 2.14/2.33 tff(5345,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5346,plain,
% 2.14/2.33 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5347,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5346])).
% 2.14/2.33 tff(5348,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5347, 5345])).
% 2.14/2.33 tff(5349,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5350,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5349, 5348])).
% 2.14/2.33 tff(5351,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5350, 67, 5332, 5344, 2142])).
% 2.14/2.33 tff(5352,plain,(r(s(s(elem!1)), elem!1) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~r(s(s(s(z))), z)) | (elem!1 = z) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5353,plain,
% 2.14/2.33 (r(s(s(elem!1)), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5352, 5244, 5261, 2141, 2323, 2142, 308, 2209, 5217, 5215, 5317])).
% 2.14/2.33 tff(5354,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 2.14/2.33 tff(5355,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(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), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5356,plain,
% 2.14/2.33 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5357,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5356])).
% 2.14/2.33 tff(5358,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5357, 5355])).
% 2.14/2.33 tff(5359,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5360,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 2.14/2.33 tff(5361,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5360, 67, 938, 5354, 5245])).
% 2.14/2.33 tff(5362,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5363,plain,
% 2.14/2.33 (~r(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5362, 5353, 938])).
% 2.14/2.33 tff(5364,plain,
% 2.14/2.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5365,plain,
% 2.14/2.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5366,plain,
% 2.14/2.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5365, 5364])).
% 2.14/2.33 tff(5367,plain,
% 2.14/2.33 (b(s(z), elem!1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5366, 50, 5363, 5322])).
% 2.14/2.33 tff(5368,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5369,plain,
% 2.14/2.33 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5370,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5369])).
% 2.14/2.33 tff(5371,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5370, 5368])).
% 2.14/2.34 tff(5372,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5373,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5372, 5371])).
% 2.14/2.34 tff(5374,plain,
% 2.14/2.34 ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5373, 204])).
% 2.14/2.34 tff(5375,plain,
% 2.14/2.34 (~b(elem!1, z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5374, 5367, 5215, 5243, 5317])).
% 2.14/2.34 tff(5376,plain,
% 2.14/2.34 (r(elem!1, z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5184, 5375, 2209])).
% 2.14/2.34 tff(5377,plain,
% 2.14/2.34 (~r(s(s(s(z))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5341, 5376, 308])).
% 2.14/2.34 tff(5378,plain,
% 2.14/2.34 (b(s(s(s(z))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5281, 5377, 5244])).
% 2.14/2.34 tff(5379,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5380,plain,
% 2.14/2.34 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5381,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5380])).
% 2.14/2.34 tff(5382,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5381, 5379])).
% 2.14/2.34 tff(5383,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5384,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 2.14/2.34 tff(5385,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5384, 204, 5317, 5367, 444, 5378, 566])).
% 2.14/2.34 tff(5386,plain,((s(s(s(z))) = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (elem!1 = z) | (~b(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5387,plain,
% 2.14/2.34 (s(s(s(z))) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5386, 5243, 566, 308, 2209, 444, 938, 2141, 2323, 2142, 1287, 5154, 260, 389])).
% 2.14/2.34 tff(5388,plain,
% 2.14/2.34 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5387])).
% 2.14/2.34 tff(5389,plain,
% 2.14/2.34 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 2.14/2.34 inference(symmetry,[status(thm)],[5388])).
% 2.14/2.34 tff(5390,plain,
% 2.14/2.34 (b(z, s(s(s(z))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5243, 5389])).
% 2.14/2.34 tff(5391,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[250, 5390])).
% 2.14/2.34 tff(5392,plain,((~b(z, elem!1)) | b(z, s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (elem!1 = z) | (~b(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (elem!1 = s(z)) | (elem!1 = s(s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5393,plain,
% 2.14/2.34 (~b(z, elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5392, 250, 566, 5233, 2209, 444, 938, 5242, 5240, 2142, 5238, 5154, 389])).
% 2.14/2.34 tff(5394,plain,
% 2.14/2.34 (r(z, elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5297, 5393, 5234])).
% 2.14/2.34 tff(5395,plain,
% 2.14/2.34 (~r(s(s(s(z))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5292, 5394, 260])).
% 2.14/2.34 tff(5396,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5397,plain,
% 2.14/2.34 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5398,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), 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, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5397])).
% 2.14/2.34 tff(5399,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), 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, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5398, 5396])).
% 2.14/2.34 tff(5400,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5401,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5400, 5399])).
% 2.14/2.34 tff(5402,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5401, 67, 5284, 2142, 5245])).
% 2.14/2.34 tff(5403,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5404,plain,
% 2.14/2.34 (~r(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5403, 5394, 2142])).
% 2.14/2.34 tff(5405,plain,
% 2.14/2.34 (((~![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(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, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5406,plain,
% 2.14/2.34 (((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5407,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5406])).
% 2.14/2.34 tff(5408,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5407, 5405])).
% 2.14/2.34 tff(5409,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5410,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5409, 5408])).
% 2.14/2.34 tff(5411,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5410, 67, 5284, 2365, 2142])).
% 2.14/2.34 tff(5412,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5413,plain,
% 2.14/2.34 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5412, 5394, 2142])).
% 2.14/2.34 tff(5414,plain,
% 2.14/2.34 (~b(s(s(s(z))), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5276, 5413, 5261, 5242, 5240, 5404])).
% 2.14/2.34 tff(5415,plain,
% 2.14/2.34 (s(s(s(z))) = elem!1),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5281, 5414, 5395])).
% 2.14/2.34 tff(5416,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 2.14/2.34 tff(5417,plain,
% 2.14/2.34 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5416])).
% 2.14/2.34 tff(5418,plain,
% 2.14/2.34 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 2.14/2.34 inference(symmetry,[status(thm)],[5417])).
% 2.14/2.34 tff(5419,plain,
% 2.14/2.34 ((~b(elem!1, s(z))) <=> (~b(s(s(s(z))), s(z)))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5418])).
% 2.14/2.34 tff(5420,plain,
% 2.14/2.34 (~b(s(s(s(z))), s(z))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[3702, 5419])).
% 2.14/2.34 tff(5421,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[444, 5420])).
% 2.14/2.34 tff(5422,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(s(s(z))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5423,plain,
% 2.14/2.34 (b(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5422, 5415, 444])).
% 2.14/2.34 tff(5424,plain,
% 2.14/2.34 (b(elem!1, s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2351, 5413, 5154])).
% 2.14/2.34 tff(5425,plain,
% 2.14/2.34 (b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5267, 5404, 5261])).
% 2.14/2.34 tff(5426,plain,
% 2.14/2.34 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5415])).
% 2.14/2.34 tff(5427,plain,
% 2.14/2.34 (b(s(z), elem!1)),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[566, 5426])).
% 2.14/2.34 tff(5428,plain,
% 2.14/2.34 (~b(s(z), s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[3716, 5427, 5425, 5424, 5423])).
% 2.14/2.34 tff(5429,plain,
% 2.14/2.34 (r(s(z), s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[936, 5428])).
% 2.14/2.34 tff(5430,plain,
% 2.14/2.34 (((~![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), 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, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5431,plain,
% 2.14/2.34 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5432,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(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), s(s(elem!1)))) | (~r(z, s(s(elem!1))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5431])).
% 2.14/2.34 tff(5433,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(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), s(s(elem!1)))) | (~r(z, s(s(elem!1)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5432, 5430])).
% 2.14/2.34 tff(5434,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5435,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5434, 5433])).
% 2.14/2.34 tff(5436,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5435, 67, 5394, 5429, 2142, 389])).
% 2.14/2.34 tff(5437,plain,(b(z, s(s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (elem!1 = s(s(elem!1))) | (elem!1 = z) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5438,plain,
% 2.14/2.34 (b(z, s(s(s(z))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5437, 389, 2142, 566, 444, 5154, 2209, 938, 628])).
% 2.14/2.34 tff(5439,plain,
% 2.14/2.34 (~(s(z) = elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5321, 5238])).
% 2.14/2.34 tff(5440,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 2.14/2.34 tff(5441,plain,
% 2.14/2.34 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5313, 67, 938, 4659])).
% 2.14/2.34 tff(5442,plain,
% 2.14/2.34 (b(elem!1, s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[2351, 5441, 5154])).
% 2.14/2.34 tff(5443,plain,
% 2.14/2.34 (((~![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)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5444,plain,
% 2.14/2.34 (((~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)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5445,plain,
% 2.14/2.34 (((~![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))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5444])).
% 2.14/2.34 tff(5446,plain,
% 2.14/2.34 (((~![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)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5445, 5443])).
% 2.14/2.34 tff(5447,plain,
% 2.14/2.34 ((~![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)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5448,plain,
% 2.14/2.34 ((~![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))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5447, 5446])).
% 2.14/2.34 tff(5449,plain,
% 2.14/2.34 ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5448, 67])).
% 2.14/2.34 tff(5450,plain,
% 2.14/2.34 (~r(s(z), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5449, 5284, 389])).
% 2.14/2.34 tff(5451,plain,
% 2.14/2.34 (b(s(z), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5366, 50, 5450, 5440])).
% 2.14/2.34 tff(5452,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5453,plain,
% 2.14/2.34 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5454,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5453])).
% 2.14/2.34 tff(5455,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5454, 5452])).
% 2.14/2.34 tff(5456,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5457,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5456, 5455])).
% 2.14/2.34 tff(5458,plain,
% 2.14/2.34 (~b(s(z), s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5457, 204, 1026, 1102, 5451, 1065])).
% 2.14/2.34 tff(5459,plain,
% 2.14/2.34 (r(s(z), s(s(elem!1)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[936, 5458])).
% 2.14/2.34 tff(5460,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5435, 67, 5284, 5459, 2142, 389])).
% 2.14/2.34 tff(5461,plain,((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5462,plain,
% 2.14/2.34 (~r(z, elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5461, 5256, 389, 2142, 5217, 1065, 5440])).
% 2.14/2.34 tff(5463,plain,
% 2.14/2.34 (b(z, elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5297, 5462, 5234])).
% 2.14/2.34 tff(5464,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5304, 204, 5463, 5256, 5442, 5217, 1065])).
% 2.14/2.34 tff(5465,plain,((~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5466,plain,
% 2.14/2.34 (~b(s(s(elem!1)), elem!1)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5465, 4659, 389, 2142, 5440, 5154, 938, 2209])).
% 2.14/2.34 tff(5467,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5267, 5466, 5254, 5261])).
% 2.14/2.34 tff(5468,plain,((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (s(z) = elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5469,plain,
% 2.14/2.34 (~r(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5468, 389, 2142, 5439, 5154, 938, 2209])).
% 2.14/2.34 tff(5470,plain,
% 2.14/2.34 (b(elem!1, s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5197, 5469, 5238])).
% 2.14/2.34 tff(5471,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5472,plain,
% 2.14/2.34 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5473,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5472])).
% 2.14/2.35 tff(5474,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5473, 5471])).
% 2.14/2.35 tff(5475,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5476,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5475, 5474])).
% 2.14/2.35 tff(5477,plain,
% 2.14/2.35 (~b(elem!1, z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5476, 204, 5215, 5470, 5438, 566])).
% 2.14/2.35 tff(5478,plain,
% 2.14/2.35 (r(elem!1, z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5184, 5477, 2209])).
% 2.14/2.35 tff(5479,plain,
% 2.14/2.35 (~r(s(s(s(z))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5341, 5478, 5233])).
% 2.14/2.35 tff(5480,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5481,plain,
% 2.14/2.35 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5482,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5481])).
% 2.14/2.35 tff(5483,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5482, 5480])).
% 2.14/2.35 tff(5484,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5485,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5484, 5483])).
% 2.14/2.35 tff(5486,plain,
% 2.14/2.35 (~r(elem!1, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5485, 67, 5478, 5233])).
% 2.14/2.35 tff(5487,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5488,plain,
% 2.14/2.35 (((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5489,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5488])).
% 2.14/2.35 tff(5490,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5489, 5487])).
% 2.14/2.35 tff(5491,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5492,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5491, 5490])).
% 2.14/2.35 tff(5493,plain,
% 2.14/2.35 ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5492, 67])).
% 2.14/2.35 tff(5494,plain,
% 2.14/2.35 (~r(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5493, 5478, 389])).
% 2.14/2.35 tff(5495,plain,
% 2.14/2.35 (b(s(z), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5366, 50, 5494, 5439])).
% 2.14/2.35 tff(5496,plain,
% 2.14/2.35 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 2.14/2.35 inference(commutativity,[status(thm)],[])).
% 2.14/2.35 tff(5497,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 2.14/2.35 tff(5498,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.14/2.35 tff(5499,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 2.14/2.35 tff(5500,plain,
% 2.14/2.35 (((~![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)))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5501,plain,
% 2.14/2.35 ((~![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)))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5502,plain,
% 2.14/2.35 ((~![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))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5501, 5500])).
% 2.14/2.35 tff(5503,plain,
% 2.14/2.35 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5502, 50])).
% 2.14/2.35 tff(5504,plain,
% 2.14/2.35 (b(elem!1, s(s(s(z))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5503, 5499, 5498])).
% 2.14/2.35 tff(5505,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5506,plain,
% 2.14/2.35 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5507,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5506])).
% 2.14/2.35 tff(5508,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5507, 5505])).
% 2.14/2.35 tff(5509,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5510,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5509, 5508])).
% 2.14/2.35 tff(5511,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5510, 204, 5202, 3299, 4605, 444, 4445])).
% 2.14/2.35 tff(5512,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5513,plain,
% 2.14/2.35 (~b(s(s(s(z))), elem!1)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5512, 5504, 3299, 5202, 444])).
% 2.14/2.35 tff(5514,plain,
% 2.14/2.35 (s(s(s(z))) = elem!1),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5281, 5513, 5497])).
% 2.14/2.35 tff(5515,plain,
% 2.14/2.35 (elem!1 = s(s(s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5514, 5496])).
% 2.14/2.35 tff(5516,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5499, 5515])).
% 2.14/2.35 tff(5517,plain,((elem!1 = s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | r(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5518,plain,
% 2.14/2.35 (elem!1 = s(s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5517, 5495, 5486, 5470, 5479, 444])).
% 2.14/2.35 tff(5519,plain,
% 2.14/2.35 (s(elem!1) = s(s(s(s(z))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5518])).
% 2.14/2.35 tff(5520,plain,
% 2.14/2.35 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5519])).
% 2.14/2.35 tff(5521,plain,
% 2.14/2.35 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5520])).
% 2.14/2.35 tff(5522,plain,
% 2.14/2.35 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5521])).
% 2.14/2.35 tff(5523,plain,
% 2.14/2.35 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5522])).
% 2.14/2.35 tff(5524,plain,
% 2.14/2.35 (r(z, s(s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[2142, 5523])).
% 2.14/2.35 tff(5525,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 2.14/2.35 tff(5526,plain,
% 2.14/2.35 (s(elem!1) = s(s(s(s(z))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5525])).
% 2.14/2.35 tff(5527,plain,
% 2.14/2.35 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5526])).
% 2.14/2.35 tff(5528,plain,
% 2.14/2.35 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5527])).
% 2.14/2.35 tff(5529,plain,
% 2.14/2.35 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5528])).
% 2.14/2.35 tff(5530,plain,
% 2.14/2.35 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5529])).
% 2.14/2.35 tff(5531,plain,
% 2.14/2.35 (r(z, s(s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[2142, 5530])).
% 2.14/2.35 tff(5532,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5528])).
% 2.14/2.35 tff(5533,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5532])).
% 2.14/2.35 tff(5534,plain,
% 2.14/2.35 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[2127, 5533])).
% 2.14/2.35 tff(5535,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), 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))))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5536,plain,
% 2.14/2.35 (((~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))))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5537,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5536])).
% 2.14/2.35 tff(5538,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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))))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5537, 5535])).
% 2.14/2.35 tff(5539,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5540,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5539, 5538])).
% 2.14/2.35 tff(5541,plain,
% 2.14/2.35 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5540, 67, 308])).
% 2.14/2.35 tff(5542,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5541, 5534, 5531])).
% 2.14/2.35 tff(5543,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~(elem!1 = s(s(s(z))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5544,plain,
% 2.14/2.35 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5543, 5233, 5518, 2142])).
% 2.14/2.35 tff(5545,plain,
% 2.14/2.35 (b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3335, 5544, 3837])).
% 2.14/2.35 tff(5546,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5547,plain,
% 2.14/2.35 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), 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(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5548,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5547])).
% 2.14/2.35 tff(5549,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5548, 5546])).
% 2.14/2.35 tff(5550,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z), 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))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5551,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5550, 5549])).
% 2.14/2.35 tff(5552,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5551, 204, 2222, 362, 405, 566, 2141])).
% 2.14/2.35 tff(5553,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5554,plain,
% 2.14/2.35 (~b(s(z), s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5553, 5545, 566, 5438, 5215])).
% 2.14/2.35 tff(5555,plain,
% 2.14/2.35 (r(s(z), s(s(elem!1)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[936, 5554])).
% 2.14/2.35 tff(5556,plain,
% 2.14/2.35 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(elem!1)))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5528])).
% 2.14/2.35 tff(5557,plain,
% 2.14/2.35 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5556])).
% 2.14/2.35 tff(5558,plain,
% 2.14/2.35 (r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[907, 5557])).
% 2.14/2.35 tff(5559,assumption,(~r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.14/2.35 tff(5560,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5559, 5558])).
% 2.14/2.35 tff(5561,plain,(r(s(z), s(s(s(s(s(z)))))) | (~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5562,plain,
% 2.14/2.36 (r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5561, 5555, 5518])).
% 2.14/2.36 tff(5563,plain,
% 2.14/2.36 (((~![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(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5564,plain,
% 2.14/2.36 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5565,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5564])).
% 2.14/2.36 tff(5566,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5565, 5563])).
% 2.14/2.36 tff(5567,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5568,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5567, 5566])).
% 2.14/2.36 tff(5569,plain,
% 2.14/2.36 (~r(z, s(s(s(s(s(z))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5568, 67, 389, 5562])).
% 2.14/2.36 tff(5570,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5569, 5524])).
% 2.14/2.36 tff(5571,plain,((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5572,plain,
% 2.14/2.36 (~r(z, s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5571, 5213, 389, 5013, 5011, 2209, 5180, 4995])).
% 2.14/2.36 tff(5573,plain,
% 2.14/2.36 (b(z, s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2160, 5572])).
% 2.14/2.36 tff(5574,plain,
% 2.14/2.36 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5056, 5573, 361, 1135, 359, 1129])).
% 2.14/2.36 tff(5575,plain,
% 2.14/2.36 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5574])).
% 2.14/2.36 tff(5576,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[919, 5575, 20])).
% 2.14/2.36 tff(5577,plain,
% 2.14/2.36 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5576])).
% 2.14/2.36 tff(5578,plain,
% 2.14/2.36 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5577])).
% 2.14/2.36 tff(5579,plain,
% 2.14/2.36 (s(s(z)) = elem!1),
% 2.14/2.36 inference(transitivity,[status(thm)],[84, 5578, 902])).
% 2.14/2.36 tff(5580,plain,
% 2.14/2.36 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5579])).
% 2.14/2.36 tff(5581,plain,
% 2.14/2.36 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5580])).
% 2.14/2.36 tff(5582,plain,
% 2.14/2.36 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[853, 3586])).
% 2.14/2.36 tff(5583,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3814, 5582])).
% 2.14/2.36 tff(5584,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5585,plain,
% 2.14/2.36 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5584, 5574])).
% 2.14/2.36 tff(5586,plain,
% 2.14/2.36 (elem!1 = s(s(s(z)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5416])).
% 2.14/2.36 tff(5587,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5586])).
% 2.14/2.36 tff(5588,plain,
% 2.14/2.36 (s(elem!1) = s(s(elem!1))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5587, 1124])).
% 2.14/2.36 tff(5589,plain,
% 2.14/2.36 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5588])).
% 2.14/2.36 tff(5590,plain,
% 2.14/2.36 (elem!1 = s(s(elem!1))),
% 2.14/2.36 inference(transitivity,[status(thm)],[1009, 5589, 904, 5587, 1124])).
% 2.14/2.36 tff(5591,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5154, 5590])).
% 2.14/2.36 tff(5592,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5593,plain,
% 2.14/2.36 (~(s(s(s(z))) = elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5592, 5585, 5213])).
% 2.14/2.36 tff(5594,plain,
% 2.14/2.36 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.14/2.36 inference(symmetry,[status(thm)],[5496])).
% 2.14/2.36 tff(5595,plain,
% 2.14/2.36 (s(s(s(z))) = elem!1),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5525, 5594])).
% 2.14/2.36 tff(5596,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5244, 5595])).
% 2.14/2.36 tff(5597,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5598,plain,
% 2.14/2.36 (~(elem!1 = s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5597, 5593])).
% 2.14/2.36 tff(5599,plain,
% 2.14/2.36 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5579])).
% 2.14/2.36 tff(5600,plain,
% 2.14/2.36 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5599])).
% 2.14/2.36 tff(5601,plain,
% 2.14/2.36 (elem!1 = s(s(z))),
% 2.14/2.36 inference(transitivity,[status(thm)],[1009, 5577, 83])).
% 2.14/2.36 tff(5602,plain,
% 2.14/2.36 (r(elem!1, z) <=> r(s(s(z)), z)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5601])).
% 2.14/2.36 tff(5603,plain,
% 2.14/2.36 (r(s(s(z)), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5185, 5602])).
% 2.14/2.36 tff(5604,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5605,plain,
% 2.14/2.36 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5606,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5605])).
% 2.14/2.36 tff(5607,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5606, 5604])).
% 2.14/2.36 tff(5608,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5609,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5608, 5607])).
% 2.14/2.36 tff(5610,plain,
% 2.14/2.36 (~r(s(s(z)), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5609, 67, 308, 5603])).
% 2.14/2.36 tff(5611,plain,
% 2.14/2.36 (~r(elem!1, s(s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5610, 5600])).
% 2.14/2.36 tff(5612,plain,
% 2.14/2.36 (b(elem!1, s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5503, 5611, 5598])).
% 2.14/2.36 tff(5613,plain,
% 2.14/2.36 (b(s(s(z)), s(s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5612, 5581])).
% 2.14/2.36 tff(5614,plain,
% 2.14/2.36 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5579])).
% 2.14/2.36 tff(5615,plain,
% 2.14/2.36 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5614, 3752])).
% 2.14/2.36 tff(5616,plain,
% 2.14/2.36 ((elem!1 = s(z)) <=> (s(z) = s(s(z)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5615])).
% 2.14/2.36 tff(5617,plain,
% 2.14/2.36 ((~(elem!1 = s(z))) <=> (~(s(z) = s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5616])).
% 2.14/2.36 tff(5618,plain,
% 2.14/2.36 (~(s(z) = s(s(z)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[1287, 5617])).
% 2.14/2.36 tff(5619,plain,
% 2.14/2.36 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5601])).
% 2.14/2.36 tff(5620,plain,
% 2.14/2.36 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5619])).
% 2.14/2.36 tff(5621,plain,
% 2.14/2.36 (~r(s(z), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5493, 5185, 389])).
% 2.14/2.36 tff(5622,plain,
% 2.14/2.36 (~r(s(z), s(s(z)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 2.14/2.36 tff(5623,plain,
% 2.14/2.36 ((s(z) = s(s(z))) | b(s(z), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4151, 50, 5622])).
% 2.14/2.36 tff(5624,plain,
% 2.14/2.36 (b(s(z), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5623, 5618])).
% 2.14/2.36 tff(5625,plain,
% 2.14/2.36 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5601])).
% 2.14/2.36 tff(5626,plain,
% 2.14/2.36 (b(s(s(z)), s(z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5198, 5625])).
% 2.14/2.36 tff(5627,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5628,plain,
% 2.14/2.36 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5629,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5628])).
% 2.14/2.36 tff(5630,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5629, 5627])).
% 2.14/2.36 tff(5631,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5632,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5631, 5630])).
% 2.14/2.36 tff(5633,plain,
% 2.14/2.36 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5632, 204, 5013, 5011, 5626])).
% 2.14/2.36 tff(5634,plain,
% 2.14/2.36 (~b(s(s(z)), s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5633, 5624])).
% 2.14/2.36 tff(5635,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5634, 5613])).
% 2.14/2.36 tff(5636,plain,((elem!1 = z) | (elem!1 = s(z)) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(s(z)))), s(s(elem!1))) | (~r(s(z), z)) | b(s(s(elem!1)), s(z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5637,plain,
% 2.14/2.36 (b(elem!1, z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5636, 5178, 308, 361, 5138, 5167, 5165, 389, 5140, 1287])).
% 2.14/2.36 tff(5638,plain,
% 2.14/2.36 (b(s(s(z)), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5637, 5131])).
% 2.14/2.36 tff(5639,plain,
% 2.14/2.36 (elem!1 = s(s(z))),
% 2.14/2.36 inference(transitivity,[status(thm)],[1009, 5127, 83])).
% 2.14/2.36 tff(5640,plain,
% 2.14/2.36 (b(elem!1, s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5639, 5124])).
% 2.14/2.36 tff(5641,plain,
% 2.14/2.36 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.36 inference(commutativity,[status(thm)],[])).
% 2.14/2.36 tff(5642,plain,
% 2.14/2.36 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5124])).
% 2.14/2.36 tff(5643,plain,
% 2.14/2.36 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.36 inference(transitivity,[status(thm)],[5642, 5641])).
% 2.14/2.36 tff(5644,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5643])).
% 2.14/2.36 tff(5645,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5129])).
% 2.14/2.36 tff(5646,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5645, 5644])).
% 2.14/2.36 tff(5647,plain,
% 2.14/2.36 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5646])).
% 2.14/2.36 tff(5648,plain,
% 2.14/2.36 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[2122, 5647])).
% 2.14/2.36 tff(5649,plain,
% 2.14/2.36 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5124])).
% 2.14/2.36 tff(5650,plain,
% 2.14/2.36 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5649])).
% 2.14/2.36 tff(5651,plain,
% 2.14/2.36 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5129])).
% 2.14/2.36 tff(5652,plain,
% 2.14/2.36 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5651, 5650])).
% 2.14/2.36 tff(5653,plain,
% 2.14/2.36 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5652])).
% 2.14/2.36 tff(5654,plain,
% 2.14/2.36 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5129])).
% 2.14/2.36 tff(5655,plain,
% 2.14/2.36 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5654])).
% 2.14/2.36 tff(5656,plain,
% 2.14/2.36 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5639])).
% 2.14/2.36 tff(5657,plain,
% 2.14/2.36 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5656])).
% 2.14/2.36 tff(5658,plain,
% 2.14/2.36 ((~b(s(s(z)), s(z))) <=> (~b(elem!1, s(z)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5657])).
% 2.14/2.36 tff(5659,plain,
% 2.14/2.36 (~r(s(s(elem!1)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[946, 5180, 389])).
% 2.14/2.36 tff(5660,plain,
% 2.14/2.36 (b(s(s(elem!1)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1099, 5659])).
% 2.14/2.36 tff(5661,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1194, 2, 389])).
% 2.14/2.36 tff(5662,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[335, 5661])).
% 2.14/2.36 tff(5663,plain,
% 2.14/2.36 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1148, 5662, 361, 5660, 1129, 1135])).
% 2.14/2.36 tff(5664,plain,
% 2.14/2.36 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5663])).
% 2.14/2.36 tff(5665,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[919, 5664, 20])).
% 2.14/2.36 tff(5666,plain,
% 2.14/2.36 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5665])).
% 2.14/2.36 tff(5667,plain,
% 2.14/2.36 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5666])).
% 2.14/2.36 tff(5668,plain,
% 2.14/2.36 (s(s(z)) = elem!1),
% 2.14/2.36 inference(transitivity,[status(thm)],[84, 5667, 902])).
% 2.14/2.36 tff(5669,plain,
% 2.14/2.36 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5668])).
% 2.14/2.36 tff(5670,plain,
% 2.14/2.36 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5669])).
% 2.14/2.36 tff(5671,plain,
% 2.14/2.36 (elem!1 = s(s(z))),
% 2.14/2.36 inference(transitivity,[status(thm)],[1009, 5666, 83])).
% 2.14/2.36 tff(5672,plain,
% 2.14/2.36 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5671])).
% 2.14/2.36 tff(5673,plain,
% 2.14/2.36 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5663])).
% 2.14/2.36 tff(5674,plain,
% 2.14/2.36 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5673])).
% 2.14/2.36 tff(5675,plain,
% 2.14/2.36 (r(s(z), s(s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[2, 5674])).
% 2.14/2.36 tff(5676,plain,
% 2.14/2.36 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[2303])).
% 2.14/2.36 tff(5677,plain,
% 2.14/2.36 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 2.14/2.36 inference(symmetry,[status(thm)],[5676])).
% 2.14/2.36 tff(5678,plain,
% 2.14/2.36 (b(s(s(z)), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[1102, 5677])).
% 2.14/2.36 tff(5679,plain,
% 2.14/2.36 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[2302])).
% 2.14/2.36 tff(5680,plain,
% 2.14/2.36 (z = elem!1),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5164, 2300])).
% 2.14/2.36 tff(5681,plain,
% 2.14/2.36 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5159, 5680])).
% 2.14/2.36 tff(5682,plain,
% 2.14/2.36 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1139, 5681, 1135])).
% 2.14/2.36 tff(5683,plain,
% 2.14/2.36 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5682, 5679])).
% 2.14/2.36 tff(5684,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[2303])).
% 2.14/2.36 tff(5685,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5684])).
% 2.14/2.36 tff(5686,plain,
% 2.14/2.36 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1127, 5681])).
% 2.14/2.36 tff(5687,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[1133, 5686])).
% 2.14/2.36 tff(5688,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5687, 5685])).
% 2.14/2.36 tff(5689,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5690,plain,
% 2.14/2.36 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5691,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5690])).
% 2.14/2.36 tff(5692,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5691, 5689])).
% 2.14/2.36 tff(5693,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5694,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5693, 5692])).
% 2.14/2.36 tff(5695,plain,
% 2.14/2.36 (~b(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5694, 204, 361, 5688, 5683, 359])).
% 2.14/2.36 tff(5696,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5695, 5678])).
% 2.14/2.36 tff(5697,plain,((~(elem!1 = z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | r(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5698,plain,
% 2.14/2.36 (~(elem!1 = z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5697, 5662, 361, 5660, 1129, 1135])).
% 2.14/2.36 tff(5699,plain,
% 2.14/2.36 (b(elem!1, z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5636, 5698, 308, 361, 1135, 5662, 1129, 389, 5179, 1287])).
% 2.14/2.36 tff(5700,plain,
% 2.14/2.36 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.36 tff(5701,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.36 inference(symmetry,[status(thm)],[5700])).
% 2.14/2.36 tff(5702,plain,
% 2.14/2.36 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.36 tff(5703,plain,
% 2.14/2.36 (s(elem!1) = s(s(s(z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[919, 5702, 20])).
% 2.14/2.36 tff(5704,plain,
% 2.14/2.36 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5703])).
% 2.14/2.36 tff(5705,plain,
% 2.14/2.36 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5704])).
% 2.14/2.36 tff(5706,plain,
% 2.14/2.36 (s(s(z)) = elem!1),
% 2.14/2.36 inference(transitivity,[status(thm)],[84, 5705, 902])).
% 2.14/2.36 tff(5707,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5706])).
% 2.14/2.36 tff(5708,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 2.14/2.36 inference(transitivity,[status(thm)],[5707, 5701])).
% 2.14/2.36 tff(5709,plain,
% 2.14/2.36 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(elem!1)), elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5708])).
% 2.14/2.36 tff(5710,plain,
% 2.14/2.36 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5706])).
% 2.14/2.36 tff(5711,plain,
% 2.14/2.36 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.14/2.36 inference(symmetry,[status(thm)],[5710])).
% 2.14/2.36 tff(5712,plain,
% 2.14/2.36 (b(s(s(z)), z)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[1026, 5711])).
% 2.14/2.36 tff(5713,plain,
% 2.14/2.36 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5706])).
% 2.14/2.36 tff(5714,plain,
% 2.14/2.36 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5713])).
% 2.14/2.36 tff(5715,plain,
% 2.14/2.36 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.36 tff(5716,plain,
% 2.14/2.36 (b(elem!1, s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5715, 5714])).
% 2.14/2.36 tff(5717,plain,
% 2.14/2.36 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.36 tff(5718,plain,
% 2.14/2.36 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.36 inference(transitivity,[status(thm)],[5717, 5641])).
% 2.14/2.36 tff(5719,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.36 inference(symmetry,[status(thm)],[5718])).
% 2.14/2.36 tff(5720,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5706])).
% 2.14/2.36 tff(5721,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5720, 5719])).
% 2.14/2.36 tff(5722,plain,
% 2.14/2.36 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5721])).
% 2.14/2.36 tff(5723,plain,
% 2.14/2.36 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[2122, 5722])).
% 2.14/2.36 tff(5724,plain,
% 2.14/2.36 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4639, 4659, 907])).
% 2.14/2.36 tff(5725,plain,
% 2.14/2.36 (b(elem!1, s(s(elem!1)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2351, 5724, 5723])).
% 2.14/2.36 tff(5726,plain,
% 2.14/2.36 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5725, 5716])).
% 2.14/2.36 tff(5727,plain,
% 2.14/2.36 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5694, 204, 361, 5726, 359])).
% 2.14/2.36 tff(5728,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5727, 5712])).
% 2.14/2.36 tff(5729,plain,
% 2.14/2.36 (~b(s(s(elem!1)), elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5728, 5709])).
% 2.14/2.36 tff(5730,plain,
% 2.14/2.36 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 2.14/2.36 inference(transitivity,[status(thm)],[5720, 5719, 5207])).
% 2.14/2.36 tff(5731,plain,
% 2.14/2.36 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5730])).
% 2.14/2.36 tff(5732,plain,
% 2.14/2.36 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[2122, 5731])).
% 2.14/2.36 tff(5733,plain,
% 2.14/2.36 (b(s(s(elem!1)), elem!1)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5267, 5254, 5732])).
% 2.14/2.36 tff(5734,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5733, 5729])).
% 2.14/2.36 tff(5735,plain,((~r(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5736,plain,
% 2.14/2.36 (~r(elem!1, s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5735, 5663, 361, 5662, 5699, 5675, 5180])).
% 2.14/2.36 tff(5737,plain,
% 2.14/2.36 (b(elem!1, s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5197, 5736, 1287])).
% 2.14/2.36 tff(5738,plain,
% 2.14/2.36 (b(s(s(z)), s(z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5737, 5672])).
% 2.14/2.36 tff(5739,plain,
% 2.14/2.36 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5668])).
% 2.14/2.36 tff(5740,plain,
% 2.14/2.37 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5739, 3752])).
% 2.14/2.37 tff(5741,plain,
% 2.14/2.37 ((elem!1 = s(z)) <=> (s(z) = s(s(z)))),
% 2.14/2.37 inference(symmetry,[status(thm)],[5740])).
% 2.14/2.37 tff(5742,plain,
% 2.14/2.37 ((~(elem!1 = s(z))) <=> (~(s(z) = s(s(z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5741])).
% 2.14/2.37 tff(5743,plain,
% 2.14/2.37 (~(s(z) = s(s(z)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[1287, 5742])).
% 2.14/2.37 tff(5744,plain,
% 2.14/2.37 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5668])).
% 2.14/2.37 tff(5745,plain,
% 2.14/2.37 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.14/2.37 inference(symmetry,[status(thm)],[5744])).
% 2.14/2.37 tff(5746,plain,
% 2.14/2.37 (b(s(s(z)), z)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5699, 5745])).
% 2.14/2.37 tff(5747,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5748,plain,
% 2.14/2.37 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5749,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5748])).
% 2.14/2.37 tff(5750,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5749, 5747])).
% 2.14/2.37 tff(5751,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5752,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5751, 5750])).
% 2.14/2.37 tff(5753,plain,
% 2.14/2.37 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5752, 204, 362, 5662, 5738])).
% 2.14/2.37 tff(5754,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5753, 5746])).
% 2.14/2.37 tff(5755,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3420, 50, 5754, 2122])).
% 2.14/2.37 tff(5756,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.14/2.37 tff(5757,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5758,plain,
% 2.14/2.37 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5759,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5758])).
% 2.14/2.37 tff(5760,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5759, 5757])).
% 2.14/2.37 tff(5761,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5762,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5761, 5760])).
% 2.14/2.37 tff(5763,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5762, 67, 2, 5756, 4139])).
% 2.14/2.37 tff(5764,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5765,plain,
% 2.14/2.37 (~r(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5764, 5755, 2])).
% 2.14/2.37 tff(5766,plain,
% 2.14/2.37 ((s(z) = s(s(z))) | b(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[4151, 50, 5765])).
% 2.14/2.37 tff(5767,plain,
% 2.14/2.37 (b(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5766, 5743])).
% 2.14/2.37 tff(5768,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5769,plain,
% 2.14/2.37 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5770,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5769])).
% 2.14/2.37 tff(5771,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5770, 5768])).
% 2.14/2.37 tff(5772,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5773,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5772, 5771])).
% 2.14/2.37 tff(5774,plain,
% 2.14/2.37 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5773, 204, 5013, 5011, 5767, 5738])).
% 2.14/2.37 tff(5775,plain,
% 2.14/2.37 (~b(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5774, 5670])).
% 2.14/2.37 tff(5776,plain,
% 2.14/2.37 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5584, 5663])).
% 2.14/2.37 tff(5777,plain,
% 2.14/2.37 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5663])).
% 2.14/2.37 tff(5778,plain,
% 2.14/2.37 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.37 inference(transitivity,[status(thm)],[5777, 5641])).
% 2.14/2.37 tff(5779,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.37 inference(symmetry,[status(thm)],[5778])).
% 2.14/2.37 tff(5780,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5668])).
% 2.14/2.37 tff(5781,plain,
% 2.14/2.37 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5780, 5779])).
% 2.14/2.37 tff(5782,plain,
% 2.14/2.37 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5781])).
% 2.14/2.37 tff(5783,plain,
% 2.14/2.37 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[2122, 5782])).
% 2.14/2.37 tff(5784,plain,
% 2.14/2.37 (~(s(s(s(z))) = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5592, 5783, 5776])).
% 2.14/2.37 tff(5785,plain,
% 2.14/2.37 (~(z = elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2211, 5698])).
% 2.14/2.37 tff(5786,plain,
% 2.14/2.37 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5671])).
% 2.14/2.37 tff(5787,plain,
% 2.14/2.37 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 2.14/2.37 inference(symmetry,[status(thm)],[5786])).
% 2.14/2.37 tff(5788,plain,
% 2.14/2.37 (b(s(z), elem!1)),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5767, 5787])).
% 2.14/2.37 tff(5789,plain,
% 2.14/2.37 (~b(z, elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5374, 5788, 362, 5699, 5737])).
% 2.14/2.37 tff(5790,plain,
% 2.14/2.37 (r(z, elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5297, 5789, 5785])).
% 2.14/2.37 tff(5791,plain,
% 2.14/2.37 (~r(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5292, 5790, 3])).
% 2.14/2.37 tff(5792,plain,
% 2.14/2.37 (b(s(s(s(z))), elem!1)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5281, 5791, 5784])).
% 2.14/2.37 tff(5793,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5792, 5775])).
% 2.14/2.37 tff(5794,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (elem!1 = s(z)) | (~b(z, s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5795,plain,
% 2.14/2.37 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5794, 5178, 362, 1287, 361, 3, 5138, 308, 389, 5140])).
% 2.14/2.37 tff(5796,plain,
% 2.14/2.37 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[431, 5795])).
% 2.14/2.37 tff(5797,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 2.14/2.37 tff(5798,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5799,plain,
% 2.14/2.37 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5800,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5799])).
% 2.14/2.37 tff(5801,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5800, 5798])).
% 2.14/2.37 tff(5802,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5803,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5802, 5801])).
% 2.14/2.37 tff(5804,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5803, 204, 362, 456, 361, 5797, 3300])).
% 2.14/2.37 tff(5805,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5806,plain,
% 2.14/2.37 (~b(s(s(z)), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5805, 5796, 362, 361, 5638])).
% 2.14/2.37 tff(5807,plain,
% 2.14/2.37 (~b(elem!1, s(z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5806, 5658])).
% 2.14/2.37 tff(5808,plain,
% 2.14/2.37 (r(elem!1, s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5197, 5807, 1287])).
% 2.14/2.37 tff(5809,plain,
% 2.14/2.37 (r(s(s(z)), s(z))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5808, 5655])).
% 2.14/2.37 tff(5810,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5811,plain,
% 2.14/2.37 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5812,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5811])).
% 2.14/2.37 tff(5813,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5812, 5810])).
% 2.14/2.37 tff(5814,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5815,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5814, 5813])).
% 2.14/2.37 tff(5816,plain,
% 2.14/2.37 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5815, 67, 56, 5809])).
% 2.14/2.37 tff(5817,plain,
% 2.14/2.37 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5816, 5653])).
% 2.14/2.37 tff(5818,plain,
% 2.14/2.37 (b(elem!1, s(s(elem!1)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[2351, 5817, 5648])).
% 2.14/2.37 tff(5819,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5818, 5640])).
% 2.14/2.37 tff(5820,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5821,plain,
% 2.14/2.37 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5822,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5821])).
% 2.14/2.37 tff(5823,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[5822, 5820])).
% 2.14/2.38 tff(5824,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(5825,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5824, 5823])).
% 2.14/2.38 tff(5826,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5825, 67, 56, 5809])).
% 2.14/2.38 tff(5827,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3420, 50, 5826, 2122])).
% 2.14/2.38 tff(5828,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5694, 204, 361, 5827, 5819, 5167, 5638])).
% 2.14/2.38 tff(5829,plain,((~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (elem!1 = s(z)) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5830,plain,
% 2.14/2.38 (~r(s(z), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5829, 361, 1287, 362, 308, 260, 5])).
% 2.14/2.38 tff(5831,plain,
% 2.14/2.38 (b(s(z), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[376, 5830])).
% 2.14/2.38 tff(5832,plain,
% 2.14/2.38 (~r(s(s(elem!1)), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2967, 1113, 136])).
% 2.14/2.38 tff(5833,plain,
% 2.14/2.38 (b(s(s(elem!1)), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[952, 5832])).
% 2.14/2.38 tff(5834,plain,
% 2.14/2.38 (~b(s(s(elem!1)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2958, 5833, 363, 361, 1113, 362])).
% 2.14/2.38 tff(5835,plain,
% 2.14/2.38 (r(s(s(elem!1)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1099, 5834])).
% 2.14/2.38 tff(5836,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3821, 67, 5835, 1113, 538])).
% 2.14/2.38 tff(5837,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5838,plain,
% 2.14/2.38 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5837, 538, 5831, 361, 362, 56])).
% 2.14/2.38 tff(5839,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1212, 538, 308])).
% 2.14/2.38 tff(5840,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[108, 5839])).
% 2.14/2.38 tff(5841,assumption,(b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 2.14/2.38 tff(5842,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5843,plain,
% 2.14/2.38 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5844,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5843])).
% 2.14/2.38 tff(5845,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[5844, 5842])).
% 2.14/2.38 tff(5846,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(5847,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5846, 5845])).
% 2.14/2.38 tff(5848,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5847, 204, 3720, 1102, 2258, 361, 5841])).
% 2.14/2.38 tff(5849,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5850,plain,
% 2.14/2.38 (~b(z, s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5849, 1140, 1102, 361, 1134])).
% 2.14/2.38 tff(5851,plain,
% 2.14/2.38 (r(z, s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2160, 5850])).
% 2.14/2.38 tff(5852,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5042, 5851, 3])).
% 2.14/2.38 tff(5853,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2182, 50, 3837, 5852])).
% 2.14/2.38 tff(5854,plain,
% 2.14/2.38 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3794, 5853, 1101, 194, 1129, 1135])).
% 2.14/2.38 tff(5855,plain,
% 2.14/2.38 (r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1165, 50, 628, 5854])).
% 2.14/2.38 tff(5856,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3782, 67, 5851, 3, 5855])).
% 2.14/2.38 tff(5857,plain,((s(s(elem!1)) = s(s(s(s(z))))) | (~r(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5858,plain,
% 2.14/2.38 (~b(s(s(elem!1)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5857, 1129, 3, 194, 628, 1101, 1135, 361])).
% 2.14/2.38 tff(5859,plain,
% 2.14/2.38 (r(s(s(elem!1)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1099, 5858])).
% 2.14/2.38 tff(5860,plain,
% 2.14/2.38 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3851, 67, 5859, 308])).
% 2.14/2.38 tff(5861,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1132, 50, 1128, 1129])).
% 2.14/2.38 tff(5862,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5863,plain,
% 2.14/2.38 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5864,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5863])).
% 2.14/2.38 tff(5865,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[5864, 5862])).
% 2.14/2.38 tff(5866,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(5867,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5866, 5865])).
% 2.14/2.38 tff(5868,plain,
% 2.14/2.38 ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5867, 204, 4996, 194, 153])).
% 2.14/2.38 tff(5869,plain,
% 2.14/2.38 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5868, 5861])).
% 2.14/2.38 tff(5870,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1167, 5869, 5860, 628])).
% 2.14/2.38 tff(5871,plain,(r(s(s(s(s(z)))), s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5872,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5871, 1135, 3542, 5840, 308, 3, 1101, 628, 361])).
% 2.14/2.38 tff(5873,plain,
% 2.14/2.38 (~r(s(s(elem!1)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3835, 5872, 538])).
% 2.14/2.38 tff(5874,plain,
% 2.14/2.38 (b(s(s(elem!1)), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1099, 5873])).
% 2.14/2.38 tff(5875,plain,
% 2.14/2.38 ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2931, 204, 363, 4996, 361])).
% 2.14/2.38 tff(5876,plain,
% 2.14/2.38 (~b(s(z), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5875, 5874])).
% 2.14/2.38 tff(5877,plain,
% 2.14/2.38 (r(s(z), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[936, 5876])).
% 2.14/2.38 tff(5878,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5879,plain,
% 2.14/2.38 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5880,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5879])).
% 2.14/2.38 tff(5881,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[5880, 5878])).
% 2.14/2.38 tff(5882,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(5883,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5882, 5881])).
% 2.14/2.38 tff(5884,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5883, 67, 5877, 136, 5872])).
% 2.14/2.38 tff(5885,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5886,plain,
% 2.14/2.38 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5885, 5838, 5831, 361, 538, 308, 260, 56, 4995])).
% 2.14/2.38 tff(5887,plain,
% 2.14/2.38 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5886])).
% 2.14/2.38 tff(5888,plain,
% 2.14/2.38 (s(elem!1) = s(s(s(z)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[919, 5887, 20])).
% 2.14/2.38 tff(5889,plain,
% 2.14/2.38 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5888])).
% 2.14/2.38 tff(5890,plain,
% 2.14/2.38 (elem!1 = s(s(z))),
% 2.14/2.38 inference(transitivity,[status(thm)],[1009, 5889, 83])).
% 2.14/2.38 tff(5891,plain,
% 2.14/2.38 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5890])).
% 2.14/2.38 tff(5892,plain,
% 2.14/2.38 (~(z = elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5159, 5886])).
% 2.14/2.38 tff(5893,plain,
% 2.14/2.38 (~(elem!1 = z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5164, 5892])).
% 2.14/2.38 tff(5894,plain,
% 2.14/2.38 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5706])).
% 2.14/2.38 tff(5895,plain,
% 2.14/2.38 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[5894])).
% 2.14/2.38 tff(5896,plain,
% 2.14/2.38 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.38 tff(5897,plain,
% 2.14/2.38 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.38 tff(5898,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 2.14/2.38 inference(symmetry,[status(thm)],[5897])).
% 2.14/2.38 tff(5899,plain,
% 2.14/2.38 (r(s(s(elem!1)), z)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[538, 5898])).
% 2.14/2.38 tff(5900,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5901,plain,
% 2.14/2.38 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5902,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5901])).
% 2.14/2.38 tff(5903,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[5902, 5900])).
% 2.14/2.38 tff(5904,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(5905,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5904, 5903])).
% 2.14/2.38 tff(5906,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5905, 67, 5333, 900, 5245])).
% 2.14/2.38 tff(5907,plain,((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5908,plain,
% 2.14/2.38 (~r(s(s(elem!1)), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5907, 5333, 5899])).
% 2.14/2.38 tff(5909,plain,
% 2.14/2.38 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5584, 853])).
% 2.14/2.38 tff(5910,plain,
% 2.14/2.38 (~(s(s(s(z))) = elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5592, 5723, 5909])).
% 2.14/2.38 tff(5911,plain,
% 2.14/2.38 (~r(s(s(s(z))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5341, 5333, 308])).
% 2.14/2.38 tff(5912,plain,
% 2.14/2.38 (b(s(s(s(z))), elem!1)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5281, 5911, 5910])).
% 2.14/2.38 tff(5913,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5914,plain,
% 2.14/2.38 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(5915,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5914])).
% 2.14/2.38 tff(5916,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[5915, 5913])).
% 2.14/2.38 tff(5917,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(5918,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5917, 5916])).
% 2.14/2.38 tff(5919,plain,
% 2.14/2.38 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5918, 67, 900, 308])).
% 2.14/2.38 tff(5920,plain,
% 2.14/2.38 (b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[2182, 50, 3837, 5919])).
% 2.14/2.38 tff(5921,plain,
% 2.14/2.38 (b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[1165, 50, 628, 3852])).
% 2.14/2.38 tff(5922,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5276, 5921, 5920, 4445, 5210, 5257, 5269])).
% 2.14/2.38 tff(5923,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(s(z))), elem!1)) | (s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5924,plain,
% 2.14/2.38 (r(elem!1, s(s(elem!1)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5923, 5912, 628, 308, 5899, 5732, 5908])).
% 2.14/2.38 tff(5925,plain,
% 2.14/2.38 (r(elem!1, s(s(s(s(z)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5924, 5896])).
% 2.14/2.38 tff(5926,plain,
% 2.14/2.38 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5925, 5895])).
% 2.14/2.38 tff(5927,plain,
% 2.14/2.38 (elem!1 = s(s(z))),
% 2.14/2.38 inference(transitivity,[status(thm)],[1009, 5704, 83])).
% 2.14/2.38 tff(5928,plain,
% 2.14/2.38 (r(elem!1, z) <=> r(s(s(z)), z)),
% 2.14/2.38 inference(monotonicity,[status(thm)],[5927])).
% 2.14/2.38 tff(5929,plain,
% 2.14/2.38 (r(s(s(z)), z)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5333, 5928])).
% 2.14/2.38 tff(5930,plain,
% 2.14/2.38 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3428, 67, 5929, 538])).
% 2.14/2.38 tff(5931,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5930, 5926])).
% 2.14/2.38 tff(5932,plain,((~r(elem!1, z)) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(5933,plain,
% 2.14/2.38 (~r(elem!1, z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5932, 5886, 538, 4995, 308])).
% 2.14/2.38 tff(5934,plain,
% 2.14/2.38 (b(elem!1, z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5184, 5933, 5893])).
% 2.14/2.38 tff(5935,plain,
% 2.14/2.38 (b(s(s(z)), z)),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[5934, 5891])).
% 2.14/2.38 tff(5936,plain,
% 2.14/2.38 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5886])).
% 2.14/2.39 tff(5937,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[5936])).
% 2.14/2.39 tff(5938,plain,
% 2.14/2.39 (b(s(s(elem!1)), s(s(s(z))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[3542, 5937])).
% 2.14/2.39 tff(5939,plain,
% 2.14/2.39 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5886])).
% 2.14/2.39 tff(5940,plain,
% 2.14/2.39 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.39 inference(symmetry,[status(thm)],[5939])).
% 2.14/2.39 tff(5941,plain,
% 2.14/2.39 (b(s(s(s(z))), s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5840, 5940])).
% 2.14/2.39 tff(5942,plain,
% 2.14/2.39 (~b(s(s(elem!1)), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5137, 5886, 5])).
% 2.14/2.39 tff(5943,plain,
% 2.14/2.39 (r(s(s(elem!1)), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[952, 5942])).
% 2.14/2.39 tff(5944,plain,
% 2.14/2.39 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5927])).
% 2.14/2.39 tff(5945,plain,
% 2.14/2.39 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 2.14/2.39 inference(symmetry,[status(thm)],[5944])).
% 2.14/2.39 tff(5946,plain,
% 2.14/2.39 ((~b(s(s(z)), s(z))) <=> (~b(elem!1, s(z)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5945])).
% 2.14/2.39 tff(5947,plain,
% 2.14/2.39 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.39 tff(5948,plain,
% 2.14/2.39 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[2222, 5947])).
% 2.14/2.39 tff(5949,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(5950,plain,
% 2.14/2.39 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(5951,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5950])).
% 2.14/2.39 tff(5952,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[5951, 5949])).
% 2.14/2.39 tff(5953,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(5954,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5953, 5952])).
% 2.14/2.39 tff(5955,plain,
% 2.14/2.39 (~b(s(s(z)), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5954, 204, 363, 5948, 361, 3300])).
% 2.14/2.39 tff(5956,plain,
% 2.14/2.39 (~b(elem!1, s(z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5955, 5946])).
% 2.14/2.39 tff(5957,plain,
% 2.14/2.39 (r(elem!1, s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5197, 5956, 1287])).
% 2.14/2.39 tff(5958,plain,
% 2.14/2.39 (~r(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5253, 5957, 938])).
% 2.14/2.39 tff(5959,plain,
% 2.14/2.39 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(symmetry,[status(thm)],[5896])).
% 2.14/2.39 tff(5960,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[5894, 5959])).
% 2.14/2.39 tff(5961,plain,
% 2.14/2.39 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5960])).
% 2.14/2.39 tff(5962,plain,
% 2.14/2.39 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5706])).
% 2.14/2.39 tff(5963,plain,
% 2.14/2.39 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 2.14/2.39 inference(symmetry,[status(thm)],[5962])).
% 2.14/2.39 tff(5964,plain,
% 2.14/2.39 (r(s(s(z)), s(z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5957, 5963])).
% 2.14/2.39 tff(5965,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(5966,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(5967,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5966, 5965])).
% 2.14/2.39 tff(5968,plain,
% 2.14/2.39 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5967, 67, 538, 136, 5964])).
% 2.14/2.39 tff(5969,plain,
% 2.14/2.39 (~r(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5968, 5961])).
% 2.14/2.39 tff(5970,plain,
% 2.14/2.39 (~b(s(s(s(z))), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5276, 5969, 2141, 2323, 5732, 5958])).
% 2.14/2.39 tff(5971,plain,
% 2.14/2.39 (r(s(s(s(z))), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5281, 5970, 5910])).
% 2.14/2.39 tff(5972,plain,
% 2.14/2.39 (~(z = elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5159, 853])).
% 2.14/2.39 tff(5973,plain,
% 2.14/2.39 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[1124])).
% 2.14/2.39 tff(5974,plain,
% 2.14/2.39 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(symmetry,[status(thm)],[5973])).
% 2.14/2.39 tff(5975,plain,
% 2.14/2.39 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(s(s(z))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5974])).
% 2.14/2.39 tff(5976,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 2.14/2.39 tff(5977,plain,
% 2.14/2.39 (~b(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5976, 5975])).
% 2.14/2.39 tff(5978,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[361, 5977])).
% 2.14/2.39 tff(5979,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(5980,plain,
% 2.14/2.39 (b(z, s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5979, 5909, 361])).
% 2.14/2.39 tff(5981,plain,
% 2.14/2.39 (~(elem!1 = z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5164, 5972])).
% 2.14/2.39 tff(5982,plain,
% 2.14/2.39 (b(elem!1, s(s(elem!1)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[2351, 5969, 5723])).
% 2.14/2.39 tff(5983,plain,
% 2.14/2.39 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 2.14/2.39 inference(symmetry,[status(thm)],[3752])).
% 2.14/2.39 tff(5984,plain,
% 2.14/2.39 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5983])).
% 2.14/2.39 tff(5985,plain,
% 2.14/2.39 (~(s(z) = elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[1287, 5984])).
% 2.14/2.39 tff(5986,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(5987,plain,
% 2.14/2.39 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(5988,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5987])).
% 2.14/2.39 tff(5989,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[5988, 5986])).
% 2.14/2.39 tff(5990,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(5991,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 2.14/2.39 tff(5992,plain,
% 2.14/2.39 (~b(s(z), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5991, 204, 5243, 4660, 2222, 362])).
% 2.14/2.39 tff(5993,plain,
% 2.14/2.39 ((s(z) = elem!1) | r(s(z), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5366, 50, 5992])).
% 2.14/2.39 tff(5994,plain,
% 2.14/2.39 (r(s(z), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5993, 5985])).
% 2.14/2.39 tff(5995,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(5996,plain,
% 2.14/2.39 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))) <=> ((~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(5997,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5996])).
% 2.14/2.39 tff(5998,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[5997, 5995])).
% 2.14/2.39 tff(5999,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6000,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5999, 5998])).
% 2.14/2.39 tff(6001,plain,
% 2.14/2.39 ((~b(z, elem!1)) | (~b(elem!1, s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6000, 204, 4660, 2222, 362])).
% 2.14/2.39 tff(6002,plain,
% 2.14/2.39 (~b(elem!1, s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6001, 5243])).
% 2.14/2.39 tff(6003,plain,
% 2.14/2.39 (r(elem!1, s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5197, 6002, 1287])).
% 2.14/2.39 tff(6004,plain,
% 2.14/2.39 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[5207])).
% 2.14/2.39 tff(6005,plain,
% 2.14/2.39 (~(s(s(elem!1)) = elem!1)),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[5154, 6004])).
% 2.14/2.39 tff(6006,plain,
% 2.14/2.39 (~r(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5251, 67, 938, 6003])).
% 2.14/2.39 tff(6007,plain,
% 2.14/2.39 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5265, 50, 6006])).
% 2.14/2.39 tff(6008,plain,
% 2.14/2.39 (b(s(s(elem!1)), elem!1)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6007, 6005])).
% 2.14/2.39 tff(6009,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6010,plain,
% 2.14/2.39 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6011,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6010])).
% 2.14/2.39 tff(6012,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6011, 6009])).
% 2.14/2.39 tff(6013,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6014,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6013, 6012])).
% 2.14/2.39 tff(6015,plain,
% 2.14/2.39 (~b(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6014, 204, 5243, 4660, 3720, 6008])).
% 2.14/2.39 tff(6016,plain,
% 2.14/2.39 (r(elem!1, z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5184, 6015, 2209])).
% 2.14/2.39 tff(6017,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6018,plain,
% 2.14/2.39 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6019,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6018])).
% 2.14/2.39 tff(6020,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6019, 6017])).
% 2.14/2.39 tff(6021,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6022,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6021, 6020])).
% 2.14/2.39 tff(6023,plain,
% 2.14/2.39 (~b(s(z), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6022, 204, 5243, 2222, 3720, 6008])).
% 2.14/2.39 tff(6024,plain,
% 2.14/2.39 (r(s(z), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[376, 6023])).
% 2.14/2.39 tff(6025,plain,
% 2.14/2.39 (((~![X0: $i, 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), elem!1)) | (~r(elem!1, 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(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6026,plain,
% 2.14/2.39 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6027,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6026])).
% 2.14/2.39 tff(6028,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6027, 6025])).
% 2.14/2.39 tff(6029,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6030,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6029, 6028])).
% 2.14/2.39 tff(6031,plain,
% 2.14/2.39 ((~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6030, 67])).
% 2.14/2.39 tff(6032,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6031, 6024, 6016, 6003, 5994])).
% 2.14/2.40 tff(6033,plain,((~b(z, elem!1)) | (elem!1 = z) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (elem!1 = s(z)) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.40 tff(6034,plain,
% 2.14/2.40 (~b(z, elem!1)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[6033, 5982, 362, 938, 5981, 5723, 1287, 5980, 2222])).
% 2.14/2.40 tff(6035,plain,
% 2.14/2.40 (r(z, elem!1)),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[5297, 6034, 5972])).
% 2.14/2.40 tff(6036,plain,
% 2.14/2.40 ($false),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[5292, 6035, 5971, 3])).
% 2.14/2.40 tff(6037,plain,((~b(s(z), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.40 tff(6038,plain,
% 2.14/2.40 (~b(s(z), s(s(elem!1)))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[6037, 5943, 362, 260, 1287, 5941, 5938, 5886, 538, 56, 5831, 361, 5935])).
% 2.14/2.40 tff(6039,plain,
% 2.14/2.40 (r(s(z), s(s(elem!1)))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[936, 6038])).
% 2.14/2.40 tff(6040,plain,
% 2.14/2.40 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 2.14/2.40 inference(monotonicity,[status(thm)],[5886])).
% 2.14/2.40 tff(6041,plain,
% 2.14/2.40 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 2.14/2.40 inference(symmetry,[status(thm)],[6040])).
% 2.14/2.40 tff(6042,plain,
% 2.14/2.40 (r(s(s(elem!1)), z)),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[538, 6041])).
% 2.14/2.40 tff(6043,plain,
% 2.14/2.40 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[5888])).
% 2.14/2.40 tff(6044,plain,
% 2.14/2.40 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 2.14/2.40 inference(symmetry,[status(thm)],[6043])).
% 2.14/2.40 tff(6045,plain,
% 2.14/2.40 ((~b(z, s(s(s(z))))) <=> (~b(z, s(elem!1)))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[6044])).
% 2.14/2.40 tff(6046,plain,
% 2.14/2.40 (~b(z, s(elem!1))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[250, 6045])).
% 2.14/2.40 tff(6047,plain,
% 2.14/2.40 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[5526])).
% 2.14/2.40 tff(6048,plain,
% 2.14/2.40 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 2.14/2.40 inference(symmetry,[status(thm)],[6047])).
% 2.14/2.40 tff(6049,plain,
% 2.14/2.40 (b(z, s(elem!1))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[361, 6048])).
% 2.14/2.40 tff(6050,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 2.14/2.40 tff(6051,plain,
% 2.14/2.40 ($false),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[6050, 6049])).
% 2.14/2.40 tff(6052,plain,((~b(z, s(s(s(s(z)))))) | b(z, s(elem!1)) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.40 tff(6053,plain,
% 2.14/2.40 (~(elem!1 = s(s(s(z))))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[6052, 6046, 361])).
% 2.14/2.40 tff(6054,plain,
% 2.14/2.40 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[5886])).
% 2.14/2.40 tff(6055,plain,
% 2.14/2.40 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.40 inference(transitivity,[status(thm)],[6054, 5641])).
% 2.14/2.40 tff(6056,plain,
% 2.14/2.40 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.40 inference(symmetry,[status(thm)],[6055])).
% 2.14/2.40 tff(6057,plain,
% 2.14/2.40 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.14/2.40 inference(symmetry,[status(thm)],[5889])).
% 2.14/2.40 tff(6058,plain,
% 2.14/2.40 (s(s(z)) = elem!1),
% 2.14/2.40 inference(transitivity,[status(thm)],[84, 6057, 902])).
% 2.14/2.40 tff(6059,plain,
% 2.14/2.40 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.14/2.40 inference(monotonicity,[status(thm)],[6058])).
% 2.14/2.40 tff(6060,plain,
% 2.14/2.40 ((s(s(s(s(z)))) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 2.14/2.40 inference(transitivity,[status(thm)],[6059, 6056])).
% 2.14/2.40 tff(6061,plain,
% 2.14/2.40 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.14/2.40 inference(monotonicity,[status(thm)],[6060])).
% 2.14/2.40 tff(6062,plain,
% 2.14/2.40 (~(elem!1 = s(s(elem!1)))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[2122, 6061])).
% 2.14/2.40 tff(6063,plain,
% 2.14/2.40 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.14/2.40 inference(monotonicity,[status(thm)],[853])).
% 2.14/2.40 tff(6064,plain,
% 2.14/2.40 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.14/2.40 inference(symmetry,[status(thm)],[6063])).
% 2.24/2.40 tff(6065,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5706])).
% 2.24/2.40 tff(6066,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(elem!1)), elem!1)),
% 2.24/2.40 inference(transitivity,[status(thm)],[6065, 6064])).
% 2.24/2.40 tff(6067,plain,
% 2.24/2.40 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(elem!1)), elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6066])).
% 2.24/2.40 tff(6068,plain,
% 2.24/2.40 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[853])).
% 2.24/2.40 tff(6069,plain,
% 2.24/2.40 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[2141, 6068])).
% 2.24/2.40 tff(6070,plain,
% 2.24/2.40 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(symmetry,[status(thm)],[5707])).
% 2.24/2.40 tff(6071,plain,
% 2.24/2.40 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[5700, 6070])).
% 2.24/2.40 tff(6072,plain,
% 2.24/2.40 (b(s(s(elem!1)), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5267, 5254, 5261])).
% 2.24/2.40 tff(6073,plain,
% 2.24/2.40 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6072, 6071])).
% 2.24/2.40 tff(6074,plain,
% 2.24/2.40 (b(elem!1, s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5927, 853])).
% 2.24/2.40 tff(6075,plain,
% 2.24/2.40 (b(elem!1, s(s(elem!1)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2351, 5724, 5154])).
% 2.24/2.40 tff(6076,plain,
% 2.24/2.40 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6075, 6074])).
% 2.24/2.40 tff(6077,plain,
% 2.24/2.40 (r(s(s(z)), z) <=> r(elem!1, z)),
% 2.24/2.40 inference(symmetry,[status(thm)],[5928])).
% 2.24/2.40 tff(6078,plain,
% 2.24/2.40 ((~r(s(s(z)), z)) <=> (~r(elem!1, z))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6077])).
% 2.24/2.40 tff(6079,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5706])).
% 2.24/2.40 tff(6080,plain,
% 2.24/2.40 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.24/2.40 inference(symmetry,[status(thm)],[6079])).
% 2.24/2.40 tff(6081,plain,
% 2.24/2.40 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5706])).
% 2.24/2.40 tff(6082,plain,
% 2.24/2.40 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6081])).
% 2.24/2.40 tff(6083,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6084,plain,
% 2.24/2.40 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6085,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6084])).
% 2.24/2.40 tff(6086,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6085, 6083])).
% 2.24/2.40 tff(6087,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6088,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6087, 6086])).
% 2.24/2.40 tff(6089,plain,
% 2.24/2.40 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6088, 204, 3460, 194, 153])).
% 2.24/2.40 tff(6090,plain,
% 2.24/2.40 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6089, 3461])).
% 2.24/2.40 tff(6091,plain,
% 2.24/2.40 (~b(elem!1, s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6090, 6082])).
% 2.24/2.40 tff(6092,plain,
% 2.24/2.40 (r(elem!1, s(s(s(z))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5503, 6091, 5499])).
% 2.24/2.40 tff(6093,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6092, 6080])).
% 2.24/2.40 tff(6094,plain,
% 2.24/2.40 (~r(s(s(z)), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4133, 67, 3, 6093])).
% 2.24/2.40 tff(6095,plain,
% 2.24/2.40 (~r(elem!1, z)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6094, 6078])).
% 2.24/2.40 tff(6096,plain,
% 2.24/2.40 ((~b(s(s(z)), z)) <=> (~b(elem!1, z))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5710])).
% 2.24/2.40 tff(6097,plain,
% 2.24/2.40 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5706])).
% 2.24/2.40 tff(6098,plain,
% 2.24/2.40 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.24/2.40 inference(symmetry,[status(thm)],[6097])).
% 2.24/2.40 tff(6099,plain,
% 2.24/2.40 (b(z, s(s(z)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[5243, 6098])).
% 2.24/2.40 tff(6100,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6101,plain,
% 2.24/2.40 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6102,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6101])).
% 2.24/2.40 tff(6103,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6102, 6100])).
% 2.24/2.40 tff(6104,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6105,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6104, 6103])).
% 2.24/2.40 tff(6106,plain,
% 2.24/2.40 ((~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6105, 204, 361, 3461, 3460])).
% 2.24/2.40 tff(6107,plain,
% 2.24/2.40 (~b(s(s(z)), z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6106, 6099])).
% 2.24/2.40 tff(6108,plain,
% 2.24/2.40 (~b(elem!1, z)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6107, 6096])).
% 2.24/2.40 tff(6109,plain,
% 2.24/2.40 (r(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5184, 6108, 5981])).
% 2.24/2.40 tff(6110,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6109, 6095])).
% 2.24/2.40 tff(6111,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6112,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6111, 6076, 3, 361, 853, 5499, 5243, 194, 153])).
% 2.24/2.40 tff(6113,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6112, 6073])).
% 2.24/2.40 tff(6114,plain,((~r(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6115,plain,
% 2.24/2.40 (~r(elem!1, s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6114, 5154, 3, 361, 5499, 5243, 194, 6069, 853, 938, 907])).
% 2.24/2.40 tff(6116,plain,
% 2.24/2.40 (b(elem!1, s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5197, 6115, 1287])).
% 2.24/2.40 tff(6117,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6118,plain,
% 2.24/2.40 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6119,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6118])).
% 2.24/2.40 tff(6120,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6119, 6117])).
% 2.24/2.40 tff(6121,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6122,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6121, 6120])).
% 2.24/2.40 tff(6123,plain,
% 2.24/2.40 ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6122, 204])).
% 2.24/2.40 tff(6124,plain,
% 2.24/2.40 (~b(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6123, 6116, 363, 5243, 362])).
% 2.24/2.40 tff(6125,plain,
% 2.24/2.40 (r(elem!1, z)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5184, 6124, 5981])).
% 2.24/2.40 tff(6126,plain,
% 2.24/2.40 (r(s(s(z)), z)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6125, 5928])).
% 2.24/2.40 tff(6127,plain,
% 2.24/2.40 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3416, 67, 6126, 538])).
% 2.24/2.40 tff(6128,plain,
% 2.24/2.40 (~r(s(s(elem!1)), elem!1)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6127, 6067])).
% 2.24/2.40 tff(6129,plain,
% 2.24/2.40 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.24/2.40 inference(symmetry,[status(thm)],[853])).
% 2.24/2.40 tff(6130,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5706, 6129])).
% 2.24/2.40 tff(6131,plain,
% 2.24/2.40 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(elem!1))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6130])).
% 2.24/2.40 tff(6132,plain,
% 2.24/2.40 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3428, 67, 6126, 538])).
% 2.24/2.40 tff(6133,plain,
% 2.24/2.40 (~r(elem!1, s(s(elem!1)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6132, 6131])).
% 2.24/2.40 tff(6134,plain,
% 2.24/2.40 (elem!1 = s(s(s(z)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[5416, 5496])).
% 2.24/2.40 tff(6135,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5499, 6134])).
% 2.24/2.40 tff(6136,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6137,plain,
% 2.24/2.40 (~(s(s(s(z))) = elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6136, 5499])).
% 2.24/2.40 tff(6138,plain,
% 2.24/2.40 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 2.24/2.40 inference(monotonicity,[status(thm)],[5706])).
% 2.24/2.40 tff(6139,plain,
% 2.24/2.40 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6138])).
% 2.24/2.40 tff(6140,plain,
% 2.24/2.40 (~r(s(s(s(z))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[2892, 67, 308, 6126])).
% 2.24/2.40 tff(6141,plain,
% 2.24/2.40 (~r(s(s(s(z))), elem!1)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6140, 6139])).
% 2.24/2.40 tff(6142,plain,
% 2.24/2.40 (b(s(s(s(z))), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5281, 6141, 6137])).
% 2.24/2.40 tff(6143,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5276, 6142, 6133, 2323, 5261, 2141, 6128])).
% 2.24/2.40 tff(6144,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = s(z)) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6145,plain,
% 2.24/2.40 (~b(z, elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6144, 6039, 538, 5886, 6062, 308, 5831, 5938, 362, 1287, 260, 361, 5941, 3542, 5943, 6053])).
% 2.24/2.40 tff(6146,plain,
% 2.24/2.40 (r(z, elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5297, 6145, 5892])).
% 2.24/2.40 tff(6147,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6148,plain,
% 2.24/2.40 (((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6149,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, 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(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6148])).
% 2.24/2.40 tff(6150,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, 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(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6149, 6147])).
% 2.24/2.40 tff(6151,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6152,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6151, 6150])).
% 2.24/2.40 tff(6153,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6152, 67, 5284, 900, 5245])).
% 2.24/2.40 tff(6154,plain,((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6155,plain,
% 2.24/2.40 (~r(s(s(elem!1)), elem!1)),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6154, 6146, 6042])).
% 2.24/2.40 tff(6156,plain,
% 2.24/2.40 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 2.24/2.40 inference(transitivity,[status(thm)],[6059, 6056, 5207])).
% 2.24/2.40 tff(6157,plain,
% 2.24/2.40 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6156])).
% 2.24/2.40 tff(6158,plain,
% 2.24/2.40 (~(s(s(elem!1)) = elem!1)),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[2122, 6157])).
% 2.24/2.40 tff(6159,plain,
% 2.24/2.40 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5584, 5886])).
% 2.24/2.40 tff(6160,plain,
% 2.24/2.40 (~(s(s(s(z))) = elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5592, 6062, 6159])).
% 2.24/2.41 tff(6161,plain,
% 2.24/2.41 (~r(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5292, 6146, 260])).
% 2.24/2.41 tff(6162,plain,
% 2.24/2.41 (b(s(s(s(z))), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5281, 6161, 6160])).
% 2.24/2.41 tff(6163,plain,
% 2.24/2.41 (r(elem!1, s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5923, 6162, 4995, 308, 6042, 6158, 6155])).
% 2.24/2.41 tff(6164,plain,
% 2.24/2.41 (~r(elem!1, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4639, 6163, 6039])).
% 2.24/2.41 tff(6165,plain,
% 2.24/2.41 (b(z, s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5979, 6159, 361])).
% 2.24/2.41 tff(6166,plain,
% 2.24/2.41 (b(s(s(elem!1)), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5267, 6155, 6158])).
% 2.24/2.41 tff(6167,plain,
% 2.24/2.41 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4668, 6162, 5941, 5938, 6166])).
% 2.24/2.41 tff(6168,assumption,(~r(elem!1, z)), introduced(assumption)).
% 2.24/2.41 tff(6169,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.24/2.41 tff(6170,plain,
% 2.24/2.41 (r(elem!1, s(s(elem!1)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[2351, 6169, 5154])).
% 2.24/2.41 tff(6171,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6172,plain,
% 2.24/2.41 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6173,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6172])).
% 2.24/2.41 tff(6174,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6173, 6171])).
% 2.24/2.41 tff(6175,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6176,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6175, 6174])).
% 2.24/2.41 tff(6177,plain,
% 2.24/2.41 ((~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6176, 67])).
% 2.24/2.41 tff(6178,plain,
% 2.24/2.41 (~r(s(z), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6177, 6170, 907])).
% 2.24/2.41 tff(6179,plain,
% 2.24/2.41 (b(s(z), elem!1)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5366, 50, 6178, 5440])).
% 2.24/2.41 tff(6180,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6181,plain,
% 2.24/2.41 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6182,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6181])).
% 2.24/2.41 tff(6183,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6182, 6180])).
% 2.24/2.41 tff(6184,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6185,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6184, 6183])).
% 2.24/2.41 tff(6186,plain,
% 2.24/2.41 ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6185, 204])).
% 2.24/2.41 tff(6187,plain,
% 2.24/2.41 (~b(elem!1, z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6186, 6179, 363, 5202, 362])).
% 2.24/2.41 tff(6188,plain,
% 2.24/2.41 (elem!1 = z),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5184, 6187, 6168])).
% 2.24/2.41 tff(6189,plain,
% 2.24/2.41 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6188])).
% 2.24/2.41 tff(6190,plain,
% 2.24/2.41 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.24/2.41 inference(symmetry,[status(thm)],[6189])).
% 2.24/2.41 tff(6191,plain,
% 2.24/2.41 (b(elem!1, s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[3720, 6190])).
% 2.24/2.41 tff(6192,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6169, 6191])).
% 2.24/2.41 tff(6193,plain,(b(elem!1, s(s(elem!1))) | (~b(z, s(s(elem!1)))) | r(elem!1, z) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (s(z) = elem!1) | (~r(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6194,plain,
% 2.24/2.41 (~b(elem!1, s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6193, 6167, 362, 5831, 6165, 5933, 5322, 6039, 6062])).
% 2.24/2.41 tff(6195,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5197, 6194, 6164, 1287])).
% 2.24/2.41 tff(6196,plain,((~r(s(s(s(s(z)))), z)) | (elem!1 = s(z)) | (~b(z, s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | b(z, s(s(s(z)))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6197,plain,
% 2.24/2.41 (elem!1 = s(z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6196, 308, 5, 538, 362, 250, 361])).
% 2.24/2.41 tff(6198,plain,
% 2.24/2.41 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3885, 308, 538, 153])).
% 2.24/2.41 tff(6199,plain,
% 2.24/2.41 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[822, 6198])).
% 2.24/2.41 tff(6200,plain,
% 2.24/2.41 (s(elem!1) = s(s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6197])).
% 2.24/2.41 tff(6201,plain,
% 2.24/2.41 (s(s(elem!1)) = s(s(s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6200])).
% 2.24/2.41 tff(6202,plain,
% 2.24/2.41 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6201])).
% 2.24/2.41 tff(6203,plain,
% 2.24/2.41 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6202])).
% 2.24/2.41 tff(6204,plain,
% 2.24/2.41 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6203])).
% 2.24/2.41 tff(6205,plain,
% 2.24/2.41 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6204])).
% 2.24/2.41 tff(6206,plain,
% 2.24/2.41 (r(z, s(s(s(s(s(s(elem!1))))))) <=> r(z, s(s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6205])).
% 2.24/2.41 tff(6207,plain,
% 2.24/2.41 (r(z, s(s(s(s(s(s(s(z)))))))) <=> r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.41 inference(symmetry,[status(thm)],[6206])).
% 2.24/2.41 tff(6208,plain,
% 2.24/2.41 ((~r(z, s(s(s(s(s(s(s(z))))))))) <=> (~r(z, s(s(s(s(s(s(elem!1))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6207])).
% 2.24/2.41 tff(6209,plain,
% 2.24/2.41 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(commutativity,[status(thm)],[])).
% 2.24/2.41 tff(6210,plain,
% 2.24/2.41 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(symmetry,[status(thm)],[6209])).
% 2.24/2.41 tff(6211,plain,
% 2.24/2.41 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6210])).
% 2.24/2.41 tff(6212,plain,
% 2.24/2.41 (s(s(s(z))) = s(s(elem!1))),
% 2.24/2.41 inference(symmetry,[status(thm)],[6201])).
% 2.24/2.41 tff(6213,plain,
% 2.24/2.41 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6212])).
% 2.24/2.41 tff(6214,plain,
% 2.24/2.41 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6213])).
% 2.24/2.41 tff(6215,plain,
% 2.24/2.41 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[1319, 6214])).
% 2.24/2.41 tff(6216,plain,
% 2.24/2.41 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[879, 6215])).
% 2.24/2.41 tff(6217,plain,
% 2.24/2.41 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[1337, 6216, 6197])).
% 2.24/2.41 tff(6218,plain,
% 2.24/2.41 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6217, 6211])).
% 2.24/2.41 tff(6219,plain,
% 2.24/2.41 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(s(s(s(s(z))))))), z)),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6205])).
% 2.24/2.41 tff(6220,plain,
% 2.24/2.41 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6199, 6219])).
% 2.24/2.41 tff(6221,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6222,plain,
% 2.24/2.41 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6223,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6222])).
% 2.24/2.41 tff(6224,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6223, 6221])).
% 2.24/2.41 tff(6225,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6226,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6225, 6224])).
% 2.24/2.41 tff(6227,plain,
% 2.24/2.41 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6226, 204, 362, 1469, 443, 6220])).
% 2.24/2.41 tff(6228,plain,
% 2.24/2.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6229,plain,
% 2.24/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6230,plain,
% 2.24/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6229, 6228])).
% 2.24/2.41 tff(6231,plain,
% 2.24/2.41 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6230, 50, 6227])).
% 2.24/2.41 tff(6232,plain,
% 2.24/2.41 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6231, 6218])).
% 2.24/2.41 tff(6233,plain,
% 2.24/2.41 (((~![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(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6234,plain,
% 2.24/2.41 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6235,plain,
% 2.24/2.41 (((~![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(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6234])).
% 2.24/2.41 tff(6236,plain,
% 2.24/2.41 (((~![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(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6235, 6233])).
% 2.24/2.41 tff(6237,plain,
% 2.24/2.41 ((~![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(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6238,plain,
% 2.24/2.41 ((~![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(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6237, 6236])).
% 2.24/2.41 tff(6239,plain,
% 2.24/2.41 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6238, 67, 4975, 6232])).
% 2.24/2.41 tff(6240,plain,
% 2.24/2.41 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6239, 6208])).
% 2.24/2.41 tff(6241,plain,
% 2.24/2.41 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(elem!1))))))),
% 2.24/2.41 inference(symmetry,[status(thm)],[6205])).
% 2.24/2.41 tff(6242,plain,
% 2.24/2.41 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6241])).
% 2.24/2.41 tff(6243,plain,
% 2.24/2.41 ((~r(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6242])).
% 2.24/2.41 tff(6244,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6245,plain,
% 2.24/2.41 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6246,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6245])).
% 2.24/2.41 tff(6247,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6246, 6244])).
% 2.24/2.41 tff(6248,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6249,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6248, 6247])).
% 2.24/2.41 tff(6250,plain,
% 2.24/2.41 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6249, 204, 4973, 362, 1469, 443])).
% 2.24/2.41 tff(6251,plain,
% 2.24/2.41 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[489, 50, 6250, 249])).
% 2.24/2.41 tff(6252,plain,
% 2.24/2.41 (((~![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(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6253,plain,
% 2.24/2.41 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6254,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6253])).
% 2.24/2.41 tff(6255,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6254, 6252])).
% 2.24/2.42 tff(6256,plain,
% 2.24/2.42 ((~![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(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6257,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6256, 6255])).
% 2.24/2.42 tff(6258,plain,
% 2.24/2.42 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6257, 67, 6251, 6232])).
% 2.24/2.42 tff(6259,plain,
% 2.24/2.42 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6258, 6243])).
% 2.24/2.42 tff(6260,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.24/2.42 inference(monotonicity,[status(thm)],[1352])).
% 2.24/2.42 tff(6261,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.42 inference(symmetry,[status(thm)],[6260])).
% 2.24/2.42 tff(6262,plain,
% 2.24/2.42 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.24/2.42 inference(symmetry,[status(thm)],[1018])).
% 2.24/2.42 tff(6263,plain,
% 2.24/2.42 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[1352])).
% 2.24/2.42 tff(6264,plain,
% 2.24/2.42 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.24/2.42 inference(transitivity,[status(thm)],[6263, 6262])).
% 2.24/2.42 tff(6265,plain,
% 2.24/2.42 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6264])).
% 2.24/2.42 tff(6266,plain,
% 2.24/2.42 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[669, 6265])).
% 2.24/2.42 tff(6267,plain,
% 2.24/2.42 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[1322])).
% 2.24/2.42 tff(6268,plain,
% 2.24/2.42 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.24/2.42 inference(symmetry,[status(thm)],[6267])).
% 2.24/2.42 tff(6269,plain,
% 2.24/2.42 ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) <=> (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6268])).
% 2.24/2.42 tff(6270,plain,
% 2.24/2.42 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[672, 6269])).
% 2.24/2.42 tff(6271,plain,
% 2.24/2.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6272,plain,
% 2.24/2.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6273,plain,
% 2.24/2.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6272, 6271])).
% 2.24/2.42 tff(6274,plain,
% 2.24/2.42 ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6273, 50])).
% 2.24/2.42 tff(6275,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6274, 6270, 6266])).
% 2.24/2.42 tff(6276,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6275, 6261])).
% 2.24/2.42 tff(6277,plain,
% 2.24/2.42 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3155, 50, 3152, 3151])).
% 2.24/2.42 tff(6278,plain,
% 2.24/2.42 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3126, 6277])).
% 2.24/2.42 tff(6279,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6278, 6276])).
% 2.24/2.42 tff(6280,plain,(r(z, s(s(s(s(s(s(elem!1))))))) | (~(elem!1 = s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6281,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6280, 6259, 6240, 4973, 6199, 362, 6197])).
% 2.24/2.42 tff(6282,plain,((~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(s(z)))), z)) | b(z, s(s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6283,plain,
% 2.24/2.42 (~r(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6282, 4994, 1469, 443, 5, 538, 250, 362, 153])).
% 2.24/2.42 tff(6284,plain,
% 2.24/2.42 (b(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[402, 6283])).
% 2.24/2.42 tff(6285,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2056, 204, 6284, 4994, 153, 1469, 4985])).
% 2.24/2.42 tff(6286,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | b(s(s(s(s(z)))), s(z)) | b(z, s(s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6287,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6286, 4969, 109, 245, 5, 250, 4971])).
% 2.24/2.42 tff(6288,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[335, 6287])).
% 2.24/2.42 tff(6289,plain,
% 2.24/2.42 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[536, 389, 339])).
% 2.24/2.42 tff(6290,plain,
% 2.24/2.42 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[431, 6289])).
% 2.24/2.42 tff(6291,plain,
% 2.24/2.42 (~r(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1831, 389, 3])).
% 2.24/2.42 tff(6292,plain,
% 2.24/2.42 (b(s(z), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[478, 6291])).
% 2.24/2.42 tff(6293,plain,
% 2.24/2.42 (~r(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[397, 389, 57])).
% 2.24/2.42 tff(6294,plain,
% 2.24/2.42 (b(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[402, 6293])).
% 2.24/2.42 tff(6295,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2573, 204, 6294, 6292, 6290, 153, 359])).
% 2.24/2.42 tff(6296,plain,((~r(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6297,plain,
% 2.24/2.42 (~r(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6296, 339, 359, 153, 3, 57])).
% 2.24/2.42 tff(6298,plain,
% 2.24/2.42 (b(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[376, 6297])).
% 2.24/2.42 tff(6299,plain,
% 2.24/2.42 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1993, 6298, 443, 307, 1469])).
% 2.24/2.42 tff(6300,plain,
% 2.24/2.42 (r(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[604, 50, 601, 6299])).
% 2.24/2.42 tff(6301,plain,
% 2.24/2.42 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4987, 6300, 3])).
% 2.24/2.42 tff(6302,plain,
% 2.24/2.42 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[134, 6301])).
% 2.24/2.42 tff(6303,plain,
% 2.24/2.42 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2034, 6300, 339])).
% 2.24/2.42 tff(6304,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[190, 6303])).
% 2.24/2.42 tff(6305,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6306,plain,
% 2.24/2.42 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6307,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6306])).
% 2.24/2.42 tff(6308,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6307, 6305])).
% 2.24/2.42 tff(6309,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6310,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6309, 6308])).
% 2.24/2.42 tff(6311,plain,
% 2.24/2.42 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6310, 204, 153, 359, 1469])).
% 2.24/2.42 tff(6312,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6311, 6304, 6302])).
% 2.24/2.42 tff(6313,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6314,plain,
% 2.24/2.42 (~r(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6313, 6288, 109, 4969, 260, 245, 57])).
% 2.24/2.42 tff(6315,plain,
% 2.24/2.42 (b(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[357, 6314])).
% 2.24/2.42 tff(6316,plain,
% 2.24/2.42 (~b(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4965, 204, 6315, 4780, 109, 6288])).
% 2.24/2.42 tff(6317,plain,
% 2.24/2.42 (r(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[402, 6316])).
% 2.24/2.42 tff(6318,plain,
% 2.24/2.42 (~r(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[397, 6317, 57])).
% 2.24/2.42 tff(6319,plain,
% 2.24/2.42 (b(s(z), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[376, 6318])).
% 2.24/2.42 tff(6320,plain,
% 2.24/2.42 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1993, 6319, 245, 4971, 4969])).
% 2.24/2.42 tff(6321,plain,
% 2.24/2.42 (r(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[604, 50, 601, 6320])).
% 2.24/2.42 tff(6322,plain,
% 2.24/2.42 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4987, 6321, 260])).
% 2.24/2.42 tff(6323,plain,
% 2.24/2.42 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[134, 6322])).
% 2.24/2.42 tff(6324,plain,
% 2.24/2.42 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6310, 204, 109, 6288, 4969])).
% 2.24/2.42 tff(6325,plain,
% 2.24/2.42 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6324, 6323])).
% 2.24/2.42 tff(6326,plain,
% 2.24/2.42 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[190, 6325])).
% 2.24/2.42 tff(6327,plain,
% 2.24/2.42 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2673, 204, 6319, 4971, 6315, 6288])).
% 2.24/2.42 tff(6328,plain,
% 2.24/2.42 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[431, 6327])).
% 2.24/2.42 tff(6329,plain,
% 2.24/2.42 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1640, 67, 6328, 6326])).
% 2.24/2.42 tff(6330,plain,
% 2.24/2.42 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[489, 50, 6329, 249])).
% 2.24/2.42 tff(6331,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6249, 204, 6319, 4971, 4969, 6330, 245])).
% 2.24/2.42 tff(6332,plain,(b(z, s(s(s(z)))) | (~r(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6333,plain,
% 2.24/2.42 (b(z, s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6332, 57, 5])).
% 2.24/2.42 tff(6334,plain,
% 2.24/2.42 (~r(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[1503, 286, 136])).
% 2.24/2.42 tff(6335,plain,
% 2.24/2.42 (b(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[357, 6334])).
% 2.24/2.42 tff(6336,plain,
% 2.24/2.42 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.24/2.42 inference(symmetry,[status(thm)],[75])).
% 2.24/2.42 tff(6337,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 2.24/2.42 tff(6338,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.24/2.42 tff(6339,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 2.24/2.42 tff(6340,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[150, 6339, 6338])).
% 2.24/2.42 tff(6341,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6342,plain,
% 2.24/2.42 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6343,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6342])).
% 2.24/2.42 tff(6344,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6343, 6341])).
% 2.24/2.42 tff(6345,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6346,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6345, 6344])).
% 2.24/2.42 tff(6347,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6346, 204, 405, 404, 361, 194, 153])).
% 2.24/2.42 tff(6348,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6349,plain,
% 2.24/2.42 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6348, 6340, 404, 361, 405])).
% 2.24/2.42 tff(6350,plain,
% 2.24/2.42 (s(s(s(z))) = s(s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[107, 6349, 6337])).
% 2.24/2.42 tff(6351,plain,
% 2.24/2.42 (s(s(s(s(z)))) = s(s(s(z)))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6350, 6336])).
% 2.24/2.42 tff(6352,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6339, 6351])).
% 2.24/2.42 tff(6353,plain,((s(s(s(s(z)))) = s(s(s(z)))) | r(s(s(s(z))), s(s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | r(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6354,plain,
% 2.24/2.42 (r(s(s(s(z))), s(s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6353, 102])).
% 2.24/2.42 tff(6355,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6354, 2332, 6335, 4779, 262, 405])).
% 2.24/2.42 tff(6356,plain,((~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6357,plain,
% 2.24/2.42 (~r(z, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6356, 6333, 57, 56])).
% 2.24/2.42 tff(6358,plain,
% 2.24/2.42 (b(z, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[306, 6357])).
% 2.24/2.42 tff(6359,plain,
% 2.24/2.42 (~b(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6354, 361, 4779, 262, 405])).
% 2.24/2.42 tff(6360,plain,
% 2.24/2.42 (r(s(s(s(z))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[402, 6359])).
% 2.24/2.42 tff(6361,plain,
% 2.24/2.42 (~r(z, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[2003, 6360, 57])).
% 2.24/2.42 tff(6362,plain,
% 2.24/2.42 (b(z, s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[306, 6361])).
% 2.24/2.42 tff(6363,plain,
% 2.24/2.42 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[4931, 6362, 6360, 57, 136])).
% 2.24/2.42 tff(6364,plain,
% 2.24/2.42 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[641, 6363])).
% 2.24/2.42 tff(6365,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6249, 204, 363, 362, 1469, 2404, 443])).
% 2.24/2.42 tff(6366,plain,((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6367,plain,
% 2.24/2.42 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6366, 6362, 363, 6364, 4792])).
% 2.24/2.42 tff(6368,plain,
% 2.24/2.42 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[489, 50, 6367, 249])).
% 2.24/2.42 tff(6369,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6370,plain,
% 2.24/2.42 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6371,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6370])).
% 2.24/2.42 tff(6372,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6371, 6369])).
% 2.24/2.42 tff(6373,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6374,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6373, 6372])).
% 2.24/2.42 tff(6375,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6374, 204, 363, 405, 456, 361, 4780])).
% 2.24/2.42 tff(6376,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6377,plain,
% 2.24/2.42 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6376, 361, 405, 363])).
% 2.24/2.42 tff(6378,plain,
% 2.24/2.42 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[431, 6377])).
% 2.24/2.43 tff(6379,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1640, 67, 2, 1, 3578])).
% 2.24/2.43 tff(6380,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6381,plain,
% 2.24/2.43 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6380, 6378, 6368])).
% 2.24/2.43 tff(6382,plain,
% 2.24/2.43 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[190, 6381])).
% 2.24/2.43 tff(6383,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6384,plain,
% 2.24/2.43 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6385,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6384])).
% 2.24/2.43 tff(6386,plain,
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% 2.24/2.43 inference(transitivity,[status(thm)],[6385, 6383])).
% 2.24/2.43 tff(6387,plain,
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% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6388,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6387, 6386])).
% 2.24/2.43 tff(6389,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6388, 204, 405, 361, 4780, 6382, 6364])).
% 2.24/2.43 tff(6390,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6391,plain,
% 2.24/2.43 (~b(z, s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6390, 1618, 405, 57, 136])).
% 2.24/2.43 tff(6392,plain,
% 2.24/2.43 (r(z, s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[357, 6391])).
% 2.24/2.43 tff(6393,plain,
% 2.24/2.43 (~r(z, s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1503, 6392, 136])).
% 2.24/2.43 tff(6394,plain,
% 2.24/2.43 (b(z, s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[306, 6393])).
% 2.24/2.43 tff(6395,plain,
% 2.24/2.43 (~r(s(s(s(z))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4931, 3108, 6394, 57, 136])).
% 2.24/2.43 tff(6396,plain,
% 2.24/2.43 (b(s(s(s(z))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[402, 6395])).
% 2.24/2.43 tff(6397,plain,
% 2.24/2.43 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4953, 6396, 3108, 4, 263])).
% 2.24/2.43 tff(6398,plain,
% 2.24/2.43 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[284, 6397])).
% 2.24/2.43 tff(6399,plain,
% 2.24/2.43 (~b(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2494, 204, 1618, 6394, 405, 6396])).
% 2.24/2.43 tff(6400,plain,
% 2.24/2.43 (r(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[478, 6399])).
% 2.24/2.43 tff(6401,plain,
% 2.24/2.43 (((~![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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6402,plain,
% 2.24/2.43 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6403,plain,
% 2.24/2.43 (((~![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(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6402])).
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% 2.24/2.43 inference(transitivity,[status(thm)],[6403, 6401])).
% 2.24/2.43 tff(6405,plain,
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% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6406,plain,
% 2.24/2.43 ((~![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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6405, 6404])).
% 2.24/2.43 tff(6407,plain,
% 2.24/2.43 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6406, 67, 6400, 6398])).
% 2.24/2.43 tff(6408,plain,
% 2.24/2.43 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[489, 50, 6407, 249])).
% 2.24/2.43 tff(6409,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4943, 3108, 538])).
% 2.24/2.43 tff(6410,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[218, 6409])).
% 2.24/2.43 tff(6411,plain,
% 2.24/2.43 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[526, 204, 6410, 4, 6408, 4792])).
% 2.24/2.43 tff(6412,plain,
% 2.24/2.43 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[431, 6411])).
% 2.24/2.43 tff(6413,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4943, 261, 538])).
% 2.24/2.43 tff(6414,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[218, 6413])).
% 2.24/2.43 tff(6415,plain,
% 2.24/2.43 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3267, 204, 3877, 4304, 6414, 4])).
% 2.24/2.43 tff(6416,plain,
% 2.24/2.43 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[851, 6415])).
% 2.24/2.43 tff(6417,plain,
% 2.24/2.43 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6416])).
% 2.24/2.43 tff(6418,plain,
% 2.24/2.43 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[664, 6417, 121])).
% 2.24/2.43 tff(6419,plain,
% 2.24/2.43 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6418])).
% 2.24/2.43 tff(6420,plain,
% 2.24/2.43 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[875, 6419, 119])).
% 2.24/2.43 tff(6421,plain,
% 2.24/2.43 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6420])).
% 2.24/2.43 tff(6422,plain,
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% 2.24/2.43 inference(transitivity,[status(thm)],[699, 6421, 20])).
% 2.24/2.43 tff(6423,plain,
% 2.24/2.43 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6422])).
% 2.24/2.43 tff(6424,plain,
% 2.24/2.43 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.43 inference(symmetry,[status(thm)],[6423])).
% 2.24/2.43 tff(6425,plain,
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% 2.24/2.43 inference(transitivity,[status(thm)],[84, 6424, 753])).
% 2.24/2.43 tff(6426,plain,
% 2.24/2.43 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6425])).
% 2.24/2.43 tff(6427,plain,
% 2.24/2.43 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6426, 2223])).
% 2.24/2.43 tff(6428,plain,
% 2.24/2.43 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6427, 2224])).
% 2.24/2.43 tff(6429,plain,
% 2.24/2.43 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6428])).
% 2.24/2.43 tff(6430,plain,
% 2.24/2.43 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[2125, 6429])).
% 2.24/2.43 tff(6431,plain,
% 2.24/2.43 (s(s(elem!1)) = s(s(z))),
% 2.24/2.43 inference(transitivity,[status(thm)],[754, 6423, 83])).
% 2.24/2.43 tff(6432,plain,
% 2.24/2.43 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6431])).
% 2.24/2.43 tff(6433,plain,
% 2.24/2.43 (s(elem!1) = s(z)),
% 2.24/2.43 inference(transitivity,[status(thm)],[919, 6432, 78])).
% 2.24/2.43 tff(6434,plain,
% 2.24/2.43 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6433])).
% 2.24/2.43 tff(6435,plain,
% 2.24/2.43 (elem!1 = z),
% 2.24/2.43 inference(transitivity,[status(thm)],[1009, 6434, 15])).
% 2.24/2.43 tff(6436,plain,
% 2.24/2.43 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6435])).
% 2.24/2.43 tff(6437,plain,
% 2.24/2.43 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.24/2.43 inference(symmetry,[status(thm)],[6436])).
% 2.24/2.43 tff(6438,plain,
% 2.24/2.43 (b(s(z), elem!1)),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[1618, 6437])).
% 2.24/2.43 tff(6439,plain,
% 2.24/2.43 (~b(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2494, 204, 1618, 362, 405, 404])).
% 2.24/2.43 tff(6440,plain,
% 2.24/2.43 (r(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[478, 6439])).
% 2.24/2.43 tff(6441,plain,
% 2.24/2.43 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.24/2.43 inference(symmetry,[status(thm)],[6434])).
% 2.24/2.43 tff(6442,plain,
% 2.24/2.43 (z = elem!1),
% 2.24/2.43 inference(transitivity,[status(thm)],[2194, 6441, 902])).
% 2.24/2.43 tff(6443,plain,
% 2.24/2.43 (elem!1 = z),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2211, 6442])).
% 2.24/2.43 tff(6444,plain,
% 2.24/2.43 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6420, 6416])).
% 2.24/2.43 tff(6445,plain,
% 2.24/2.43 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6444, 163])).
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% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.43 inference(symmetry,[status(thm)],[6445])).
% 2.24/2.43 tff(6447,plain,
% 2.24/2.43 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6446])).
% 2.24/2.43 tff(6448,plain,
% 2.24/2.43 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[185, 6447])).
% 2.24/2.43 tff(6449,plain,
% 2.24/2.43 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6416])).
% 2.24/2.43 tff(6450,plain,
% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(symmetry,[status(thm)],[6449])).
% 2.24/2.43 tff(6451,plain,
% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6425])).
% 2.24/2.43 tff(6452,plain,
% 2.24/2.43 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6451, 6450])).
% 2.24/2.43 tff(6453,plain,
% 2.24/2.43 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6452])).
% 2.24/2.43 tff(6454,plain,
% 2.24/2.43 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[182, 6453])).
% 2.24/2.43 tff(6455,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3416, 67, 2791, 538])).
% 2.24/2.43 tff(6456,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3421, 6455])).
% 2.24/2.43 tff(6457,plain,
% 2.24/2.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3428, 67, 2791, 538])).
% 2.24/2.43 tff(6458,plain,
% 2.24/2.43 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3438, 6457])).
% 2.24/2.43 tff(6459,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3469, 6458, 6456, 538, 824, 1051, 1335, 2300, 2791])).
% 2.24/2.43 tff(6460,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6461,plain,
% 2.24/2.43 (~r(s(s(z)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6460, 824, 538, 6454, 6448, 6443])).
% 2.24/2.43 tff(6462,plain,
% 2.24/2.43 (b(s(s(z)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3393, 6461])).
% 2.24/2.43 tff(6463,plain,
% 2.24/2.43 (~b(s(s(elem!1)), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3351, 6462, 362, 404, 6416, 6440, 6438])).
% 2.24/2.43 tff(6464,plain,
% 2.24/2.43 (r(s(s(elem!1)), s(z))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[952, 6463])).
% 2.24/2.43 tff(6465,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[5005, 67, 938, 136, 1103])).
% 2.24/2.43 tff(6466,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6467,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6466, 6464, 136])).
% 2.24/2.43 tff(6468,plain,
% 2.24/2.43 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6425])).
% 2.24/2.43 tff(6469,plain,
% 2.24/2.43 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6468, 1123])).
% 2.24/2.43 tff(6470,plain,
% 2.24/2.43 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6469])).
% 2.24/2.43 tff(6471,plain,
% 2.24/2.43 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[2122, 6470])).
% 2.24/2.43 tff(6472,plain,
% 2.24/2.43 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2967, 6464, 136])).
% 2.24/2.43 tff(6473,plain,
% 2.24/2.43 (((~![X0: $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(z))), 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(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6474,plain,
% 2.24/2.43 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6475,plain,
% 2.24/2.43 (((~![X0: $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(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6474])).
% 2.24/2.43 tff(6476,plain,
% 2.24/2.43 (((~![X0: $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(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6475, 6473])).
% 2.24/2.43 tff(6477,plain,
% 2.24/2.43 ((~![X0: $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(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6478,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6477, 6476])).
% 2.24/2.43 tff(6479,plain,
% 2.24/2.43 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6478, 67, 938, 3137])).
% 2.24/2.43 tff(6480,plain,
% 2.24/2.43 (b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3335, 6479, 3837])).
% 2.24/2.43 tff(6481,plain,
% 2.24/2.43 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2233, 67, 938, 3137])).
% 2.24/2.43 tff(6482,plain,
% 2.24/2.43 (b(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1167, 6481, 628])).
% 2.24/2.43 tff(6483,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3794, 6482, 1101, 1135, 1129, 6480])).
% 2.24/2.43 tff(6484,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[151, 6483])).
% 2.24/2.43 tff(6485,plain,
% 2.24/2.43 (~b(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2494, 204, 363, 362, 405, 404])).
% 2.24/2.43 tff(6486,plain,
% 2.24/2.43 (r(s(z), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[478, 6485])).
% 2.24/2.43 tff(6487,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[451, 67, 6486, 2, 6484])).
% 2.24/2.43 tff(6488,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(s(s(z)))), s(s(elem!1))) | (s(s(elem!1)) = s(s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6489,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6488, 6472, 6464, 1618, 6471, 404, 6467, 405, 6430, 362, 2])).
% 2.24/2.43 tff(6490,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6491,plain,
% 2.24/2.43 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6490, 6396, 405, 6394, 6412, 136, 538, 4, 3108])).
% 2.24/2.43 tff(6492,plain,
% 2.24/2.43 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[822, 6491])).
% 2.24/2.43 tff(6493,plain,
% 2.24/2.43 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3145, 6492, 405, 6394, 6396, 1618])).
% 2.24/2.43 tff(6494,plain,
% 2.24/2.43 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3157, 6493])).
% 2.24/2.43 tff(6495,plain,
% 2.24/2.43 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3168, 6494, 538])).
% 2.24/2.43 tff(6496,plain,
% 2.24/2.43 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3173, 6495])).
% 2.24/2.43 tff(6497,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6498,plain,
% 2.24/2.43 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6499,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6498])).
% 2.24/2.43 tff(6500,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6499, 6497])).
% 2.24/2.43 tff(6501,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(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(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6502,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6501, 6500])).
% 2.24/2.44 tff(6503,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6502, 204, 6396, 6492, 6496, 4780])).
% 2.24/2.44 tff(6504,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2434, 50, 706, 6503])).
% 2.24/2.44 tff(6505,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6506,plain,
% 2.24/2.44 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(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(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6507,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6506])).
% 2.24/2.44 tff(6508,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6507, 6505])).
% 2.24/2.44 tff(6509,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6510,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6509, 6508])).
% 2.24/2.44 tff(6511,plain,
% 2.24/2.44 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6510, 67, 3108, 6398, 6504])).
% 2.24/2.44 tff(6512,plain,
% 2.24/2.44 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3214, 6494, 6392])).
% 2.24/2.44 tff(6513,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[766, 6512])).
% 2.24/2.44 tff(6514,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3267, 204, 6513, 6496, 6410, 4])).
% 2.24/2.44 tff(6515,plain,
% 2.24/2.44 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[850, 50, 6514])).
% 2.24/2.44 tff(6516,plain,
% 2.24/2.44 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6515, 6511])).
% 2.24/2.44 tff(6517,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6516])).
% 2.24/2.44 tff(6518,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.44 inference(symmetry,[status(thm)],[6517])).
% 2.24/2.44 tff(6519,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(s(z)))))), z)) <=> (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6518])).
% 2.24/2.44 tff(6520,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[3107, 6519])).
% 2.24/2.44 tff(6521,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6492, 6520])).
% 2.24/2.44 tff(6522,plain,(b(s(s(s(s(s(s(z)))))), z) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6523,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6522, 4, 538, 405, 136, 57])).
% 2.24/2.44 tff(6524,plain,
% 2.24/2.44 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6366, 6523, 1618, 6394, 4792])).
% 2.24/2.44 tff(6525,assumption,(~r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.24/2.44 tff(6526,assumption,(~b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.24/2.44 tff(6527,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[489, 50, 6526, 6525, 249])).
% 2.24/2.44 tff(6528,plain,(r(s(z), s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6529,plain,
% 2.24/2.44 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6528, 6524])).
% 2.24/2.44 tff(6530,plain,
% 2.24/2.44 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1993, 6523, 4792, 1618, 6394])).
% 2.24/2.44 tff(6531,plain,
% 2.24/2.44 (r(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[604, 50, 601, 6530])).
% 2.24/2.44 tff(6532,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6533,plain,
% 2.24/2.44 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6534,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6533])).
% 2.24/2.44 tff(6535,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6534, 6532])).
% 2.24/2.44 tff(6536,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6537,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6536, 6535])).
% 2.24/2.44 tff(6538,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6537, 67, 339, 510, 2032])).
% 2.24/2.44 tff(6539,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6540,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6539, 6531, 6392])).
% 2.24/2.44 tff(6541,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[218, 6540])).
% 2.24/2.44 tff(6542,plain,
% 2.24/2.44 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[212, 6541, 4780, 263, 4])).
% 2.24/2.44 tff(6543,plain,
% 2.24/2.44 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[134, 6542])).
% 2.24/2.44 tff(6544,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1229, 67, 57, 6543, 6529])).
% 2.24/2.44 tff(6545,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6546,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6545, 538, 57, 405, 136])).
% 2.24/2.44 tff(6547,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[190, 6546])).
% 2.24/2.44 tff(6548,plain,
% 2.24/2.44 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4784, 6547, 538])).
% 2.24/2.44 tff(6549,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[641, 6548])).
% 2.24/2.44 tff(6550,plain,
% 2.24/2.44 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1993, 6549, 4792, 1618, 6394])).
% 2.24/2.44 tff(6551,plain,
% 2.24/2.44 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2034, 6547, 6392])).
% 2.24/2.44 tff(6552,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[604, 50, 601, 6551, 6550])).
% 2.24/2.44 tff(6553,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6554,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6553, 57, 6333, 56])).
% 2.24/2.44 tff(6555,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[335, 6554])).
% 2.24/2.44 tff(6556,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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)))), 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(X1, 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)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6557,plain,
% 2.24/2.44 (((~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(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6558,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6557])).
% 2.24/2.44 tff(6559,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6558, 6556])).
% 2.24/2.44 tff(6560,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6561,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 2.24/2.44 tff(6562,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6561, 204, 405, 404, 4780, 153, 359])).
% 2.24/2.44 tff(6563,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6564,plain,
% 2.24/2.44 (~b(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6563, 6333, 109, 6555])).
% 2.24/2.44 tff(6565,plain,
% 2.24/2.44 (r(s(s(s(z))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[402, 6564])).
% 2.24/2.44 tff(6566,plain,
% 2.24/2.44 (~r(s(z), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[397, 6565, 57])).
% 2.24/2.44 tff(6567,plain,
% 2.24/2.44 (b(s(z), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[376, 6566])).
% 2.24/2.44 tff(6568,plain,
% 2.24/2.44 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4931, 6565, 6358, 57, 56])).
% 2.24/2.44 tff(6569,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[641, 6568])).
% 2.24/2.44 tff(6570,plain,
% 2.24/2.44 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6366, 6569, 6567, 6358, 245])).
% 2.24/2.44 tff(6571,plain,
% 2.24/2.44 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6528, 6570])).
% 2.24/2.44 tff(6572,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6573,plain,
% 2.24/2.44 (((~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(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6574,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6573])).
% 2.24/2.44 tff(6575,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6574, 6572])).
% 2.24/2.44 tff(6576,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6577,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6576, 6575])).
% 2.24/2.44 tff(6578,plain,
% 2.24/2.44 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6577, 204, 6567, 6333, 4780, 6555])).
% 2.24/2.44 tff(6579,plain,
% 2.24/2.44 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[431, 6578])).
% 2.24/2.44 tff(6580,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6581,plain,
% 2.24/2.44 (((~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(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6582,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6581])).
% 2.24/2.44 tff(6583,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6582, 6580])).
% 2.24/2.44 tff(6584,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6585,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6584, 6583])).
% 2.24/2.44 tff(6586,plain,
% 2.24/2.44 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6585, 204, 6333, 4780, 6555, 6569])).
% 2.24/2.44 tff(6587,plain,
% 2.24/2.44 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[190, 6586])).
% 2.24/2.44 tff(6588,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6380, 6587, 6579, 6571])).
% 2.24/2.44 tff(6589,plain,((~r(s(s(s(z))), s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6590,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6589, 5])).
% 2.24/2.44 tff(6591,plain,
% 2.24/2.44 (b(s(s(s(z))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[558, 6590])).
% 2.24/2.44 tff(6592,plain,
% 2.24/2.44 (~r(z, s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1503, 339, 56])).
% 2.24/2.44 tff(6593,plain,
% 2.24/2.44 (b(z, s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[306, 6592])).
% 2.24/2.44 tff(6594,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1922, 339, 260])).
% 2.24/2.44 tff(6595,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[108, 6594])).
% 2.24/2.44 tff(6596,plain,
% 2.24/2.44 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[161, 1, 56])).
% 2.24/2.44 tff(6597,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[244, 6596])).
% 2.24/2.44 tff(6598,plain,
% 2.24/2.44 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4788, 1, 339])).
% 2.24/2.44 tff(6599,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[641, 6598])).
% 2.24/2.44 tff(6600,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6286, 6599, 6597, 250, 6595, 5, 538, 6593])).
% 2.24/2.44 tff(6601,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | b(z, s(s(s(z)))) | b(s(s(s(s(z)))), s(z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6602,plain,
% 2.24/2.44 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6601, 538, 5, 250, 339])).
% 2.24/2.44 tff(6603,plain,
% 2.24/2.44 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[190, 6602])).
% 2.24/2.44 tff(6604,plain,
% 2.24/2.44 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4939, 204, 4780, 153, 4])).
% 2.24/2.44 tff(6605,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6604, 6414, 285])).
% 2.24/2.44 tff(6606,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6607,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6606, 6603, 6595, 538, 260])).
% 2.24/2.45 tff(6608,plain,
% 2.24/2.45 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[641, 6607])).
% 2.24/2.45 tff(6609,plain,
% 2.24/2.45 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6286, 6608, 250, 6595, 5, 538, 6593])).
% 2.24/2.45 tff(6610,plain,
% 2.24/2.45 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[244, 6609])).
% 2.24/2.45 tff(6611,plain,
% 2.24/2.45 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[225, 67, 56, 6610])).
% 2.24/2.45 tff(6612,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[218, 6611])).
% 2.24/2.45 tff(6613,plain,
% 2.24/2.45 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[212, 6612, 4780, 6595, 6603])).
% 2.24/2.45 tff(6614,plain,
% 2.24/2.45 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[134, 6613])).
% 2.24/2.45 tff(6615,plain,
% 2.24/2.45 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4987, 6614, 260])).
% 2.24/2.45 tff(6616,plain,
% 2.24/2.45 (b(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[604, 50, 601, 6615])).
% 2.24/2.45 tff(6617,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2659, 261, 389])).
% 2.24/2.45 tff(6618,plain,
% 2.24/2.45 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[244, 6617])).
% 2.24/2.45 tff(6619,plain,
% 2.24/2.45 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6528, 486])).
% 2.24/2.45 tff(6620,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[574, 204, 444, 6292, 6619, 6618, 285])).
% 2.24/2.45 tff(6621,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6622,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6621, 389, 444, 3])).
% 2.24/2.45 tff(6623,plain,
% 2.24/2.45 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[641, 6622])).
% 2.24/2.45 tff(6624,plain,
% 2.24/2.45 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1922, 339, 3])).
% 2.24/2.45 tff(6625,plain,
% 2.24/2.45 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[108, 6624])).
% 2.24/2.45 tff(6626,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6627,plain,
% 2.24/2.45 (((~b(s(s(s(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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6628,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6627])).
% 2.24/2.45 tff(6629,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6628, 6626])).
% 2.24/2.45 tff(6630,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6631,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6630, 6629])).
% 2.24/2.45 tff(6632,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6631, 204, 444, 6292, 3983, 4780, 6625])).
% 2.24/2.45 tff(6633,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6634,plain,
% 2.24/2.45 (~r(z, s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6633, 389, 444, 3])).
% 2.24/2.45 tff(6635,plain,
% 2.24/2.45 (b(z, s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[357, 6634])).
% 2.24/2.45 tff(6636,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6637,plain,
% 2.24/2.45 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6638,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6637])).
% 2.24/2.45 tff(6639,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6638, 6636])).
% 2.24/2.45 tff(6640,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6641,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6640, 6639])).
% 2.24/2.45 tff(6642,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6641, 204, 362, 444, 404, 4780, 359])).
% 2.24/2.45 tff(6643,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6644,plain,
% 2.24/2.45 (~b(z, s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6643, 404, 444, 548])).
% 2.24/2.45 tff(6645,plain,
% 2.24/2.45 (r(z, s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[306, 6644])).
% 2.24/2.45 tff(6646,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[161, 110, 136])).
% 2.24/2.45 tff(6647,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2659, 110, 389])).
% 2.24/2.45 tff(6648,plain,
% 2.24/2.45 (b(s(s(s(s(s(s(z)))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[641, 6647])).
% 2.24/2.45 tff(6649,plain,
% 2.24/2.45 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3485, 204, 361, 359, 4, 6648])).
% 2.24/2.45 tff(6650,plain,
% 2.24/2.45 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4008, 110, 286])).
% 2.24/2.45 tff(6651,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[604, 50, 601, 6650, 6649])).
% 2.24/2.45 tff(6652,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6653,plain,
% 2.24/2.45 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6652, 110, 548, 361, 286, 389])).
% 2.24/2.45 tff(6654,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[190, 6653, 6646])).
% 2.24/2.45 tff(6655,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6656,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6655, 6645, 6635, 389, 136])).
% 2.24/2.45 tff(6657,plain,
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[134, 6667])).
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% 2.24/2.45 tff(6673,plain,
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% 2.24/2.45 tff(6677,plain,
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[536, 6683, 389])).
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[431, 6684])).
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% 2.24/2.45 tff(6688,plain,
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[244, 6690])).
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% 2.24/2.45 tff(6696,plain,
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[108, 6698])).
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[6631, 204, 444, 6292, 4780, 6699])).
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[431, 6700])).
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[6380, 2, 1])).
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[6528, 6702])).
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% 2.24/2.45 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3979, 308, 389])).
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% 2.24/2.45 inference(unit_resolution,[status(thm)],[822, 6704])).
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% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6707,plain,
% 2.24/2.45 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6708,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6707])).
% 2.24/2.45 tff(6709,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6708, 6706])).
% 2.24/2.45 tff(6710,plain,
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% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6711,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6710, 6709])).
% 2.24/2.45 tff(6712,plain,
% 2.24/2.45 ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6711, 204, 6705, 1469, 6703])).
% 2.24/2.45 tff(6713,plain,
% 2.24/2.45 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6712, 722])).
% 2.24/2.45 tff(6714,plain,
% 2.24/2.45 (((~![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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6715,plain,
% 2.24/2.45 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6716,plain,
% 2.24/2.45 (((~![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(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6715])).
% 2.24/2.45 tff(6717,plain,
% 2.24/2.45 (((~![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(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6716, 6714])).
% 2.24/2.45 tff(6718,plain,
% 2.24/2.45 ((~![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(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6719,plain,
% 2.24/2.45 ((~![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(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6718, 6717])).
% 2.24/2.45 tff(6720,plain,
% 2.24/2.45 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6719, 67, 656, 1])).
% 2.24/2.46 tff(6721,plain,
% 2.24/2.46 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[850, 50, 6720])).
% 2.24/2.46 tff(6722,plain,
% 2.24/2.46 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6721, 6713])).
% 2.24/2.46 tff(6723,plain,
% 2.24/2.46 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6722])).
% 2.24/2.46 tff(6724,plain,
% 2.24/2.46 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.46 inference(symmetry,[status(thm)],[6723])).
% 2.24/2.46 tff(6725,plain,
% 2.24/2.46 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6722])).
% 2.24/2.46 tff(6726,plain,
% 2.24/2.46 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[664, 6725, 121])).
% 2.24/2.46 tff(6727,plain,
% 2.24/2.46 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6726])).
% 2.24/2.46 tff(6728,plain,
% 2.24/2.46 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[875, 6727, 119])).
% 2.24/2.46 tff(6729,plain,
% 2.24/2.46 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6728])).
% 2.24/2.46 tff(6730,plain,
% 2.24/2.46 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.24/2.46 inference(transitivity,[status(thm)],[699, 6729, 20])).
% 2.24/2.46 tff(6731,plain,
% 2.24/2.46 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6730])).
% 2.24/2.46 tff(6732,plain,
% 2.24/2.46 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.46 inference(symmetry,[status(thm)],[6731])).
% 2.24/2.46 tff(6733,plain,
% 2.24/2.46 (s(s(z)) = s(s(elem!1))),
% 2.24/2.46 inference(transitivity,[status(thm)],[84, 6732, 753])).
% 2.24/2.46 tff(6734,plain,
% 2.24/2.46 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6733])).
% 2.24/2.46 tff(6735,plain,
% 2.24/2.46 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6734, 6724])).
% 2.24/2.46 tff(6736,plain,
% 2.24/2.46 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6735])).
% 2.24/2.46 tff(6737,plain,
% 2.24/2.46 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[182, 6736])).
% 2.24/2.46 tff(6738,plain,
% 2.24/2.46 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6733])).
% 2.24/2.46 tff(6739,plain,
% 2.24/2.46 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6738, 1123])).
% 2.24/2.46 tff(6740,plain,
% 2.24/2.46 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6739])).
% 2.24/2.46 tff(6741,plain,
% 2.24/2.46 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[2122, 6740])).
% 2.24/2.46 tff(6742,plain,
% 2.24/2.46 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6733])).
% 2.24/2.46 tff(6743,plain,
% 2.24/2.46 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6742, 2223])).
% 2.24/2.46 tff(6744,plain,
% 2.24/2.46 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6743, 2224])).
% 2.24/2.46 tff(6745,plain,
% 2.24/2.46 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6744])).
% 2.24/2.46 tff(6746,plain,
% 2.24/2.46 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[2125, 6745])).
% 2.24/2.46 tff(6747,plain,
% 2.24/2.46 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5079, 6746, 136, 389, 3, 308, 361, 6741])).
% 2.24/2.46 tff(6748,plain,
% 2.24/2.46 (~b(s(s(elem!1)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4892, 6747, 2, 656, 6737])).
% 2.24/2.46 tff(6749,plain,
% 2.24/2.46 (~r(s(s(elem!1)), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2967, 6747, 136])).
% 2.24/2.46 tff(6750,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[952, 6749, 6748])).
% 2.24/2.46 tff(6751,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6752,plain,
% 2.24/2.46 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6751, 6701, 136, 389, 3, 308, 361, 6697, 1])).
% 2.24/2.46 tff(6753,plain,
% 2.24/2.46 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[766, 6752])).
% 2.24/2.46 tff(6754,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6755,plain,
% 2.24/2.46 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6756,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6755])).
% 2.24/2.46 tff(6757,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6756, 6754])).
% 2.24/2.46 tff(6758,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(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(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6759,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6758, 6757])).
% 2.24/2.46 tff(6760,plain,
% 2.24/2.46 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6759, 204, 6705, 6699, 548])).
% 2.24/2.46 tff(6761,plain,
% 2.24/2.46 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6760, 6753])).
% 2.24/2.46 tff(6762,plain,
% 2.24/2.46 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[710, 50, 707, 6761])).
% 2.24/2.46 tff(6763,plain,
% 2.24/2.46 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4037, 204, 361, 6705, 548])).
% 2.24/2.46 tff(6764,plain,
% 2.24/2.46 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6763, 6753])).
% 2.24/2.46 tff(6765,plain,
% 2.24/2.46 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3157, 6764])).
% 2.24/2.46 tff(6766,plain,
% 2.24/2.46 (((~![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))), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6767,plain,
% 2.24/2.46 (((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6768,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6767])).
% 2.24/2.46 tff(6769,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6768, 6766])).
% 2.24/2.46 tff(6770,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6771,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6770, 6769])).
% 2.24/2.46 tff(6772,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6771, 67, 308, 6765, 6762])).
% 2.24/2.46 tff(6773,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6774,plain,
% 2.24/2.46 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6773, 6678, 6635, 136, 389, 3, 444])).
% 2.24/2.46 tff(6775,plain,
% 2.24/2.46 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[190, 6774])).
% 2.24/2.46 tff(6776,plain,
% 2.24/2.46 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3485, 204, 6635, 548, 6623])).
% 2.24/2.46 tff(6777,plain,
% 2.24/2.46 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6776, 6775])).
% 2.24/2.46 tff(6778,plain,
% 2.24/2.46 (r(z, s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[604, 50, 601, 6777])).
% 2.24/2.46 tff(6779,plain,
% 2.24/2.46 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4983, 6778, 3])).
% 2.24/2.46 tff(6780,plain,
% 2.24/2.46 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[284, 6779])).
% 2.24/2.46 tff(6781,plain,
% 2.24/2.46 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4987, 6778, 3])).
% 2.24/2.46 tff(6782,plain,
% 2.24/2.46 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[134, 6781])).
% 2.24/2.46 tff(6783,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1540, 6782, 6780, 444, 6292, 6689])).
% 2.24/2.46 tff(6784,plain,((~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6785,plain,
% 2.24/2.46 (~r(s(z), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6784, 260, 6591, 56])).
% 2.24/2.46 tff(6786,plain,
% 2.24/2.46 (b(s(z), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[376, 6785])).
% 2.24/2.46 tff(6787,plain,
% 2.24/2.46 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4939, 204, 4780, 6595, 6603])).
% 2.24/2.46 tff(6788,plain,
% 2.24/2.46 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6787, 6612])).
% 2.24/2.46 tff(6789,plain,
% 2.24/2.46 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[284, 6788])).
% 2.24/2.46 tff(6790,plain,
% 2.24/2.46 (~r(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[2643, 6789, 6610])).
% 2.24/2.46 tff(6791,plain,
% 2.24/2.46 (b(s(z), s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[478, 6790])).
% 2.24/2.46 tff(6792,plain,
% 2.24/2.46 (~b(s(s(s(z))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1408, 6791, 6591, 6786, 6593])).
% 2.24/2.46 tff(6793,plain,
% 2.24/2.46 (r(s(s(s(z))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[402, 6792])).
% 2.24/2.46 tff(6794,plain,
% 2.24/2.46 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3885, 6793, 538, 6595])).
% 2.24/2.46 tff(6795,plain,
% 2.24/2.46 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[822, 6794])).
% 2.24/2.46 tff(6796,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.24/2.46 tff(6797,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6798,plain,
% 2.24/2.46 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6799,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6798])).
% 2.24/2.46 tff(6800,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6799, 6797])).
% 2.24/2.46 tff(6801,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6802,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6801, 6800])).
% 2.24/2.46 tff(6803,plain,
% 2.24/2.46 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6802, 204, 784, 193, 1469])).
% 2.24/2.46 tff(6804,plain,
% 2.24/2.46 (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6803, 6796])).
% 2.24/2.46 tff(6805,plain,
% 2.24/2.46 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3173, 6804])).
% 2.24/2.46 tff(6806,plain,
% 2.24/2.46 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3902, 204, 784, 1469, 1708])).
% 2.24/2.46 tff(6807,plain,
% 2.24/2.46 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6806, 6796])).
% 2.24/2.46 tff(6808,plain,
% 2.24/2.46 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3157, 6807])).
% 2.24/2.46 tff(6809,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3168, 6808, 6805, 538])).
% 2.24/2.46 tff(6810,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6811,plain,
% 2.24/2.46 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6810, 538, 6795, 6608, 6616, 6612])).
% 2.24/2.46 tff(6812,plain,
% 2.24/2.46 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3556, 204, 6786, 6593, 6608, 6616])).
% 2.24/2.46 tff(6813,plain,
% 2.24/2.46 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6528, 6812])).
% 2.24/2.46 tff(6814,plain,
% 2.24/2.46 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6631, 204, 6591, 6791, 4780, 6595])).
% 2.24/2.46 tff(6815,plain,
% 2.24/2.46 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[431, 6814])).
% 2.24/2.46 tff(6816,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.24/2.46 tff(6817,plain,
% 2.24/2.46 (((~![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(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6818,plain,
% 2.24/2.46 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6819,plain,
% 2.24/2.46 (((~![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(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6818])).
% 2.24/2.46 tff(6820,plain,
% 2.24/2.46 (((~![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(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6819, 6817])).
% 2.24/2.46 tff(6821,plain,
% 2.24/2.46 ((~![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(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6822,plain,
% 2.24/2.46 ((~![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(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6821, 6820])).
% 2.24/2.46 tff(6823,plain,
% 2.24/2.46 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6822, 67, 499, 6816])).
% 2.24/2.46 tff(6824,plain,
% 2.24/2.46 (((~![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(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6825,plain,
% 2.24/2.47 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6826,plain,
% 2.24/2.47 (((~![X0: $i, 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(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(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(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6825])).
% 2.24/2.47 tff(6827,plain,
% 2.24/2.47 (((~![X0: $i, 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(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(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(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6826, 6824])).
% 2.24/2.47 tff(6828,plain,
% 2.24/2.47 ((~![X0: $i, 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(z)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6829,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6828, 6827])).
% 2.24/2.47 tff(6830,plain,
% 2.24/2.47 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6829, 67, 2, 3578, 6816])).
% 2.24/2.47 tff(6831,plain,
% 2.24/2.47 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4365, 6830])).
% 2.24/2.47 tff(6832,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6833,plain,
% 2.24/2.47 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), 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(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6834,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), 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(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6833])).
% 2.24/2.47 tff(6835,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), 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(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6834, 6832])).
% 2.24/2.47 tff(6836,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), 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(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6837,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6836, 6835])).
% 2.24/2.47 tff(6838,plain,
% 2.24/2.47 ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6837, 204, 363, 444, 784])).
% 2.24/2.47 tff(6839,plain,
% 2.24/2.47 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6838, 6831])).
% 2.24/2.47 tff(6840,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[710, 50, 707, 6839, 6823])).
% 2.24/2.47 tff(6841,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6842,plain,
% 2.24/2.47 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6841, 6795, 6591, 6786, 6815, 6813, 6614])).
% 2.24/2.47 tff(6843,plain,
% 2.24/2.47 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[850, 50, 6842])).
% 2.24/2.47 tff(6844,plain,
% 2.24/2.47 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6843, 6811])).
% 2.24/2.47 tff(6845,plain,
% 2.24/2.47 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6844])).
% 2.24/2.47 tff(6846,plain,
% 2.24/2.47 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[664, 6845, 121])).
% 2.24/2.47 tff(6847,plain,
% 2.24/2.47 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6846])).
% 2.24/2.47 tff(6848,plain,
% 2.24/2.47 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[875, 6847, 119])).
% 2.24/2.47 tff(6849,plain,
% 2.24/2.47 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6848])).
% 2.24/2.47 tff(6850,plain,
% 2.24/2.47 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[699, 6849, 20])).
% 2.24/2.47 tff(6851,plain,
% 2.24/2.47 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6850])).
% 2.24/2.47 tff(6852,plain,
% 2.24/2.47 (s(s(elem!1)) = s(s(z))),
% 2.24/2.47 inference(transitivity,[status(thm)],[754, 6851, 83])).
% 2.24/2.47 tff(6853,plain,
% 2.24/2.47 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6852])).
% 2.24/2.47 tff(6854,plain,
% 2.24/2.47 (s(elem!1) = s(z)),
% 2.24/2.47 inference(transitivity,[status(thm)],[919, 6853, 78])).
% 2.24/2.47 tff(6855,plain,
% 2.24/2.47 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6854])).
% 2.24/2.47 tff(6856,plain,
% 2.24/2.47 (elem!1 = z),
% 2.24/2.47 inference(transitivity,[status(thm)],[1009, 6855, 15])).
% 2.24/2.47 tff(6857,plain,
% 2.24/2.47 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6856])).
% 2.24/2.47 tff(6858,plain,
% 2.24/2.47 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6852])).
% 2.24/2.47 tff(6859,plain,
% 2.24/2.47 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(z)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6858, 6857])).
% 2.24/2.47 tff(6860,plain,
% 2.24/2.47 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6852])).
% 2.24/2.47 tff(6861,plain,
% 2.24/2.47 ((elem!1 = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6860])).
% 2.24/2.47 tff(6862,plain,
% 2.24/2.47 ((elem!1 = s(s(z))) <=> (z = s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6856])).
% 2.24/2.47 tff(6863,plain,
% 2.24/2.47 ((elem!1 = s(s(z))) <=> (s(s(z)) = z)),
% 2.24/2.47 inference(transitivity,[status(thm)],[6862, 3690])).
% 2.24/2.47 tff(6864,plain,
% 2.24/2.47 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6863])).
% 2.24/2.47 tff(6865,plain,
% 2.24/2.47 ((s(s(z)) = z) <=> (elem!1 = s(s(elem!1)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6864, 6861])).
% 2.24/2.47 tff(6866,plain,
% 2.24/2.47 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6865])).
% 2.24/2.47 tff(6867,plain,
% 2.24/2.47 (~(elem!1 = s(s(elem!1)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[97, 6866])).
% 2.24/2.47 tff(6868,plain,
% 2.24/2.47 (b(elem!1, s(z)) <=> b(z, s(z))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6856])).
% 2.24/2.47 tff(6869,plain,
% 2.24/2.47 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6868])).
% 2.24/2.47 tff(6870,plain,
% 2.24/2.47 (b(elem!1, s(z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6593, 6869])).
% 2.24/2.47 tff(6871,plain,
% 2.24/2.47 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6844])).
% 2.24/2.47 tff(6872,plain,
% 2.24/2.47 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6871])).
% 2.24/2.47 tff(6873,plain,
% 2.24/2.47 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6603, 6872])).
% 2.24/2.47 tff(6874,plain,
% 2.24/2.47 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.24/2.47 inference(symmetry,[status(thm)],[3301])).
% 2.24/2.47 tff(6875,plain,
% 2.24/2.47 ((s(s(elem!1)) = s(z)) <=> (s(s(z)) = s(z))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3297])).
% 2.24/2.47 tff(6876,plain,
% 2.24/2.47 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(z)) = s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6875])).
% 2.24/2.47 tff(6877,plain,
% 2.24/2.47 (~(s(s(z)) = s(z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[924, 6876])).
% 2.24/2.47 tff(6878,plain,
% 2.24/2.47 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3304])).
% 2.24/2.47 tff(6879,plain,
% 2.24/2.47 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6878])).
% 2.24/2.47 tff(6880,plain,
% 2.24/2.47 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1139, 1135, 3593])).
% 2.24/2.47 tff(6881,plain,
% 2.24/2.47 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6880, 6879])).
% 2.24/2.47 tff(6882,plain,
% 2.24/2.47 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3289, 3297])).
% 2.24/2.47 tff(6883,plain,
% 2.24/2.47 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6882])).
% 2.24/2.47 tff(6884,plain,
% 2.24/2.47 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6883])).
% 2.24/2.47 tff(6885,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 2.24/2.47 tff(6886,plain,
% 2.24/2.47 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[3360, 67, 110, 6885])).
% 2.24/2.47 tff(6887,plain,
% 2.24/2.47 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6886, 6884])).
% 2.24/2.47 tff(6888,plain,
% 2.24/2.47 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3289])).
% 2.24/2.47 tff(6889,plain,
% 2.24/2.47 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6888])).
% 2.24/2.47 tff(6890,plain,
% 2.24/2.47 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3304])).
% 2.24/2.47 tff(6891,plain,
% 2.24/2.47 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6890, 6889])).
% 2.24/2.47 tff(6892,plain,
% 2.24/2.47 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6891])).
% 2.24/2.47 tff(6893,plain,
% 2.24/2.47 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[182, 6892])).
% 2.24/2.47 tff(6894,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3289])).
% 2.24/2.47 tff(6895,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6894])).
% 2.24/2.47 tff(6896,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[2678, 6895])).
% 2.24/2.47 tff(6897,plain,
% 2.24/2.47 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5825, 67, 136, 6885])).
% 2.24/2.47 tff(6898,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[3421, 6897])).
% 2.24/2.47 tff(6899,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(z)))), introduced(assumption)).
% 2.24/2.47 tff(6900,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6901,plain,
% 2.24/2.47 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6902,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6901])).
% 2.24/2.47 tff(6903,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6902, 6900])).
% 2.24/2.47 tff(6904,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6905,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6904, 6903])).
% 2.24/2.47 tff(6906,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6905, 204, 785, 3461, 3460, 3175, 6899])).
% 2.24/2.47 tff(6907,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6908,plain,
% 2.24/2.47 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6907, 6898, 785, 6896, 3460])).
% 2.24/2.47 tff(6909,plain,
% 2.24/2.47 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[2302])).
% 2.24/2.47 tff(6910,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), introduced(assumption)).
% 2.24/2.47 tff(6911,plain,
% 2.24/2.47 (b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6910, 6909])).
% 2.24/2.47 tff(6912,assumption,(~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))), introduced(assumption)).
% 2.24/2.47 tff(6913,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6912, 6911])).
% 2.24/2.47 tff(6914,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6915,plain,
% 2.24/2.47 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6914, 6908, 3647])).
% 2.24/2.47 tff(6916,plain,
% 2.24/2.47 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1062, 6915, 6893])).
% 2.24/2.47 tff(6917,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6916, 6887])).
% 2.24/2.47 tff(6918,plain,((~r(s(s(z)), s(z))) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6919,plain,
% 2.24/2.47 (~r(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6918, 6881, 785, 3289, 110, 136])).
% 2.24/2.47 tff(6920,plain,
% 2.24/2.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6921,plain,
% 2.24/2.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6922,plain,
% 2.24/2.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 2.24/2.47 tff(6923,plain,
% 2.24/2.47 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6922, 50])).
% 2.24/2.47 tff(6924,plain,
% 2.24/2.47 (b(s(s(z)), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6923, 6919, 6877])).
% 2.24/2.47 tff(6925,plain,
% 2.24/2.47 (b(s(s(elem!1)), s(z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6924, 6874])).
% 2.24/2.47 tff(6926,plain,
% 2.24/2.47 (r(z, elem!1) <=> r(z, z)),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3314])).
% 2.24/2.47 tff(6927,plain,
% 2.24/2.47 (r(z, z) <=> r(z, elem!1)),
% 2.24/2.47 inference(symmetry,[status(thm)],[6926])).
% 2.24/2.47 tff(6928,plain,
% 2.24/2.47 ((~r(z, z)) <=> (~r(z, elem!1))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6927])).
% 2.24/2.47 tff(6929,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, 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, z)) | (~r(z, s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6930,plain,
% 2.24/2.47 (((~r(z, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, z))) <=> ((~r(z, z)) | (~r(z, s(s(s(z))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6931,plain,
% 2.24/2.47 (((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, z)) | (~r(z, s(s(s(z)))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6930])).
% 2.24/2.47 tff(6932,plain,
% 2.24/2.47 (((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, z)) | (~r(z, s(s(s(z))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6931, 6929])).
% 2.24/2.47 tff(6933,plain,
% 2.24/2.47 ((~![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(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, z)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6934,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, z)) | (~r(z, s(s(s(z)))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6933, 6932])).
% 2.24/2.47 tff(6935,plain,
% 2.24/2.47 (~r(z, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6934, 67, 3])).
% 2.24/2.47 tff(6936,plain,
% 2.24/2.47 (~r(z, elem!1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6935, 6928])).
% 2.24/2.47 tff(6937,plain,
% 2.24/2.47 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 2.24/2.47 inference(monotonicity,[status(thm)],[3314])).
% 2.24/2.47 tff(6938,plain,
% 2.24/2.47 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(symmetry,[status(thm)],[6937])).
% 2.24/2.47 tff(6939,plain,
% 2.24/2.47 (r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[308, 6938])).
% 2.24/2.47 tff(6940,plain,
% 2.24/2.47 (~r(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5341, 5283, 308])).
% 2.24/2.47 tff(6941,assumption,(~r(z, elem!1)), introduced(assumption)).
% 2.24/2.47 tff(6942,plain,
% 2.24/2.47 (r(elem!1, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5197, 3702, 1287])).
% 2.24/2.47 tff(6943,plain,
% 2.24/2.47 (~r(elem!1, s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4639, 6942, 907])).
% 2.24/2.47 tff(6944,plain,
% 2.24/2.47 (b(elem!1, s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2351, 6943, 5154])).
% 2.24/2.47 tff(6945,plain,
% 2.24/2.47 (~(z = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[3705, 3702, 362])).
% 2.24/2.47 tff(6946,plain,
% 2.24/2.47 (~(elem!1 = z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5164, 6945])).
% 2.24/2.47 tff(6947,plain,
% 2.24/2.47 (b(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5184, 6946, 6168])).
% 2.24/2.47 tff(6948,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6949,plain,
% 2.24/2.48 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6950,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6949])).
% 2.24/2.48 tff(6951,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6950, 6948])).
% 2.24/2.48 tff(6952,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6953,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6952, 6951])).
% 2.24/2.48 tff(6954,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6953, 204, 1026, 990, 4660, 3720, 362])).
% 2.24/2.48 tff(6955,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6956,plain,
% 2.24/2.48 (~b(z, s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6955, 6947, 362, 990, 6944])).
% 2.24/2.48 tff(6957,plain,
% 2.24/2.48 (r(z, s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2160, 6956])).
% 2.24/2.48 tff(6958,plain,
% 2.24/2.48 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5042, 6957, 3])).
% 2.24/2.48 tff(6959,plain,
% 2.24/2.48 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3651, 4995])).
% 2.24/2.48 tff(6960,plain,
% 2.24/2.48 (b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2182, 50, 6959, 6958])).
% 2.24/2.48 tff(6961,plain,
% 2.24/2.48 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3784, 6957, 3])).
% 2.24/2.48 tff(6962,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[1165, 50, 4995, 6961])).
% 2.24/2.48 tff(6963,plain,
% 2.24/2.48 (b(z, elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5297, 6945, 6941])).
% 2.24/2.48 tff(6964,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6965,plain,
% 2.24/2.48 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))) <=> ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6966,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6965])).
% 2.24/2.48 tff(6967,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6966, 6964])).
% 2.24/2.48 tff(6968,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6969,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6968, 6967])).
% 2.24/2.48 tff(6970,plain,
% 2.24/2.48 ((~b(elem!1, z)) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6969, 204])).
% 2.24/2.48 tff(6971,plain,
% 2.24/2.48 (~b(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6970, 6947, 362, 6963, 363])).
% 2.24/2.48 tff(6972,plain,
% 2.24/2.48 (r(s(z), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5366, 50, 6971, 5322])).
% 2.24/2.48 tff(6973,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6974,plain,
% 2.24/2.48 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6975,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6974])).
% 2.24/2.48 tff(6976,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6975, 6973])).
% 2.24/2.48 tff(6977,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6978,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6977, 6976])).
% 2.24/2.48 tff(6979,plain,
% 2.24/2.48 (~r(s(s(s(z))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6978, 67, 6972, 5283])).
% 2.24/2.48 tff(6980,plain,
% 2.24/2.48 (b(s(s(s(z))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[558, 6979])).
% 2.24/2.48 tff(6981,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), 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))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6982,plain,
% 2.24/2.48 (((~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(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), 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))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6983,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), 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)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6982])).
% 2.24/2.48 tff(6984,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), 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))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6983, 6981])).
% 2.24/2.48 tff(6985,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6986,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6985, 6984])).
% 2.24/2.48 tff(6987,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6986, 204, 990, 6980, 566, 6962, 6960])).
% 2.24/2.48 tff(6988,plain,(b(elem!1, s(z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | r(elem!1, z) | (elem!1 = s(s(elem!1))) | r(z, elem!1) | (~r(s(z), s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6989,plain,
% 2.24/2.48 (b(elem!1, s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6988, 5283, 566, 990, 3, 362, 363, 6940, 5154, 6941, 907, 1287])).
% 2.24/2.48 tff(6990,plain,
% 2.24/2.48 (b(elem!1, z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5184, 2209, 6168])).
% 2.24/2.48 tff(6991,plain,
% 2.24/2.48 (b(z, elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5297, 5234, 6941])).
% 2.24/2.48 tff(6992,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6123, 6991, 6990, 363, 5202, 362])).
% 2.24/2.48 tff(6993,plain,((elem!1 = z) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | r(z, elem!1) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6994,plain,
% 2.24/2.48 (elem!1 = z),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6993, 6989, 363, 362, 6941, 6940])).
% 2.24/2.48 tff(6995,plain,
% 2.24/2.48 (s(elem!1) = s(z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6994])).
% 2.24/2.48 tff(6996,plain,
% 2.24/2.48 (s(s(elem!1)) = s(s(z))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6995])).
% 2.24/2.48 tff(6997,plain,
% 2.24/2.48 (s(s(z)) = s(s(elem!1))),
% 2.24/2.48 inference(symmetry,[status(thm)],[6996])).
% 2.24/2.48 tff(6998,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6997])).
% 2.24/2.48 tff(6999,plain,
% 2.24/2.48 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.48 inference(symmetry,[status(thm)],[6998])).
% 2.24/2.48 tff(7000,plain,
% 2.24/2.48 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6996])).
% 2.24/2.48 tff(7001,plain,
% 2.24/2.48 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7000])).
% 2.24/2.48 tff(7002,plain,
% 2.24/2.48 (b(elem!1, s(s(elem!1)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6193, 3720, 6940, 363, 5202, 362, 5440, 907, 5154])).
% 2.24/2.48 tff(7003,plain,
% 2.24/2.48 (~b(elem!1, z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6955, 7002, 362, 990, 3720])).
% 2.24/2.48 tff(7004,plain,
% 2.24/2.48 (elem!1 = z),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5184, 7003, 6940])).
% 2.24/2.48 tff(7005,plain,
% 2.24/2.48 (s(elem!1) = s(z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7004])).
% 2.24/2.48 tff(7006,plain,
% 2.24/2.48 (s(s(elem!1)) = s(s(z))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7005])).
% 2.24/2.48 tff(7007,plain,
% 2.24/2.48 (s(s(z)) = s(s(elem!1))),
% 2.24/2.48 inference(symmetry,[status(thm)],[7006])).
% 2.24/2.48 tff(7008,plain,
% 2.24/2.48 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7007])).
% 2.24/2.48 tff(7009,plain,
% 2.24/2.48 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(symmetry,[status(thm)],[7008])).
% 2.24/2.48 tff(7010,plain,
% 2.24/2.48 (~b(elem!1, z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6955, 4660, 362, 990, 3720])).
% 2.24/2.48 tff(7011,plain,
% 2.24/2.48 (elem!1 = z),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5184, 7010, 6168])).
% 2.24/2.48 tff(7012,plain,
% 2.24/2.48 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7011])).
% 2.24/2.48 tff(7013,plain,
% 2.24/2.48 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.24/2.48 inference(symmetry,[status(thm)],[7012])).
% 2.24/2.48 tff(7014,plain,
% 2.24/2.48 (b(s(z), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[363, 7013])).
% 2.24/2.48 tff(7015,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(7016,plain,
% 2.24/2.48 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(7017,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7016])).
% 2.24/2.48 tff(7018,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[7017, 7015])).
% 2.24/2.48 tff(7019,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(7020,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[7019, 7018])).
% 2.24/2.48 tff(7021,plain,
% 2.24/2.48 ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7020, 204, 990, 3720, 5202])).
% 2.24/2.48 tff(7022,plain,
% 2.24/2.48 (~b(z, elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7021, 4660])).
% 2.24/2.48 tff(7023,plain,
% 2.24/2.48 (z = elem!1),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5297, 7022, 6941])).
% 2.24/2.48 tff(7024,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(z))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2319, 7011, 1162, 2179])).
% 2.24/2.48 tff(7025,plain,
% 2.24/2.48 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[2298, 7024, 7023])).
% 2.24/2.48 tff(7026,plain,
% 2.24/2.48 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[2290])).
% 2.24/2.48 tff(7027,plain,
% 2.24/2.48 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(symmetry,[status(thm)],[7026])).
% 2.24/2.48 tff(7028,plain,
% 2.24/2.48 (r(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[5283, 7027])).
% 2.24/2.48 tff(7029,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(7030,plain,
% 2.24/2.48 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(7031,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[7030])).
% 2.24/2.48 tff(7032,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[7031, 7029])).
% 2.24/2.48 tff(7033,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(7034,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[7033, 7032])).
% 2.24/2.48 tff(7035,plain,
% 2.24/2.48 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7034, 67, 5245, 2277])).
% 2.24/2.48 tff(7036,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7035, 7028])).
% 2.24/2.48 tff(7037,plain,((~r(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(7038,plain,
% 2.24/2.48 (~r(s(s(elem!1)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[7037, 7025, 5283, 7023])).
% 2.24/2.48 tff(7039,plain,
% 2.24/2.48 (b(s(s(elem!1)), elem!1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5267, 7038, 5210])).
% 2.24/2.48 tff(7040,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(7041,plain,
% 2.24/2.48 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(7042,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7041])).
% 2.24/2.49 tff(7043,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[7042, 7040])).
% 2.24/2.49 tff(7044,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(7045,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7044, 7043])).
% 2.24/2.49 tff(7046,plain,
% 2.24/2.49 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7045, 204])).
% 2.24/2.49 tff(7047,plain,
% 2.24/2.49 (~b(s(z), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7046, 7039, 990, 5202, 4660])).
% 2.24/2.49 tff(7048,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7047, 7014])).
% 2.24/2.49 tff(7049,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(z))), elem!1)) | b(s(s(elem!1)), s(s(s(z)))) | (s(s(s(z))) = s(s(elem!1))) | r(z, elem!1) | r(elem!1, z) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7050,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7049, 7002, 990, 5202, 5261, 5283, 363, 2179, 6941, 6940, 3720, 362])).
% 2.24/2.49 tff(7051,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7050, 7009])).
% 2.24/2.49 tff(7052,plain,
% 2.24/2.49 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7007])).
% 2.24/2.49 tff(7053,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 2.24/2.49 inference(symmetry,[status(thm)],[7052])).
% 2.24/2.49 tff(7054,plain,
% 2.24/2.49 (b(s(s(z)), s(z))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[990, 7053])).
% 2.24/2.49 tff(7055,plain,
% 2.24/2.49 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7007])).
% 2.24/2.49 tff(7056,plain,
% 2.24/2.49 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.24/2.49 inference(symmetry,[status(thm)],[7055])).
% 2.24/2.49 tff(7057,plain,
% 2.24/2.49 (b(z, s(s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[3720, 7056])).
% 2.24/2.49 tff(7058,plain,
% 2.24/2.49 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7006])).
% 2.24/2.49 tff(7059,plain,
% 2.24/2.49 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7058])).
% 2.24/2.49 tff(7060,plain,
% 2.24/2.49 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7059, 7006])).
% 2.24/2.49 tff(7061,plain,
% 2.24/2.49 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5156, 5154])).
% 2.24/2.49 tff(7062,plain,
% 2.24/2.49 (r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3670, 7004, 907])).
% 2.24/2.49 tff(7063,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5764, 7062, 2])).
% 2.24/2.49 tff(7064,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[3442, 2303])).
% 2.24/2.49 tff(7065,plain,
% 2.24/2.49 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(symmetry,[status(thm)],[7064])).
% 2.24/2.49 tff(7066,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[4683, 7065])).
% 2.24/2.49 tff(7067,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.24/2.49 tff(7068,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7067, 7066])).
% 2.24/2.49 tff(7069,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(z))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7070,plain,
% 2.24/2.49 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7069, 7063, 7004])).
% 2.24/2.49 tff(7071,plain,
% 2.24/2.49 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4696, 7070, 7061])).
% 2.24/2.49 tff(7072,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7071, 7060])).
% 2.24/2.49 tff(7073,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7074,plain,
% 2.24/2.49 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7075,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7074])).
% 2.24/2.49 tff(7076,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[7075, 7073])).
% 2.24/2.49 tff(7077,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(7078,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7077, 7076])).
% 2.24/2.49 tff(7079,plain,
% 2.24/2.49 ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7078, 204, 362, 7072])).
% 2.24/2.49 tff(7080,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7079, 7057, 7054])).
% 2.24/2.49 tff(7081,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[335, 7080])).
% 2.24/2.49 tff(7082,plain,
% 2.24/2.49 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1212, 7081, 308])).
% 2.24/2.49 tff(7083,plain,
% 2.24/2.49 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[108, 7082])).
% 2.24/2.49 tff(7084,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7006])).
% 2.24/2.49 tff(7085,plain,
% 2.24/2.49 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7007])).
% 2.24/2.49 tff(7086,plain,
% 2.24/2.49 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7085])).
% 2.24/2.49 tff(7087,plain,
% 2.24/2.49 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7004])).
% 2.24/2.49 tff(7088,plain,
% 2.24/2.49 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7087])).
% 2.24/2.49 tff(7089,plain,
% 2.24/2.49 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7004])).
% 2.24/2.49 tff(7090,plain,
% 2.24/2.49 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.24/2.49 inference(symmetry,[status(thm)],[7089])).
% 2.24/2.49 tff(7091,plain,
% 2.24/2.49 (b(s(z), elem!1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[363, 7090])).
% 2.24/2.49 tff(7092,plain,
% 2.24/2.49 (~b(s(s(elem!1)), elem!1)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7046, 7091, 990, 5202, 7002])).
% 2.24/2.49 tff(7093,plain,
% 2.24/2.49 (~b(s(s(elem!1)), z)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7092, 7088])).
% 2.24/2.49 tff(7094,plain,
% 2.24/2.49 (r(s(s(elem!1)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1099, 7093])).
% 2.24/2.49 tff(7095,plain,
% 2.24/2.49 (r(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2909, 7094, 7004])).
% 2.24/2.49 tff(7096,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3428, 67, 7095, 7081])).
% 2.24/2.49 tff(7097,plain,
% 2.24/2.49 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7096, 7086])).
% 2.24/2.49 tff(7098,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1139, 7097, 1101])).
% 2.24/2.49 tff(7099,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7098, 7084])).
% 2.24/2.49 tff(7100,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6088, 204, 7072, 7099, 194, 7083, 7051])).
% 2.24/2.49 tff(7101,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | r(z, elem!1) | (s(z) = elem!1) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7102,plain,
% 2.24/2.49 (~b(z, s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7101, 6989, 1101, 308, 362, 990, 194, 363, 2, 907, 5283, 6959, 6941, 5322, 5154])).
% 2.24/2.49 tff(7103,plain,
% 2.24/2.49 (r(z, s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2160, 7102])).
% 2.24/2.49 tff(7104,plain,
% 2.24/2.49 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3784, 7103, 3])).
% 2.24/2.49 tff(7105,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7104, 7001])).
% 2.24/2.49 tff(7106,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2319, 7105, 6994, 6959])).
% 2.24/2.49 tff(7107,plain,
% 2.24/2.49 (z = elem!1),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5164, 6994])).
% 2.24/2.49 tff(7108,plain,
% 2.24/2.49 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[6996])).
% 2.24/2.49 tff(7109,plain,
% 2.24/2.49 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[6994, 7108])).
% 2.24/2.49 tff(7110,plain,
% 2.24/2.49 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.24/2.49 inference(symmetry,[status(thm)],[7109])).
% 2.24/2.49 tff(7111,plain,
% 2.24/2.49 (r(elem!1, s(s(s(elem!1))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[3, 7110])).
% 2.24/2.49 tff(7112,plain,
% 2.24/2.49 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[6994])).
% 2.24/2.49 tff(7113,plain,
% 2.24/2.49 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.24/2.49 inference(symmetry,[status(thm)],[7112])).
% 2.24/2.49 tff(7114,plain,
% 2.24/2.49 (r(elem!1, s(s(elem!1)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7103, 7113])).
% 2.24/2.49 tff(7115,plain,
% 2.24/2.49 (b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3774, 7114, 7111, 7107])).
% 2.24/2.49 tff(7116,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[2273])).
% 2.24/2.49 tff(7117,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.49 inference(symmetry,[status(thm)],[7116])).
% 2.24/2.49 tff(7118,plain,
% 2.24/2.49 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5159, 2207])).
% 2.24/2.49 tff(7119,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1139, 7118, 1135])).
% 2.24/2.49 tff(7120,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7119, 7117])).
% 2.24/2.49 tff(7121,plain,
% 2.24/2.49 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[2141, 3747])).
% 2.24/2.49 tff(7122,plain,
% 2.24/2.49 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[2273])).
% 2.24/2.49 tff(7123,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.49 inference(symmetry,[status(thm)],[7122])).
% 2.24/2.49 tff(7124,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[2271])).
% 2.24/2.49 tff(7125,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[194, 7124])).
% 2.24/2.49 tff(7126,plain,
% 2.24/2.49 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7125, 7123])).
% 2.24/2.49 tff(7127,plain,
% 2.24/2.49 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2327, 2207, 2323])).
% 2.24/2.49 tff(7128,plain,
% 2.24/2.49 (r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3670, 4572, 907])).
% 2.24/2.49 tff(7129,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5764, 7128, 2])).
% 2.24/2.49 tff(7130,plain,
% 2.24/2.49 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7069, 7129, 4572])).
% 2.24/2.49 tff(7131,plain,
% 2.24/2.49 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4696, 7130, 877])).
% 2.24/2.49 tff(7132,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7133,plain,
% 2.24/2.49 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(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(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7134,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7133])).
% 2.24/2.49 tff(7135,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[7134, 7132])).
% 2.24/2.49 tff(7136,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(7137,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7136, 7135])).
% 2.24/2.49 tff(7138,plain,
% 2.24/2.49 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7137, 204, 7131, 7127, 7126])).
% 2.24/2.49 tff(7139,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7138, 7121, 7120])).
% 2.24/2.49 tff(7140,plain,((~(z = elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(z), s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7141,plain,
% 2.24/2.49 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7140, 7115, 194, 7061, 2, 7107, 907, 7106])).
% 2.24/2.49 tff(7142,plain,
% 2.24/2.49 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7141, 6999])).
% 2.24/2.49 tff(7143,plain,
% 2.24/2.49 (r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3670, 6994, 907])).
% 2.24/2.49 tff(7144,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7145,plain,
% 2.24/2.49 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7146,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7145])).
% 2.24/2.49 tff(7147,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[7146, 7144])).
% 2.24/2.49 tff(7148,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(7149,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7148, 7147])).
% 2.24/2.49 tff(7150,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7149, 67, 2, 7143])).
% 2.24/2.49 tff(7151,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7150, 7142])).
% 2.24/2.49 tff(7152,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | r(z, elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7153,plain,
% 2.24/2.49 (~r(s(z), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7152, 6925, 4780, 3, 363, 2, 362, 6939, 3593, 308, 3696, 6936, 566, 3584])).
% 2.24/2.49 tff(7154,plain,
% 2.24/2.49 (b(s(z), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[936, 7153])).
% 2.24/2.49 tff(7155,plain,
% 2.24/2.49 (~b(s(s(elem!1)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2946, 7154, 363, 6925, 362])).
% 2.24/2.49 tff(7156,plain,
% 2.24/2.49 (r(s(s(elem!1)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[1099, 7155])).
% 2.24/2.49 tff(7157,plain,
% 2.24/2.49 (r(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[2909, 7156, 3647])).
% 2.24/2.49 tff(7158,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[4135, 7157, 3])).
% 2.24/2.49 tff(7159,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3835, 7156, 538])).
% 2.24/2.49 tff(7160,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7161,plain,
% 2.24/2.49 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7162,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))))),
% 2.24/2.50 inference(monotonicity,[status(thm)],[7161])).
% 2.24/2.50 tff(7163,plain,
% 2.24/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 2.24/2.50 inference(transitivity,[status(thm)],[7162, 7160])).
% 2.24/2.50 tff(7164,plain,
% 2.24/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.24/2.50 inference(quant_inst,[status(thm)],[])).
% 2.24/2.50 tff(7165,plain,
% 2.24/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[7164, 7163])).
% 2.24/2.50 tff(7166,plain,
% 2.24/2.50 ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[7165, 204])).
% 2.24/2.50 tff(7167,plain,
% 2.24/2.50 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[7166, 7154, 3709, 6925, 3321])).
% 2.24/2.50 tff(7168,plain,
% 2.24/2.50 (r(elem!1, s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2351, 7167, 3696])).
% 2.24/2.50 tff(7169,plain,
% 2.24/2.50 (b(s(s(s(z))), s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[3774, 7168, 3646, 3745])).
% 2.24/2.50 tff(7170,plain,
% 2.24/2.50 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[3794, 7169, 4780, 3593, 1135, 7159])).
% 2.24/2.50 tff(7171,plain,
% 2.24/2.50 ($false),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2319, 7170, 7158, 3647, 3308])).
% 2.24/2.50 tff(7172,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(7173,plain,
% 2.24/2.50 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[7172, 538, 260, 6786, 6593, 6815, 6793, 6791, 6844, 6873, 6610, 56])).
% 2.24/2.50 tff(7174,plain,
% 2.24/2.50 (~r(s(s(elem!1)), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[2967, 7173, 56])).
% 2.24/2.50 tff(7175,plain,
% 2.24/2.50 (b(s(s(elem!1)), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[952, 7174])).
% 2.24/2.50 tff(7176,plain,
% 2.24/2.50 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.24/2.50 inference(monotonicity,[status(thm)],[6856])).
% 2.24/2.50 tff(7177,plain,
% 2.24/2.50 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.24/2.50 inference(symmetry,[status(thm)],[7176])).
% 2.24/2.50 tff(7178,plain,
% 2.24/2.50 (b(s(z), elem!1)),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[6786, 7177])).
% 2.24/2.50 tff(7179,plain,
% 2.24/2.50 (~r(s(z), s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[1121, 7173, 6815])).
% 2.24/2.50 tff(7180,plain,
% 2.24/2.50 (b(s(z), s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[936, 7179])).
% 2.24/2.50 tff(7181,plain,
% 2.24/2.50 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[7166, 7180, 7178, 7175, 6870])).
% 2.24/2.50 tff(7182,plain,
% 2.24/2.50 (r(elem!1, s(s(elem!1)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2351, 7181, 6867])).
% 2.34/2.50 tff(7183,plain,
% 2.34/2.50 (r(z, s(s(z)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7182, 6859])).
% 2.34/2.50 tff(7184,plain,
% 2.34/2.50 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[6852])).
% 2.34/2.50 tff(7185,plain,
% 2.34/2.50 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7173, 7184])).
% 2.34/2.50 tff(7186,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7187,plain,
% 2.34/2.50 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7188,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7187])).
% 2.34/2.50 tff(7189,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7188, 7186])).
% 2.34/2.50 tff(7190,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7191,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7190, 7189])).
% 2.34/2.50 tff(7192,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7191, 67, 339, 7185, 7183])).
% 2.34/2.50 tff(7193,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | b(z, s(s(s(z)))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7194,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7193, 339, 250, 5])).
% 2.34/2.50 tff(7195,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[335, 7194])).
% 2.34/2.50 tff(7196,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7197,plain,
% 2.34/2.50 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7198,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7197])).
% 2.34/2.50 tff(7199,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7198, 7196])).
% 2.34/2.50 tff(7200,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7201,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7200, 7199])).
% 2.34/2.50 tff(7202,plain,
% 2.34/2.50 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7201, 204, 6786, 6591, 6595, 7195])).
% 2.34/2.50 tff(7203,plain,
% 2.34/2.50 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[431, 7202])).
% 2.34/2.50 tff(7204,plain,
% 2.34/2.50 (~b(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6643, 7195, 6591, 6593])).
% 2.34/2.50 tff(7205,plain,
% 2.34/2.50 (r(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[402, 7204])).
% 2.34/2.50 tff(7206,plain,
% 2.34/2.50 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4788, 261, 339])).
% 2.34/2.50 tff(7207,plain,
% 2.34/2.50 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[190, 7206])).
% 2.34/2.50 tff(7208,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2619, 204, 4780, 6625, 7207, 324, 285])).
% 2.34/2.50 tff(7209,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7210,plain,
% 2.34/2.50 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7209, 7205, 339, 260])).
% 2.34/2.50 tff(7211,plain,
% 2.34/2.50 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[641, 7210])).
% 2.34/2.50 tff(7212,plain,
% 2.34/2.50 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6380, 1, 2])).
% 2.34/2.50 tff(7213,plain,
% 2.34/2.50 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6528, 7212])).
% 2.34/2.50 tff(7214,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6366, 7213, 6691, 363, 362, 1469])).
% 2.34/2.50 tff(7215,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7216,plain,
% 2.34/2.50 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7215, 6593, 6786, 7211, 7203, 56])).
% 2.34/2.50 tff(7217,plain,
% 2.34/2.50 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[190, 7216])).
% 2.34/2.50 tff(7218,plain,
% 2.34/2.50 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6310, 204, 6595, 7195, 7211])).
% 2.34/2.50 tff(7219,plain,
% 2.34/2.50 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7218, 7217])).
% 2.34/2.50 tff(7220,plain,
% 2.34/2.50 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[134, 7219])).
% 2.34/2.50 tff(7221,plain,
% 2.34/2.50 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4987, 7220, 260])).
% 2.34/2.50 tff(7222,assumption,(~b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.50 tff(7223,assumption,(~r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.50 tff(7224,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[604, 50, 601, 7223, 7222])).
% 2.34/2.50 tff(7225,plain,(b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7226,plain,
% 2.34/2.50 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7225, 7221])).
% 2.34/2.50 tff(7227,plain,
% 2.34/2.50 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1993, 7226, 6786, 7211, 6593])).
% 2.34/2.50 tff(7228,plain,
% 2.34/2.50 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[244, 7227])).
% 2.34/2.50 tff(7229,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[225, 67, 56, 7228])).
% 2.34/2.50 tff(7230,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[218, 7229])).
% 2.34/2.50 tff(7231,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4301, 204, 7195, 7230, 7217, 7211, 7226])).
% 2.34/2.50 tff(7232,plain,((~r(z, s(s(s(s(z)))))) | b(z, s(s(s(z)))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7233,plain,
% 2.34/2.50 (~r(z, s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7232, 250, 5])).
% 2.34/2.50 tff(7234,plain,
% 2.34/2.50 (b(z, s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[357, 7233])).
% 2.34/2.50 tff(7235,plain,
% 2.34/2.50 (~r(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6784, 3, 444, 136])).
% 2.34/2.50 tff(7236,plain,
% 2.34/2.50 (b(s(z), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[376, 7235])).
% 2.34/2.50 tff(7237,plain,
% 2.34/2.50 (~r(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6695, 566, 444, 261, 443, 3])).
% 2.34/2.50 tff(7238,plain,
% 2.34/2.50 (~b(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1418, 566, 444, 363, 261, 443])).
% 2.34/2.50 tff(7239,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[402, 7238, 7237])).
% 2.34/2.50 tff(7240,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7241,plain,
% 2.34/2.50 (~b(s(z), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7240, 443, 7236, 261, 444, 3])).
% 2.34/2.50 tff(7242,plain,
% 2.34/2.50 (r(s(z), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[478, 7241])).
% 2.34/2.50 tff(7243,plain,
% 2.34/2.50 (~r(z, s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1738, 7242, 3])).
% 2.34/2.50 tff(7244,plain,
% 2.34/2.50 (b(z, s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[306, 7243])).
% 2.34/2.50 tff(7245,plain,
% 2.34/2.50 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4953, 404, 1538, 4, 261])).
% 2.34/2.50 tff(7246,plain,
% 2.34/2.50 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[108, 7245])).
% 2.34/2.50 tff(7247,plain,
% 2.34/2.50 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1685, 404, 444, 363, 361])).
% 2.34/2.50 tff(7248,plain,
% 2.34/2.50 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[431, 7247])).
% 2.34/2.50 tff(7249,plain,
% 2.34/2.50 (((~![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(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)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7250,plain,
% 2.34/2.50 (((~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)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7251,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7250])).
% 2.34/2.50 tff(7252,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7251, 7249])).
% 2.34/2.50 tff(7253,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7254,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7253, 7252])).
% 2.34/2.50 tff(7255,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7254, 67, 445, 7248, 7246])).
% 2.34/2.50 tff(7256,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7257,plain,
% 2.34/2.50 (~b(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7256, 4, 1538, 445, 261, 444, 363, 361])).
% 2.34/2.50 tff(7258,plain,
% 2.34/2.50 (r(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[402, 7257])).
% 2.34/2.50 tff(7259,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[322, 67, 7258, 261])).
% 2.34/2.50 tff(7260,plain,
% 2.34/2.50 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[134, 7259])).
% 2.34/2.50 tff(7261,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1212, 378, 308])).
% 2.34/2.50 tff(7262,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[335, 7261])).
% 2.34/2.50 tff(7263,plain,
% 2.34/2.50 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2673, 204, 363, 362, 361, 7262])).
% 2.34/2.50 tff(7264,plain,
% 2.34/2.50 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[431, 7263])).
% 2.34/2.50 tff(7265,plain,
% 2.34/2.50 (((~![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(z))), 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(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7266,plain,
% 2.34/2.50 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7267,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7266])).
% 2.34/2.50 tff(7268,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7267, 7265])).
% 2.34/2.50 tff(7269,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7270,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7269, 7268])).
% 2.34/2.50 tff(7271,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7270, 67, 308, 445, 7264, 378])).
% 2.34/2.50 tff(7272,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7273,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7272, 7258, 445, 363, 362, 361])).
% 2.34/2.50 tff(7274,plain,
% 2.34/2.50 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[108, 7273])).
% 2.34/2.50 tff(7275,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2619, 204, 4780, 7274, 4, 7260, 1538])).
% 2.34/2.50 tff(7276,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7277,plain,
% 2.34/2.50 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7276, 7242, 285, 7236, 7244, 361, 261, 444])).
% 2.34/2.50 tff(7278,plain,
% 2.34/2.50 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[190, 7277])).
% 2.34/2.50 tff(7279,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4784, 7278, 261])).
% 2.34/2.50 tff(7280,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[335, 7279])).
% 2.34/2.50 tff(7281,plain,
% 2.34/2.50 (~b(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6643, 7280, 444, 7244])).
% 2.34/2.50 tff(7282,plain,
% 2.34/2.50 (r(s(s(s(z))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[402, 7281])).
% 2.34/2.50 tff(7283,plain,
% 2.34/2.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7272, 7282, 7242, 7236, 7244, 361])).
% 2.34/2.50 tff(7284,plain,
% 2.34/2.50 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[108, 7283])).
% 2.34/2.50 tff(7285,plain,
% 2.34/2.50 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[1703, 7284, 444, 285, 443])).
% 2.34/2.50 tff(7286,plain,
% 2.34/2.50 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[431, 7285])).
% 2.34/2.50 tff(7287,plain,
% 2.34/2.50 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[4896, 7286, 136, 7242, 7236, 7278, 7244, 443, 7280, 7282])).
% 2.34/2.50 tff(7288,plain,
% 2.34/2.50 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[766, 7287])).
% 2.34/2.50 tff(7289,plain,
% 2.34/2.50 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2748, 7288, 136, 7236, 7280, 361])).
% 2.34/2.50 tff(7290,plain,
% 2.34/2.50 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[822, 7289])).
% 2.34/2.50 tff(7291,plain,
% 2.34/2.50 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2880, 67, 7282, 7290])).
% 2.34/2.50 tff(7292,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2434, 50, 706, 7291])).
% 2.34/2.51 tff(7293,plain,
% 2.34/2.51 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1))))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4918, 204, 7288, 7284, 285])).
% 2.34/2.51 tff(7294,plain,
% 2.34/2.51 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7293, 7292])).
% 2.34/2.51 tff(7295,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[889, 67, 7290, 261])).
% 2.34/2.51 tff(7296,plain,
% 2.34/2.51 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2402, 50, 7295])).
% 2.34/2.51 tff(7297,plain,
% 2.34/2.51 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7296, 7294])).
% 2.34/2.51 tff(7298,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7297])).
% 2.34/2.51 tff(7299,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(symmetry,[status(thm)],[7298])).
% 2.34/2.51 tff(7300,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7288, 7299])).
% 2.34/2.51 tff(7301,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7277, 7300])).
% 2.34/2.51 tff(7302,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7303,plain,
% 2.34/2.51 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7302, 261, 136, 361, 444, 3])).
% 2.34/2.51 tff(7304,plain,
% 2.34/2.51 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[244, 7303])).
% 2.34/2.51 tff(7305,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[161, 7304, 136])).
% 2.34/2.51 tff(7306,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[190, 7305])).
% 2.34/2.51 tff(7307,plain,
% 2.34/2.51 (~r(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2663, 7304, 261])).
% 2.34/2.51 tff(7308,plain,
% 2.34/2.51 (b(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[306, 7307])).
% 2.34/2.51 tff(7309,plain,
% 2.34/2.51 (~r(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7276, 7306, 285, 7236, 7308, 361, 261, 444])).
% 2.34/2.51 tff(7310,plain,
% 2.34/2.51 (b(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[478, 7309])).
% 2.34/2.51 tff(7311,plain,
% 2.34/2.51 (~b(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1408, 7310, 444, 7236, 7308])).
% 2.34/2.51 tff(7312,plain,
% 2.34/2.51 (r(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[402, 7311])).
% 2.34/2.51 tff(7313,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7314,plain,
% 2.34/2.51 (((~b(s(s(s(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(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7315,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7314])).
% 2.34/2.51 tff(7316,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[7315, 7313])).
% 2.34/2.51 tff(7317,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(7318,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7317, 7316])).
% 2.34/2.51 tff(7319,plain,
% 2.34/2.51 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7318, 204, 7308, 7310, 361, 4780])).
% 2.34/2.51 tff(7320,plain,
% 2.34/2.51 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[431, 7319])).
% 2.34/2.51 tff(7321,plain,
% 2.34/2.51 (~b(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2970, 7320, 136, 361, 285, 7304, 444, 7310, 3, 7312])).
% 2.34/2.51 tff(7322,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[335, 7321])).
% 2.34/2.51 tff(7323,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6606, 7322, 7306, 261, 3])).
% 2.34/2.51 tff(7324,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1212, 7322, 7312])).
% 2.34/2.51 tff(7325,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[108, 7324, 7323])).
% 2.34/2.51 tff(7326,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7327,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7326, 260, 56, 7234, 6591])).
% 2.34/2.51 tff(7328,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[641, 7327])).
% 2.34/2.51 tff(7329,plain,
% 2.34/2.51 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3063, 204, 6786, 7234, 4, 7328])).
% 2.34/2.51 tff(7330,plain,
% 2.34/2.51 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6528, 7329])).
% 2.34/2.51 tff(7331,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7326, 3, 136, 361, 444])).
% 2.34/2.51 tff(7332,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[641, 7331])).
% 2.34/2.51 tff(7333,plain,
% 2.34/2.51 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1462, 204, 7236, 444, 7332])).
% 2.34/2.51 tff(7334,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7333, 6691])).
% 2.34/2.51 tff(7335,plain,
% 2.34/2.51 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[134, 7334])).
% 2.34/2.51 tff(7336,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[507, 7335, 1])).
% 2.34/2.51 tff(7337,plain,
% 2.34/2.51 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[108, 7336])).
% 2.34/2.51 tff(7338,plain,
% 2.34/2.51 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1685, 404, 444, 7236, 361])).
% 2.34/2.51 tff(7339,plain,
% 2.34/2.51 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[431, 7338])).
% 2.34/2.51 tff(7340,plain,
% 2.34/2.51 (~b(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7215, 1, 7236, 7332, 7339, 136])).
% 2.34/2.51 tff(7341,plain,
% 2.34/2.51 (r(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[306, 7340])).
% 2.34/2.51 tff(7342,plain,
% 2.34/2.51 (~r(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1738, 7341, 3])).
% 2.34/2.51 tff(7343,plain,
% 2.34/2.51 (b(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[478, 7342])).
% 2.34/2.51 tff(7344,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1624, 204, 7236, 404, 7343, 361, 7337])).
% 2.34/2.51 tff(7345,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7346,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7345, 404, 361, 3, 444, 136])).
% 2.34/2.51 tff(7347,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[190, 7346])).
% 2.34/2.51 tff(7348,plain,
% 2.34/2.51 (~b(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6664, 7347, 3, 361, 7332, 404])).
% 2.34/2.51 tff(7349,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[335, 7348])).
% 2.34/2.51 tff(7350,plain,
% 2.34/2.51 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3063, 204, 7236, 361, 7347, 7332])).
% 2.34/2.51 tff(7351,plain,
% 2.34/2.51 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6528, 7350])).
% 2.34/2.51 tff(7352,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3071, 204, 404, 361, 7347, 7332])).
% 2.34/2.51 tff(7353,plain,
% 2.34/2.51 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[134, 7352])).
% 2.34/2.51 tff(7354,plain,
% 2.34/2.51 (~r(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3081, 67, 7353, 7351])).
% 2.34/2.51 tff(7355,plain,
% 2.34/2.51 (b(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[478, 7354])).
% 2.34/2.51 tff(7356,plain,
% 2.34/2.51 (~b(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1408, 7355, 444, 7236, 404])).
% 2.34/2.51 tff(7357,plain,
% 2.34/2.51 (r(z, s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[306, 7356])).
% 2.34/2.51 tff(7358,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1493, 67, 7357, 7349, 136])).
% 2.34/2.51 tff(7359,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7360,plain,
% 2.34/2.51 (~b(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7359, 7234, 6591, 56, 260])).
% 2.34/2.51 tff(7361,plain,
% 2.34/2.51 (r(s(s(s(z))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[402, 7360])).
% 2.34/2.51 tff(7362,plain,
% 2.34/2.51 (~r(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1738, 286, 3])).
% 2.34/2.51 tff(7363,plain,
% 2.34/2.51 (b(s(z), s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[478, 7362])).
% 2.34/2.51 tff(7364,plain,
% 2.34/2.51 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1462, 204, 7236, 444, 1469])).
% 2.34/2.51 tff(7365,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7364, 6691])).
% 2.34/2.51 tff(7366,plain,
% 2.34/2.51 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[134, 7365])).
% 2.34/2.51 tff(7367,plain,
% 2.34/2.51 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4987, 7366, 3])).
% 2.34/2.51 tff(7368,plain,
% 2.34/2.51 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7225, 7367])).
% 2.34/2.51 tff(7369,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6672, 6691, 444, 566, 1])).
% 2.34/2.51 tff(7370,plain,
% 2.34/2.51 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[108, 7369])).
% 2.34/2.51 tff(7371,plain,
% 2.34/2.51 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6631, 204, 444, 566, 4780, 7370])).
% 2.34/2.51 tff(7372,plain,
% 2.34/2.51 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[431, 7371])).
% 2.34/2.51 tff(7373,plain,
% 2.34/2.51 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6380, 7372, 1])).
% 2.34/2.51 tff(7374,plain,
% 2.34/2.51 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6528, 7373])).
% 2.34/2.51 tff(7375,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7376,plain,
% 2.34/2.51 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7377,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7376])).
% 2.34/2.51 tff(7378,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[7377, 7375])).
% 2.34/2.51 tff(7379,plain,
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% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(7380,plain,
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% 2.34/2.51 inference(modus_ponens,[status(thm)],[7379, 7378])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7380, 204, 7236, 1469, 7374, 6691, 7368])).
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% 2.34/2.51 tff(7383,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7382, 7363, 444, 7332, 3, 136])).
% 2.34/2.51 tff(7384,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[190, 7383])).
% 2.34/2.51 tff(7385,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[1493, 67, 286, 136])).
% 2.34/2.51 tff(7386,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[335, 7385])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[3485, 204, 361, 7386, 7332])).
% 2.34/2.51 tff(7388,plain,
% 2.34/2.51 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7387, 7384])).
% 2.34/2.51 tff(7389,plain,
% 2.34/2.51 (r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7225, 7388])).
% 2.34/2.51 tff(7390,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4008, 7389, 286])).
% 2.34/2.51 tff(7391,plain,
% 2.34/2.51 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[244, 7390])).
% 2.34/2.51 tff(7392,plain,
% 2.34/2.51 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[4987, 7389, 3])).
% 2.34/2.51 tff(7393,plain,
% 2.34/2.51 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[134, 7392])).
% 2.34/2.51 tff(7394,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7333, 7393, 7391])).
% 2.34/2.51 tff(7395,plain,((~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7396,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7395, 260, 6591, 7234, 56])).
% 2.34/2.51 tff(7397,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[306, 7396])).
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% 2.34/2.51 (~b(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1519, 193, 7234, 7328, 4])).
% 2.34/2.51 tff(7399,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[335, 7398])).
% 2.34/2.51 tff(7400,plain,
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% 2.34/2.51 tff(7401,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7400])).
% 2.34/2.51 tff(7402,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7401])).
% 2.34/2.51 tff(7403,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7402])).
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7403])).
% 2.34/2.51 tff(7405,plain,
% 2.34/2.51 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7404])).
% 2.34/2.51 tff(7406,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7405])).
% 2.34/2.51 tff(7407,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7406])).
% 2.34/2.51 tff(7408,plain,
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% 2.34/2.51 inference(symmetry,[status(thm)],[7407])).
% 2.34/2.51 tff(7409,plain,
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% 2.34/2.51 tff(7410,plain,
% 2.34/2.51 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7409])).
% 2.34/2.51 tff(7411,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7410])).
% 2.34/2.51 tff(7412,plain,
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% 2.34/2.51 inference(modus_ponens,[status(thm)],[1319, 7411])).
% 2.34/2.51 tff(7413,plain,
% 2.34/2.51 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[879, 7412])).
% 2.34/2.51 tff(7414,plain,
% 2.34/2.51 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[1337, 7413, 7400])).
% 2.34/2.51 tff(7415,plain,
% 2.34/2.51 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7414, 6211])).
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7406])).
% 2.34/2.51 tff(7417,plain,
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% 2.34/2.51 inference(monotonicity,[status(thm)],[7416])).
% 2.34/2.51 tff(7418,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[1483, 193, 7328, 7361, 4])).
% 2.34/2.51 tff(7419,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[108, 7418])).
% 2.34/2.51 tff(7420,plain,
% 2.34/2.51 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3885, 7399, 7361, 7419])).
% 2.34/2.51 tff(7421,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[822, 7420])).
% 2.34/2.51 tff(7422,plain,
% 2.34/2.51 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
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% 2.34/2.51 tff(7423,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[134, 7422])).
% 2.34/2.51 tff(7424,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[4987, 7423, 260])).
% 2.34/2.51 tff(7425,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7225, 7424])).
% 2.34/2.51 tff(7426,plain,
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% 2.34/2.51 inference(modus_ponens,[status(thm)],[7426, 7417])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[6230, 50, 7427])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7428, 7415])).
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% 2.34/2.51 inference(modus_ponens,[status(thm)],[7429, 7408])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[3081, 67, 7423, 7330])).
% 2.34/2.51 tff(7432,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[478, 7431])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7318, 204, 7397, 7432, 7234, 4780])).
% 2.34/2.51 tff(7434,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[431, 7433])).
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% 2.34/2.51 tff(7438,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7437, 4, 5, 250])).
% 2.34/2.51 tff(7439,plain,
% 2.34/2.51 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[218, 7438])).
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% 2.34/2.51 tff(7441,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(z)) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7442,plain,
% 2.34/2.51 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7441, 250, 5])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[161, 7443, 56])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[244, 7444])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[1462, 204, 6786, 6591, 7328])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7446, 7445])).
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[1993, 7445, 6786, 7328, 7397])).
% 2.34/2.51 tff(7450,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[7225, 7449])).
% 2.34/2.51 tff(7451,plain,
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% 2.34/2.51 inference(unit_resolution,[status(thm)],[4987, 7450, 7448, 260])).
% 2.34/2.51 tff(7452,plain,(b(z, s(s(s(z)))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7453,plain,
% 2.34/2.51 (b(z, s(s(s(z))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7452, 5])).
% 2.34/2.51 tff(7454,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7455,plain,
% 2.34/2.52 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7456,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7455])).
% 2.34/2.52 tff(7457,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7456, 7454])).
% 2.34/2.52 tff(7458,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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)))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7459,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7458, 7457])).
% 2.34/2.52 tff(7460,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7459, 204, 1576, 444, 405, 4780])).
% 2.34/2.52 tff(7461,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[335, 7460])).
% 2.34/2.52 tff(7462,plain,
% 2.34/2.52 (~b(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6643, 1576, 444, 548])).
% 2.34/2.52 tff(7463,plain,
% 2.34/2.52 (r(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[402, 7462])).
% 2.34/2.52 tff(7464,plain,
% 2.34/2.52 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1479, 7463, 339])).
% 2.34/2.52 tff(7465,plain,
% 2.34/2.52 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[108, 7464])).
% 2.34/2.52 tff(7466,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7467,plain,
% 2.34/2.52 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7468,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(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(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7467])).
% 2.34/2.52 tff(7469,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(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(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7468, 7466])).
% 2.34/2.52 tff(7470,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7471,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7470, 7469])).
% 2.34/2.52 tff(7472,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7471, 204, 1576, 444, 405, 3983, 7465])).
% 2.34/2.52 tff(7473,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7474,plain,
% 2.34/2.52 (~r(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7473, 389, 405, 444, 136])).
% 2.34/2.52 tff(7475,plain,
% 2.34/2.52 (b(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[357, 7474])).
% 2.34/2.52 tff(7476,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7477,plain,
% 2.34/2.52 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7478,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7477])).
% 2.34/2.52 tff(7479,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7478, 7476])).
% 2.34/2.52 tff(7480,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7481,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7480, 7479])).
% 2.34/2.52 tff(7482,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7481, 204, 405, 404, 361, 4780, 359])).
% 2.34/2.52 tff(7483,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7484,plain,
% 2.34/2.52 (~b(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7483, 7475, 405, 548])).
% 2.34/2.52 tff(7485,plain,
% 2.34/2.52 (r(s(s(s(z))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[402, 7484])).
% 2.34/2.52 tff(7486,plain,
% 2.34/2.52 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3979, 7485, 389])).
% 2.34/2.52 tff(7487,plain,
% 2.34/2.52 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[822, 7486])).
% 2.34/2.52 tff(7488,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7489,plain,
% 2.34/2.52 (((~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(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7490,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7489])).
% 2.34/2.52 tff(7491,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7490, 7488])).
% 2.34/2.52 tff(7492,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7493,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7492, 7491])).
% 2.34/2.52 tff(7494,plain,
% 2.34/2.52 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7493, 204, 405, 7487, 4780, 548])).
% 2.34/2.52 tff(7495,plain,
% 2.34/2.52 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[766, 7494])).
% 2.34/2.52 tff(7496,plain,
% 2.34/2.52 (~r(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1773, 7485, 389])).
% 2.34/2.52 tff(7497,plain,
% 2.34/2.52 (b(s(z), s(s(s(z))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[478, 7496])).
% 2.34/2.52 tff(7498,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7499,plain,
% 2.34/2.52 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7500,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7499])).
% 2.34/2.52 tff(7501,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7500, 7498])).
% 2.34/2.52 tff(7502,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7503,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7502, 7501])).
% 2.34/2.52 tff(7504,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7503, 204, 405, 361, 4780, 153, 359])).
% 2.34/2.52 tff(7505,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7506,plain,
% 2.34/2.52 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7505, 7475, 405, 548])).
% 2.34/2.52 tff(7507,plain,
% 2.34/2.52 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[108, 7506])).
% 2.34/2.52 tff(7508,plain,
% 2.34/2.52 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2724, 7507, 444, 7497, 7495])).
% 2.34/2.52 tff(7509,plain,
% 2.34/2.52 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[431, 7508])).
% 2.34/2.52 tff(7510,plain,
% 2.34/2.52 ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7318, 204, 7497, 7475, 4780])).
% 2.34/2.52 tff(7511,plain,
% 2.34/2.52 (~b(z, s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7510, 7509])).
% 2.34/2.52 tff(7512,plain,
% 2.34/2.52 (r(z, s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[306, 7511])).
% 2.34/2.52 tff(7513,plain,
% 2.34/2.52 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6655, 7512, 389, 7475, 136])).
% 2.34/2.52 tff(7514,plain,
% 2.34/2.52 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[244, 7513])).
% 2.34/2.52 tff(7515,plain,
% 2.34/2.52 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6672, 7514, 444, 7497, 7507])).
% 2.34/2.52 tff(7516,plain,
% 2.34/2.52 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[190, 7515])).
% 2.34/2.52 tff(7517,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7518,plain,
% 2.34/2.52 (((~b(s(s(s(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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7519,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(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(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7518])).
% 2.34/2.52 tff(7520,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(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(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7519, 7517])).
% 2.34/2.52 tff(7521,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7522,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7521, 7520])).
% 2.34/2.52 tff(7523,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7522, 204, 7497, 7509, 4780, 7516, 7514])).
% 2.34/2.53 tff(7524,plain,((~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7525,plain,
% 2.34/2.53 (~r(s(z), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7524, 444, 136, 405])).
% 2.34/2.53 tff(7526,plain,
% 2.34/2.53 (b(s(z), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[376, 7525])).
% 2.34/2.53 tff(7527,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3135, 204, 363, 362, 444, 405, 404])).
% 2.34/2.53 tff(7528,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7529,plain,
% 2.34/2.53 (~b(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7528, 1576, 7526, 444, 405])).
% 2.34/2.53 tff(7530,plain,
% 2.34/2.53 (r(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[402, 7529])).
% 2.34/2.53 tff(7531,plain,
% 2.34/2.53 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1479, 7530, 339])).
% 2.34/2.53 tff(7532,plain,
% 2.34/2.53 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[108, 7531])).
% 2.34/2.53 tff(7533,plain,
% 2.34/2.53 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2034, 1, 339])).
% 2.34/2.53 tff(7534,plain,
% 2.34/2.53 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7225, 7533])).
% 2.34/2.53 tff(7535,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1993, 7534, 6691, 363, 6599, 1576])).
% 2.34/2.53 tff(7536,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7537,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7536, 339, 7526, 136])).
% 2.34/2.53 tff(7538,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[190, 7537])).
% 2.34/2.53 tff(7539,plain,
% 2.34/2.53 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[212, 6414, 4780, 4, 153])).
% 2.34/2.53 tff(7540,plain,
% 2.34/2.53 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[134, 7539])).
% 2.34/2.53 tff(7541,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[322, 67, 308, 261, 7540])).
% 2.34/2.53 tff(7542,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7543,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7542, 7530, 7538, 7532, 7461])).
% 2.34/2.53 tff(7544,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[641, 7543])).
% 2.34/2.53 tff(7545,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1582, 204, 363, 362, 444, 405, 566])).
% 2.34/2.53 tff(7546,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7547,plain,
% 2.34/2.53 (~b(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7546, 1576, 7526, 444, 405])).
% 2.34/2.53 tff(7548,plain,
% 2.34/2.53 (r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[478, 7547])).
% 2.34/2.53 tff(7549,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, 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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7550,plain,
% 2.34/2.53 (((~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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7551,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7550])).
% 2.34/2.53 tff(7552,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7551, 7549])).
% 2.34/2.53 tff(7553,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7554,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7553, 7552])).
% 2.34/2.53 tff(7555,plain,
% 2.34/2.53 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7554, 204, 405, 153, 4])).
% 2.34/2.53 tff(7556,plain,
% 2.34/2.53 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7555, 1538])).
% 2.34/2.53 tff(7557,plain,
% 2.34/2.53 (r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7225, 7556])).
% 2.34/2.53 tff(7558,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6604, 1538])).
% 2.34/2.53 tff(7559,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[218, 7558])).
% 2.34/2.53 tff(7560,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6539, 7559, 7557, 339])).
% 2.34/2.53 tff(7561,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7562,plain,
% 2.34/2.53 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7561, 339, 7532, 7538, 405])).
% 2.34/2.53 tff(7563,plain,
% 2.34/2.53 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[284, 7562])).
% 2.34/2.53 tff(7564,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2643, 7563, 7548])).
% 2.34/2.53 tff(7565,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[244, 7564])).
% 2.34/2.53 tff(7566,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6406, 67, 445, 3578, 264])).
% 2.34/2.53 tff(7567,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7568,plain,
% 2.34/2.53 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7567, 7563, 7548])).
% 2.34/2.53 tff(7569,plain,
% 2.34/2.53 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6528, 7568])).
% 2.34/2.53 tff(7570,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6366, 7569, 7565, 7526, 7544, 1576])).
% 2.34/2.53 tff(7571,plain,((~r(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7572,plain,
% 2.34/2.53 (~r(z, s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7571, 7453, 6591, 56])).
% 2.34/2.53 tff(7573,plain,
% 2.34/2.53 (b(z, s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[357, 7572])).
% 2.34/2.53 tff(7574,plain,
% 2.34/2.53 (~r(s(z), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7524, 6591, 56, 7453])).
% 2.34/2.53 tff(7575,plain,
% 2.34/2.53 (b(s(z), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[376, 7574])).
% 2.34/2.53 tff(7576,plain,
% 2.34/2.53 (~r(z, s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7571, 405, 444, 136])).
% 2.34/2.53 tff(7577,plain,
% 2.34/2.53 (b(z, s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[357, 7576])).
% 2.34/2.53 tff(7578,plain,
% 2.34/2.53 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7505, 7386, 405, 7577])).
% 2.34/2.53 tff(7579,plain,
% 2.34/2.53 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[108, 7578])).
% 2.34/2.53 tff(7580,plain,
% 2.34/2.53 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6376, 7577, 405, 7526])).
% 2.34/2.53 tff(7581,plain,
% 2.34/2.53 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[431, 7580])).
% 2.34/2.53 tff(7582,plain,
% 2.34/2.53 (~b(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7483, 7386, 405, 7577])).
% 2.34/2.53 tff(7583,plain,
% 2.34/2.53 (r(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[402, 7582])).
% 2.34/2.53 tff(7584,plain,
% 2.34/2.53 (~r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7270, 67, 7583, 7581, 7579])).
% 2.34/2.53 tff(7585,plain,
% 2.34/2.53 (b(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[478, 7584])).
% 2.34/2.53 tff(7586,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2724, 7585, 444, 7581, 7579])).
% 2.34/2.53 tff(7587,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[766, 7586])).
% 2.34/2.53 tff(7588,plain,
% 2.34/2.53 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2748, 7587, 136, 7526, 7386, 7577])).
% 2.34/2.53 tff(7589,plain,
% 2.34/2.53 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[822, 7588])).
% 2.34/2.53 tff(7590,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2880, 67, 7583, 7589])).
% 2.34/2.53 tff(7591,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2434, 50, 706, 7590])).
% 2.34/2.53 tff(7592,plain,
% 2.34/2.53 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[2756, 67, 7583, 7589])).
% 2.34/2.53 tff(7593,plain,
% 2.34/2.53 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[710, 50, 707, 7592])).
% 2.34/2.53 tff(7594,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7595,plain,
% 2.34/2.53 (((~b(s(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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7596,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7595])).
% 2.34/2.53 tff(7597,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7596, 7594])).
% 2.34/2.53 tff(7598,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7599,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7598, 7597])).
% 2.34/2.53 tff(7600,plain,
% 2.34/2.53 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7599, 204, 7526, 444, 405, 7585, 7593, 7591])).
% 2.34/2.53 tff(7601,plain,
% 2.34/2.53 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[721, 50, 669, 7600])).
% 2.34/2.53 tff(7602,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7603,plain,
% 2.34/2.53 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7604,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7603])).
% 2.34/2.53 tff(7605,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7604, 7602])).
% 2.34/2.53 tff(7606,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7607,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7606, 7605])).
% 2.34/2.53 tff(7608,plain,
% 2.34/2.53 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7607, 204, 7577, 7587, 4780, 7591])).
% 2.34/2.53 tff(7609,plain,
% 2.34/2.53 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3157, 7608])).
% 2.34/2.53 tff(7610,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(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(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7611,plain,
% 2.34/2.53 (((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7612,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(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(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7611])).
% 2.34/2.53 tff(7613,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(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(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7612, 7610])).
% 2.34/2.53 tff(7614,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(z))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7615,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7614, 7613])).
% 2.34/2.53 tff(7616,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7615, 67, 286, 7609, 7601])).
% 2.34/2.53 tff(7617,plain,((~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7618,plain,
% 2.34/2.53 (~r(z, s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7617, 6591, 7453, 56])).
% 2.34/2.53 tff(7619,plain,
% 2.34/2.53 (b(z, s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[306, 7618])).
% 2.34/2.53 tff(7620,plain,
% 2.34/2.53 (~b(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7528, 7619, 7575, 6591, 7453])).
% 2.34/2.53 tff(7621,plain,
% 2.34/2.53 (r(s(s(s(z))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[402, 7620])).
% 2.34/2.53 tff(7622,plain,
% 2.34/2.53 (~b(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7546, 7619, 7575, 6591, 7453])).
% 2.34/2.53 tff(7623,plain,
% 2.34/2.53 (r(s(z), s(s(s(z))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[478, 7622])).
% 2.34/2.53 tff(7624,plain,
% 2.34/2.53 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7272, 7623, 7619, 7575, 7621, 7573])).
% 2.34/2.53 tff(7625,plain,
% 2.34/2.53 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[108, 7624])).
% 2.34/2.53 tff(7626,plain,
% 2.34/2.53 (~b(s(s(s(s(z)))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7505, 7625, 7453, 7573])).
% 2.34/2.53 tff(7627,plain,
% 2.34/2.53 (r(s(s(s(s(z)))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[335, 7626])).
% 2.34/2.53 tff(7628,plain,
% 2.34/2.53 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6376, 7573, 7453, 7575])).
% 2.34/2.53 tff(7629,plain,
% 2.34/2.53 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[431, 7628])).
% 2.34/2.53 tff(7630,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4784, 1, 538])).
% 2.34/2.53 tff(7631,plain,
% 2.34/2.53 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7215, 1, 363, 2, 362, 136])).
% 2.34/2.53 tff(7632,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[641, 7631, 7630])).
% 2.34/2.53 tff(7633,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7634,plain,
% 2.34/2.53 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7633, 7575, 7629, 7619, 56, 7627])).
% 2.34/2.53 tff(7635,plain,
% 2.34/2.53 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[190, 7634])).
% 2.34/2.54 tff(7636,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7542, 7635, 7621, 7625, 7627])).
% 2.34/2.54 tff(7637,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[641, 7636])).
% 2.34/2.54 tff(7638,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6388, 204, 7453, 7573, 4780, 7635, 7637])).
% 2.34/2.54 tff(7639,plain,(b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7640,plain,
% 2.34/2.54 (~r(z, s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[294, 286, 57])).
% 2.34/2.54 tff(7641,plain,
% 2.34/2.54 (b(z, s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[259, 7640])).
% 2.34/2.54 tff(7642,plain,
% 2.34/2.54 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[507, 1, 378])).
% 2.34/2.54 tff(7643,plain,
% 2.34/2.54 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[134, 7642])).
% 2.34/2.54 tff(7644,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7645,plain,
% 2.34/2.54 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7646,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7645])).
% 2.34/2.54 tff(7647,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7646, 7644])).
% 2.34/2.54 tff(7648,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7649,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7648, 7647])).
% 2.34/2.54 tff(7650,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7649, 67, 57, 378, 1])).
% 2.34/2.54 tff(7651,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[284, 7650])).
% 2.34/2.54 tff(7652,plain,
% 2.34/2.54 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1783, 7651, 404, 405, 7643])).
% 2.34/2.54 tff(7653,plain,
% 2.34/2.54 (r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[641, 7652])).
% 2.34/2.54 tff(7654,plain,
% 2.34/2.54 (~r(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4784, 7653, 1])).
% 2.34/2.54 tff(7655,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[335, 7654])).
% 2.34/2.54 tff(7656,plain,
% 2.34/2.54 (~r(z, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4788, 7653, 1])).
% 2.34/2.54 tff(7657,plain,
% 2.34/2.54 (b(z, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[357, 7656])).
% 2.34/2.54 tff(7658,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7483, 7657, 7655, 404, 405])).
% 2.34/2.54 tff(7659,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7660,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7659, 378, 7641, 57, 403])).
% 2.34/2.54 tff(7661,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[190, 7660])).
% 2.34/2.54 tff(7662,plain,
% 2.34/2.54 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[386, 378, 57])).
% 2.34/2.54 tff(7663,plain,
% 2.34/2.54 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[431, 7662])).
% 2.34/2.54 tff(7664,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2663, 261, 286])).
% 2.34/2.54 tff(7665,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[244, 7664])).
% 2.34/2.54 tff(7666,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2552, 204, 456, 7639, 4, 6619, 7665])).
% 2.34/2.54 tff(7667,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7668,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7667, 7663, 7661, 389, 286])).
% 2.34/2.54 tff(7669,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[641, 7668])).
% 2.34/2.54 tff(7670,plain,
% 2.34/2.54 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6388, 204, 7641, 4780, 7661])).
% 2.34/2.54 tff(7671,plain,
% 2.34/2.54 (~b(z, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7670, 7669])).
% 2.34/2.54 tff(7672,plain,
% 2.34/2.54 (r(z, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[357, 7671])).
% 2.34/2.54 tff(7673,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3954, 7672, 57, 7663, 7669])).
% 2.34/2.54 tff(7674,plain,
% 2.34/2.54 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2513, 7639])).
% 2.34/2.54 tff(7675,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7674, 7673, 7663, 7661])).
% 2.34/2.54 tff(7676,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[218, 7675])).
% 2.34/2.54 tff(7677,plain,
% 2.34/2.54 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6539, 7676, 7672])).
% 2.34/2.54 tff(7678,plain,
% 2.34/2.54 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7225, 7677])).
% 2.34/2.54 tff(7679,plain,
% 2.34/2.54 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2027, 204, 7641, 403, 7669, 7678])).
% 2.34/2.54 tff(7680,plain,
% 2.34/2.54 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[284, 7679])).
% 2.34/2.54 tff(7681,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2552, 204, 456, 7639, 4, 2404, 443])).
% 2.34/2.54 tff(7682,plain,((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7683,plain,
% 2.34/2.54 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7682, 7663, 7661, 7673])).
% 2.34/2.54 tff(7684,plain,
% 2.34/2.54 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6528, 7683])).
% 2.34/2.54 tff(7685,plain,
% 2.34/2.54 (~r(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7567, 7684, 7680])).
% 2.34/2.54 tff(7686,plain,
% 2.34/2.54 (b(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[478, 7685])).
% 2.34/2.54 tff(7687,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7688,plain,
% 2.34/2.54 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7689,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7688])).
% 2.34/2.54 tff(7690,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(X1, 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7689, 7687])).
% 2.34/2.54 tff(7691,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7692,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7691, 7690])).
% 2.34/2.54 tff(7693,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7692, 204, 7686, 4780, 7639, 7661, 7673])).
% 2.34/2.54 tff(7694,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7695,plain,
% 2.34/2.54 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7694, 286, 389, 57])).
% 2.34/2.54 tff(7696,plain,
% 2.34/2.54 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[108, 7695])).
% 2.34/2.54 tff(7697,plain,
% 2.34/2.54 (~b(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6563, 7696, 403, 7641])).
% 2.34/2.54 tff(7698,plain,
% 2.34/2.54 (r(s(s(s(s(z)))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[335, 7697])).
% 2.34/2.54 tff(7699,plain,
% 2.34/2.54 (r(s(s(s(z))), s(s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6354, 4779])).
% 2.34/2.54 tff(7700,plain,
% 2.34/2.54 (~b(z, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7699, 7695, 403, 7641])).
% 2.34/2.54 tff(7701,plain,
% 2.34/2.54 (r(z, s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[357, 7700])).
% 2.34/2.54 tff(7702,plain,
% 2.34/2.54 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2034, 1, 7701])).
% 2.34/2.54 tff(7703,plain,
% 2.34/2.54 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7225, 7702])).
% 2.34/2.54 tff(7704,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4788, 1, 7701])).
% 2.34/2.54 tff(7705,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[641, 7704])).
% 2.34/2.54 tff(7706,plain,
% 2.34/2.54 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1887, 7701, 286])).
% 2.34/2.54 tff(7707,plain,
% 2.34/2.54 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[431, 7706])).
% 2.34/2.54 tff(7708,plain,
% 2.34/2.54 ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4314, 7639])).
% 2.34/2.54 tff(7709,plain,
% 2.34/2.54 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7708, 824, 538, 389, 456])).
% 2.34/2.54 tff(7710,plain,
% 2.34/2.54 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[766, 7709])).
% 2.34/2.54 tff(7711,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3259, 67, 7710, 824, 538])).
% 2.34/2.54 tff(7712,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7713,plain,
% 2.34/2.54 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7712, 7698, 389, 7707])).
% 2.34/2.54 tff(7714,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[822, 7713])).
% 2.34/2.54 tff(7715,plain,
% 2.34/2.54 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3617, 4780, 7639])).
% 2.34/2.54 tff(7716,plain,
% 2.34/2.54 (~b(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7715, 7707, 7696])).
% 2.34/2.54 tff(7717,plain,
% 2.34/2.54 (r(s(z), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[478, 7716])).
% 2.34/2.54 tff(7718,plain,
% 2.34/2.54 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[3954, 7705, 57, 7701, 7707])).
% 2.34/2.54 tff(7719,plain,
% 2.34/2.54 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2027, 204, 7641, 403, 7705, 7703])).
% 2.34/2.54 tff(7720,plain,
% 2.34/2.54 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[284, 7719])).
% 2.34/2.54 tff(7721,plain,
% 2.34/2.54 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7567, 7720, 7717])).
% 2.34/2.54 tff(7722,plain,
% 2.34/2.54 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[6528, 7721])).
% 2.34/2.54 tff(7723,plain,
% 2.34/2.54 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[3306, 2224])).
% 2.34/2.54 tff(7724,plain,
% 2.34/2.54 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7723])).
% 2.34/2.54 tff(7725,plain,
% 2.34/2.54 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[2125, 7724])).
% 2.34/2.54 tff(7726,plain,
% 2.34/2.54 (~r(s(z), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2184, 3308, 389, 445, 286])).
% 2.34/2.54 tff(7727,plain,
% 2.34/2.54 (b(s(z), s(s(elem!1)))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[936, 7726])).
% 2.34/2.54 tff(7728,plain,
% 2.34/2.54 ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2252, 204, 1102, 405, 2138])).
% 2.34/2.54 tff(7729,plain,
% 2.34/2.54 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7728, 2246])).
% 2.34/2.54 tff(7730,plain,
% 2.34/2.54 (r(s(s(elem!1)), s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1165, 50, 628, 7729])).
% 2.34/2.54 tff(7731,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), 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), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7732,plain,
% 2.34/2.54 (((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7733,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(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)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7732])).
% 2.34/2.54 tff(7734,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(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)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7733, 7731])).
% 2.34/2.54 tff(7735,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7736,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7735, 7734])).
% 2.34/2.54 tff(7737,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7736, 67, 938, 389, 445, 7730])).
% 2.34/2.54 tff(7738,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7739,plain,
% 2.34/2.54 (~b(s(s(elem!1)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7738, 5180, 445, 389, 628, 405, 286])).
% 2.34/2.54 tff(7740,plain,
% 2.34/2.54 (r(s(s(elem!1)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1099, 7739])).
% 2.34/2.54 tff(7741,plain,
% 2.34/2.54 (~r(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[944, 67, 389, 900])).
% 2.34/2.54 tff(7742,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[952, 7741])).
% 2.34/2.54 tff(7743,plain,
% 2.34/2.54 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[2264, 204, 7742, 2222, 4408, 3625])).
% 2.34/2.54 tff(7744,plain,
% 2.34/2.54 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1139, 7743, 1101])).
% 2.34/2.54 tff(7745,plain,
% 2.34/2.54 (((~![X0: $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(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7746,plain,
% 2.34/2.54 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7747,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(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(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7746])).
% 2.34/2.54 tff(7748,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(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(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7747, 7745])).
% 2.34/2.54 tff(7749,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7750,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7749, 7748])).
% 2.34/2.54 tff(7751,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7750, 67, 900, 286, 7744, 339])).
% 2.34/2.54 tff(7752,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7753,plain,
% 2.34/2.54 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7752, 7740, 339, 286, 2222, 389])).
% 2.34/2.54 tff(7754,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7753])).
% 2.34/2.54 tff(7755,plain,
% 2.34/2.54 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(symmetry,[status(thm)],[7754])).
% 2.34/2.54 tff(7756,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[3625, 7755])).
% 2.34/2.54 tff(7757,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[5179, 7756])).
% 2.34/2.54 tff(7758,plain,(b(s(s(elem!1)), s(z)) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (s(s(elem!1)) = s(s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7759,plain,
% 2.34/2.54 (b(s(s(elem!1)), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7758, 7727, 389, 286, 339, 445, 7725, 405])).
% 2.34/2.54 tff(7760,plain,
% 2.34/2.54 (b(s(s(z)), s(z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7759, 3301])).
% 2.34/2.54 tff(7761,plain,
% 2.34/2.54 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[3297])).
% 2.34/2.54 tff(7762,plain,
% 2.34/2.54 (b(s(z), s(s(z)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7727, 7761])).
% 2.34/2.54 tff(7763,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7764,plain,
% 2.34/2.54 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7765,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7764])).
% 2.34/2.55 tff(7766,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7765, 7763])).
% 2.34/2.55 tff(7767,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7768,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7767, 7766])).
% 2.34/2.55 tff(7769,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7768, 204, 7762, 7760, 2404, 443])).
% 2.34/2.55 tff(7770,plain,
% 2.34/2.55 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1887, 339, 286])).
% 2.34/2.55 tff(7771,plain,
% 2.34/2.55 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[431, 7770])).
% 2.34/2.55 tff(7772,plain,
% 2.34/2.55 ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2266, 7639])).
% 2.34/2.55 tff(7773,plain,
% 2.34/2.55 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7772, 7759, 7727, 7771])).
% 2.34/2.55 tff(7774,plain,
% 2.34/2.55 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1139, 7773, 3593])).
% 2.34/2.55 tff(7775,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7774, 3579])).
% 2.34/2.55 tff(7776,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7777,plain,
% 2.34/2.55 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7778,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7777])).
% 2.34/2.55 tff(7779,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7778, 7776])).
% 2.34/2.55 tff(7780,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7781,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7780, 7779])).
% 2.34/2.55 tff(7782,plain,
% 2.34/2.55 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7781, 67, 1, 7775])).
% 2.34/2.55 tff(7783,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3366, 7782, 7769])).
% 2.34/2.55 tff(7784,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7785,plain,
% 2.34/2.55 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7784, 1, 7722, 7718, 389, 286, 7701, 7717, 7641])).
% 2.34/2.55 tff(7786,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3225, 3111])).
% 2.34/2.55 tff(7787,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2434, 50, 706, 7786])).
% 2.34/2.55 tff(7788,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6806, 3111])).
% 2.34/2.55 tff(7789,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[850, 50, 7788, 3895])).
% 2.34/2.55 tff(7790,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2027, 204, 405, 404, 1469, 1708])).
% 2.34/2.55 tff(7791,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[284, 7790])).
% 2.34/2.55 tff(7792,plain,
% 2.34/2.55 (((~![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(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7793,plain,
% 2.34/2.55 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(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(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7794,plain,
% 2.34/2.55 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7793])).
% 2.34/2.55 tff(7795,plain,
% 2.34/2.55 (((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7794, 7792])).
% 2.34/2.55 tff(7796,plain,
% 2.34/2.55 ((~![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(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7797,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7796, 7795])).
% 2.34/2.55 tff(7798,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7797, 67, 1, 7791, 7789, 7787])).
% 2.34/2.55 tff(7799,plain,((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7800,plain,
% 2.34/2.55 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7799, 1, 7785, 7714, 7705, 7703, 7641, 403])).
% 2.34/2.55 tff(7801,plain,
% 2.34/2.55 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3157, 7800])).
% 2.34/2.55 tff(7802,plain,
% 2.34/2.55 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3168, 7801, 7698])).
% 2.34/2.55 tff(7803,plain,
% 2.34/2.55 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3173, 7802])).
% 2.34/2.55 tff(7804,plain,
% 2.34/2.55 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6502, 204, 403, 7714, 4780])).
% 2.34/2.55 tff(7805,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7804, 7803])).
% 2.34/2.55 tff(7806,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2434, 50, 706, 7805])).
% 2.34/2.55 tff(7807,plain,
% 2.34/2.55 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3157, 3215])).
% 2.34/2.55 tff(7808,plain,
% 2.34/2.55 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3902, 204, 784, 6599, 7534])).
% 2.34/2.55 tff(7809,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7808, 7807])).
% 2.34/2.55 tff(7810,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[850, 50, 7809, 3895, 6720])).
% 2.34/2.55 tff(7811,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7812,plain,
% 2.34/2.55 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7811, 7785, 1, 7714, 7701])).
% 2.34/2.55 tff(7813,plain,
% 2.34/2.55 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[766, 7812])).
% 2.34/2.55 tff(7814,plain,
% 2.34/2.55 ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4310, 204, 7707, 7813, 7639])).
% 2.34/2.55 tff(7815,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7814, 7803])).
% 2.34/2.55 tff(7816,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[4365, 7815])).
% 2.34/2.55 tff(7817,plain,
% 2.34/2.55 (((~![X0: $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(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(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(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(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7818,plain,
% 2.34/2.55 (((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, 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(z))) | (~r(z, s(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(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7819,plain,
% 2.34/2.55 (((~![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(s(elem!1)))))), s(z))) | (~r(z, 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(z))) | (~r(z, s(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(z)))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7818])).
% 2.34/2.55 tff(7820,plain,
% 2.34/2.55 (((~![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(s(elem!1)))))), s(z))) | (~r(z, 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(z))) | (~r(z, s(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(z))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7819, 7817])).
% 2.34/2.55 tff(7821,plain,
% 2.34/2.55 ((~![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(s(elem!1)))))), s(z))) | (~r(z, 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)))))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7822,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(z)))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7821, 7820])).
% 2.34/2.55 tff(7823,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7822, 67, 286, 7801, 7816, 7806])).
% 2.34/2.55 tff(7824,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7825,plain,
% 2.34/2.55 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7824, 286, 389, 57])).
% 2.34/2.55 tff(7826,plain,
% 2.34/2.55 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[190, 7825])).
% 2.34/2.55 tff(7827,plain,
% 2.34/2.55 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7667, 7826, 7707, 389, 286])).
% 2.34/2.55 tff(7828,plain,
% 2.34/2.55 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[641, 7827])).
% 2.34/2.55 tff(7829,plain,
% 2.34/2.55 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3954, 7828, 57, 7701, 7707])).
% 2.34/2.55 tff(7830,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7561, 7826, 7696, 7701, 7641])).
% 2.34/2.55 tff(7831,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[284, 7830])).
% 2.34/2.55 tff(7832,plain,
% 2.34/2.55 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7567, 7831, 7717])).
% 2.34/2.55 tff(7833,plain,
% 2.34/2.55 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6528, 7832])).
% 2.34/2.55 tff(7834,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7682, 7833, 7829, 7707, 7826])).
% 2.34/2.55 tff(7835,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7836,plain,
% 2.34/2.55 (~r(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7835, 57, 389])).
% 2.34/2.55 tff(7837,plain,
% 2.34/2.55 (b(z, s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[306, 7836])).
% 2.34/2.55 tff(7838,plain,
% 2.34/2.55 ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[2542, 7639])).
% 2.34/2.55 tff(7839,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7838, 2, 389, 57])).
% 2.34/2.55 tff(7840,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[335, 7839, 5661])).
% 2.34/2.55 tff(7841,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7842,plain,
% 2.34/2.55 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7841, 57, 389])).
% 2.34/2.55 tff(7843,plain,
% 2.34/2.55 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[431, 7842])).
% 2.34/2.55 tff(7844,plain,
% 2.34/2.55 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7674, 6618, 456, 4])).
% 2.34/2.55 tff(7845,plain,
% 2.34/2.55 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[218, 7844])).
% 2.34/2.55 tff(7846,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7847,plain,
% 2.34/2.55 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7848,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7847])).
% 2.34/2.55 tff(7849,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7848, 7846])).
% 2.34/2.55 tff(7850,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7851,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7850, 7849])).
% 2.34/2.55 tff(7852,plain,
% 2.34/2.55 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7851, 204, 362, 456, 4])).
% 2.34/2.55 tff(7853,plain,
% 2.34/2.55 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7852, 6618])).
% 2.34/2.55 tff(7854,plain,
% 2.34/2.55 (r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7225, 7853])).
% 2.34/2.55 tff(7855,plain,
% 2.34/2.55 (~r(z, s(s(s(s(z)))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6539, 7854, 7845])).
% 2.34/2.55 tff(7856,plain,
% 2.34/2.55 (~r(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1831, 3, 389])).
% 2.34/2.55 tff(7857,plain,
% 2.34/2.55 (b(s(z), s(s(s(z))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[478, 7856])).
% 2.34/2.55 tff(7858,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7859,plain,
% 2.34/2.55 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7860,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7859])).
% 2.34/2.56 tff(7861,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7860, 7858])).
% 2.34/2.56 tff(7862,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7863,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7862, 7861])).
% 2.34/2.56 tff(7864,plain,
% 2.34/2.56 (~b(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7863, 204, 362, 7857, 4780, 7639])).
% 2.34/2.56 tff(7865,plain,
% 2.34/2.56 (r(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[357, 7864])).
% 2.34/2.56 tff(7866,plain,
% 2.34/2.56 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[536, 7865, 389])).
% 2.34/2.56 tff(7867,plain,
% 2.34/2.56 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[431, 7866])).
% 2.34/2.56 tff(7868,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1922, 7865, 3])).
% 2.34/2.56 tff(7869,plain,
% 2.34/2.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[108, 7868])).
% 2.34/2.56 tff(7870,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7715, 7869, 7867, 7857])).
% 2.34/2.56 tff(7871,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7872,plain,
% 2.34/2.56 (~r(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7871, 362, 389])).
% 2.34/2.56 tff(7873,plain,
% 2.34/2.56 (b(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[259, 7872])).
% 2.34/2.56 tff(7874,plain,
% 2.34/2.56 ((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1819, 7639])).
% 2.34/2.56 tff(7875,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7874, 6618, 456, 261])).
% 2.34/2.56 tff(7876,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[335, 7875])).
% 2.34/2.56 tff(7877,plain,
% 2.34/2.56 (~b(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7483, 7876, 404, 7873])).
% 2.34/2.56 tff(7878,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[357, 7877, 7855])).
% 2.34/2.56 tff(7879,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7880,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7879, 4, 7843, 7837, 403, 389])).
% 2.34/2.56 tff(7881,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[641, 7880])).
% 2.34/2.56 tff(7882,plain,
% 2.34/2.56 (~r(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7871, 7837, 389])).
% 2.34/2.56 tff(7883,plain,
% 2.34/2.56 (b(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[259, 7882])).
% 2.34/2.56 tff(7884,plain,
% 2.34/2.56 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6388, 204, 7883, 4780, 4])).
% 2.34/2.56 tff(7885,plain,
% 2.34/2.56 (~b(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7884, 7881])).
% 2.34/2.56 tff(7886,plain,
% 2.34/2.56 (r(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[357, 7885])).
% 2.34/2.56 tff(7887,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3954, 7886, 57, 7881, 7843])).
% 2.34/2.56 tff(7888,plain,
% 2.34/2.56 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7674, 7887, 7843, 4])).
% 2.34/2.56 tff(7889,plain,
% 2.34/2.56 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[218, 7888])).
% 2.34/2.56 tff(7890,plain,
% 2.34/2.56 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7851, 204, 7837, 7843, 4])).
% 2.34/2.56 tff(7891,plain,
% 2.34/2.56 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7890, 7887])).
% 2.34/2.56 tff(7892,plain,
% 2.34/2.56 (r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7225, 7891])).
% 2.34/2.56 tff(7893,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6539, 7892, 7889, 7886])).
% 2.34/2.56 tff(7894,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7895,plain,
% 2.34/2.56 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7894, 57, 389])).
% 2.34/2.56 tff(7896,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[190, 7895])).
% 2.34/2.56 tff(7897,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7659, 7896, 7883, 57, 403])).
% 2.34/2.56 tff(7898,plain,
% 2.34/2.56 (~b(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7699, 7897, 403, 7883])).
% 2.34/2.56 tff(7899,plain,
% 2.34/2.56 (r(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[357, 7898])).
% 2.34/2.56 tff(7900,plain,
% 2.34/2.56 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2034, 7899, 7896])).
% 2.34/2.56 tff(7901,plain,
% 2.34/2.56 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7225, 7900])).
% 2.34/2.56 tff(7902,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4788, 7899, 7896])).
% 2.34/2.56 tff(7903,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[641, 7902])).
% 2.34/2.56 tff(7904,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3954, 7903, 57, 7899, 7843])).
% 2.34/2.56 tff(7905,plain,
% 2.34/2.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[108, 7897])).
% 2.34/2.56 tff(7906,plain,
% 2.34/2.56 (~b(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7715, 7905, 7843])).
% 2.34/2.56 tff(7907,plain,
% 2.34/2.56 (r(s(z), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[478, 7906])).
% 2.34/2.56 tff(7908,plain,
% 2.34/2.56 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[2027, 204, 7883, 403, 7903, 7901])).
% 2.34/2.56 tff(7909,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[284, 7908])).
% 2.34/2.56 tff(7910,plain,
% 2.34/2.56 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7567, 7909, 7907])).
% 2.34/2.56 tff(7911,plain,
% 2.34/2.56 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6528, 7910])).
% 2.34/2.56 tff(7912,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7913,plain,
% 2.34/2.56 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7914,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7913])).
% 2.34/2.56 tff(7915,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7914, 7912])).
% 2.34/2.56 tff(7916,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7917,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7916, 7915])).
% 2.34/2.56 tff(7918,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7917, 204, 7837, 7903, 7911, 7904, 7901])).
% 2.34/2.56 tff(7919,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7920,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7919, 389])).
% 2.34/2.56 tff(7921,plain,
% 2.34/2.56 (b(s(s(s(z))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[558, 7920])).
% 2.34/2.56 tff(7922,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7923,plain,
% 2.34/2.56 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7924,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7923])).
% 2.34/2.56 tff(7925,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7924, 7922])).
% 2.34/2.56 tff(7926,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7927,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7926, 7925])).
% 2.34/2.56 tff(7928,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7927, 204, 444, 566, 456, 194, 360])).
% 2.34/2.56 tff(7929,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7930,plain,
% 2.34/2.56 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7929, 4780, 7639])).
% 2.34/2.56 tff(7931,plain,
% 2.34/2.56 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7930, 7857, 7921])).
% 2.34/2.56 tff(7932,plain,
% 2.34/2.56 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[431, 7931])).
% 2.34/2.56 tff(7933,plain,
% 2.34/2.56 (~r(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1194, 7932, 389])).
% 2.34/2.56 tff(7934,plain,
% 2.34/2.56 (b(s(s(s(s(z)))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[335, 7933])).
% 2.34/2.56 tff(7935,plain,
% 2.34/2.56 (~r(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6633, 3, 389, 7921])).
% 2.34/2.56 tff(7936,plain,
% 2.34/2.56 (b(z, s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[357, 7935])).
% 2.34/2.56 tff(7937,plain,
% 2.34/2.56 (~b(z, s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7871, 3, 389])).
% 2.34/2.56 tff(7938,plain,
% 2.34/2.56 (r(z, s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[306, 7937])).
% 2.34/2.56 tff(7939,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6652, 4, 389, 7938, 7936, 7934])).
% 2.34/2.56 tff(7940,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[244, 7939])).
% 2.34/2.56 tff(7941,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6621, 3, 389, 7921])).
% 2.34/2.56 tff(7942,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[641, 7941])).
% 2.34/2.56 tff(7943,plain,
% 2.34/2.56 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3485, 204, 7936, 7934, 7942])).
% 2.34/2.56 tff(7944,plain,
% 2.34/2.56 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7943, 4])).
% 2.34/2.56 tff(7945,plain,
% 2.34/2.56 (r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7225, 7944])).
% 2.34/2.56 tff(7946,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4983, 7945, 3])).
% 2.34/2.56 tff(7947,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[284, 7946])).
% 2.34/2.56 tff(7948,plain,
% 2.34/2.56 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[4987, 7945, 3])).
% 2.34/2.56 tff(7949,plain,
% 2.34/2.56 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[134, 7948])).
% 2.34/2.56 tff(7950,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1540, 7949, 7947, 7921, 7857, 7940])).
% 2.34/2.56 tff(7951,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7952,plain,
% 2.34/2.56 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7951, 3, 389])).
% 2.34/2.56 tff(7953,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[190, 7952])).
% 2.34/2.56 tff(7954,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3043, 7953, 7932])).
% 2.34/2.56 tff(7955,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7956,plain,
% 2.34/2.56 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7957,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7956])).
% 2.34/2.56 tff(7958,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7957, 7955])).
% 2.34/2.56 tff(7959,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7960,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7959, 7958])).
% 2.34/2.56 tff(7961,plain,
% 2.34/2.56 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7960, 204, 7921, 7857, 4780, 7639])).
% 2.34/2.56 tff(7962,plain,
% 2.34/2.56 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[108, 7961])).
% 2.34/2.56 tff(7963,plain,
% 2.34/2.56 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[6672, 7953, 7921, 7962, 7857])).
% 2.34/2.56 tff(7964,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[244, 7963, 7954])).
% 2.34/2.56 tff(7965,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7966,plain,
% 2.34/2.56 (~r(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7965, 389])).
% 2.34/2.56 tff(7967,plain,
% 2.34/2.56 (b(z, s(s(s(z))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[259, 7966])).
% 2.34/2.56 tff(7968,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7969,plain,
% 2.34/2.56 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7970,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7969])).
% 2.34/2.56 tff(7971,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7970, 7968])).
% 2.34/2.56 tff(7972,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7973,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7972, 7971])).
% 2.34/2.57 tff(7974,plain,
% 2.34/2.57 (~b(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7973, 204, 7921, 7967, 4780, 7639])).
% 2.34/2.57 tff(7975,plain,
% 2.34/2.57 (r(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[357, 7974])).
% 2.34/2.57 tff(7976,plain,
% 2.34/2.57 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[536, 7975, 389])).
% 2.34/2.57 tff(7977,plain,
% 2.34/2.57 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[431, 7976])).
% 2.34/2.57 tff(7978,plain,
% 2.34/2.57 (~b(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7930, 7977, 7921])).
% 2.34/2.57 tff(7979,plain,
% 2.34/2.57 (r(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[478, 7978])).
% 2.34/2.57 tff(7980,plain,
% 2.34/2.57 ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3991, 7639])).
% 2.34/2.57 tff(7981,plain,
% 2.34/2.57 (~r(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7980, 7975, 389])).
% 2.34/2.57 tff(7982,plain,
% 2.34/2.57 (b(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[402, 7981])).
% 2.34/2.57 tff(7983,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2643, 110, 7979])).
% 2.34/2.57 tff(7984,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[284, 7983])).
% 2.34/2.57 tff(7985,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4263, 7984, 6648, 7982, 7967, 110, 7921])).
% 2.34/2.57 tff(7986,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7987,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7986, 389])).
% 2.34/2.57 tff(7988,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[244, 7987])).
% 2.34/2.57 tff(7989,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3569, 204, 444, 456, 4780, 153, 7639])).
% 2.34/2.57 tff(7990,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7991,plain,
% 2.34/2.57 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7990, 7921, 7977])).
% 2.34/2.57 tff(7992,plain,
% 2.34/2.57 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[108, 7991])).
% 2.34/2.57 tff(7993,plain,
% 2.34/2.57 (~b(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7973, 204, 444, 405, 4780, 7639])).
% 2.34/2.57 tff(7994,plain,
% 2.34/2.57 (r(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[357, 7993])).
% 2.34/2.57 tff(7995,plain,
% 2.34/2.57 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2034, 1, 7994])).
% 2.34/2.57 tff(7996,plain,
% 2.34/2.57 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7225, 7995])).
% 2.34/2.57 tff(7997,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1716, 7643, 7996, 444, 405, 443])).
% 2.34/2.57 tff(7998,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7999,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7998, 7921, 7967, 7988, 7992])).
% 2.34/2.57 tff(8000,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[190, 7999])).
% 2.34/2.57 tff(8001,plain,
% 2.34/2.57 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7682, 8000, 7977, 7988])).
% 2.34/2.57 tff(8002,plain,
% 2.34/2.57 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6528, 8001])).
% 2.34/2.57 tff(8003,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7567, 8002, 7979])).
% 2.34/2.57 tff(8004,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[284, 8003])).
% 2.34/2.57 tff(8005,plain,
% 2.34/2.57 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7674, 8000, 7977, 7988])).
% 2.34/2.57 tff(8006,plain,
% 2.34/2.57 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[218, 8005])).
% 2.34/2.57 tff(8007,plain,
% 2.34/2.57 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6539, 8006, 7975])).
% 2.34/2.57 tff(8008,plain,
% 2.34/2.57 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7225, 8007])).
% 2.34/2.57 tff(8009,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4788, 261, 7975])).
% 2.34/2.57 tff(8010,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[190, 8009])).
% 2.34/2.57 tff(8011,plain,
% 2.34/2.57 (~b(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7879, 8010, 7977, 261, 7982, 389])).
% 2.34/2.57 tff(8012,plain,
% 2.34/2.57 (~r(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7667, 8010, 7977, 389, 261])).
% 2.34/2.57 tff(8013,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[306, 8012, 8011])).
% 2.34/2.57 tff(8014,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8015,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8014, 389])).
% 2.34/2.57 tff(8016,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[641, 8015])).
% 2.34/2.57 tff(8017,plain,
% 2.34/2.57 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2027, 204, 7967, 7982, 8016])).
% 2.34/2.57 tff(8018,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8017, 8008, 8004])).
% 2.34/2.57 tff(8019,plain,(~r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8020,plain,
% 2.34/2.57 (b(s(z), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[376, 8019])).
% 2.34/2.57 tff(8021,plain,
% 2.34/2.57 ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3492, 7639])).
% 2.34/2.57 tff(8022,plain,
% 2.34/2.57 (~b(s(s(s(s(z)))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8021, 361, 8020, 110])).
% 2.34/2.57 tff(8023,plain,
% 2.34/2.57 (r(s(s(s(s(z)))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[335, 8022])).
% 2.34/2.57 tff(8024,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6606, 153, 3, 4, 538])).
% 2.34/2.57 tff(8025,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[641, 8024])).
% 2.34/2.57 tff(8026,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(8027,plain,
% 2.34/2.57 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(8028,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[8027])).
% 2.34/2.57 tff(8029,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[8028, 8026])).
% 2.34/2.57 tff(8030,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(8031,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[8030, 8029])).
% 2.34/2.57 tff(8032,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8031, 204, 362, 361, 7639, 4, 1469])).
% 2.34/2.57 tff(8033,plain,((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8034,plain,
% 2.34/2.57 (~b(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8033, 8025, 4, 361])).
% 2.34/2.57 tff(8035,plain,
% 2.34/2.57 (r(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[306, 8034])).
% 2.34/2.57 tff(8036,plain,
% 2.34/2.57 (~r(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1738, 8035, 3])).
% 2.34/2.57 tff(8037,plain,
% 2.34/2.57 (b(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[478, 8036])).
% 2.34/2.57 tff(8038,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[294, 8035, 3])).
% 2.34/2.57 tff(8039,plain,
% 2.34/2.57 (b(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[558, 8038])).
% 2.34/2.57 tff(8040,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7960, 204, 8039, 8037, 4780, 153, 7639])).
% 2.34/2.57 tff(8041,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8042,plain,
% 2.34/2.57 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8041, 361, 4, 3, 8023])).
% 2.34/2.57 tff(8043,plain,
% 2.34/2.57 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[108, 8042])).
% 2.34/2.57 tff(8044,plain,
% 2.34/2.57 (~r(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1212, 8043, 8023])).
% 2.34/2.57 tff(8045,plain,
% 2.34/2.57 (b(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[402, 8044])).
% 2.34/2.57 tff(8046,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[386, 8043, 2])).
% 2.34/2.57 tff(8047,plain,
% 2.34/2.57 (b(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[558, 8046])).
% 2.34/2.57 tff(8048,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(8049,plain,
% 2.34/2.57 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(8050,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[8049])).
% 2.34/2.57 tff(8051,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[8050, 8048])).
% 2.34/2.57 tff(8052,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(8053,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[8052, 8051])).
% 2.34/2.57 tff(8054,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8053, 204, 8020, 8047, 8045, 4780, 7639])).
% 2.34/2.57 tff(8055,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8056,plain,
% 2.34/2.57 (~b(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8055, 110, 4, 3, 2])).
% 2.34/2.57 tff(8057,plain,
% 2.34/2.57 (r(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[357, 8056])).
% 2.34/2.57 tff(8058,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1922, 8057, 3])).
% 2.34/2.57 tff(8059,plain,
% 2.34/2.57 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[108, 8058])).
% 2.34/2.57 tff(8060,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[284, 2605])).
% 2.34/2.57 tff(8061,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2619, 204, 4780, 153, 4, 135, 8060])).
% 2.34/2.57 tff(8062,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8063,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8062, 8059, 4, 110])).
% 2.34/2.57 tff(8064,plain,
% 2.34/2.57 (b(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[558, 8063])).
% 2.34/2.57 tff(8065,plain,
% 2.34/2.57 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3023, 204, 8064, 8059, 7639, 4])).
% 2.34/2.57 tff(8066,plain,
% 2.34/2.57 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[284, 8065])).
% 2.34/2.57 tff(8067,plain,
% 2.34/2.57 (~r(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[2643, 8066, 110])).
% 2.34/2.57 tff(8068,plain,
% 2.34/2.57 (b(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[478, 8067])).
% 2.34/2.57 tff(8069,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7960, 204, 8064, 8068, 4780, 8059, 7639])).
% 2.34/2.57 tff(8070,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8071,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8070, 4, 3, 2])).
% 2.34/2.57 tff(8072,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[244, 8071])).
% 2.34/2.57 tff(8073,plain,
% 2.34/2.57 (~r(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7254, 67, 2, 378])).
% 2.34/2.57 tff(8074,plain,
% 2.34/2.57 (b(s(z), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[478, 8073])).
% 2.34/2.57 tff(8075,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[386, 378, 2])).
% 2.34/2.57 tff(8076,plain,
% 2.34/2.57 (b(s(s(s(z))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[558, 8075])).
% 2.34/2.57 tff(8077,plain,
% 2.34/2.57 (~r(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1922, 378, 3])).
% 2.34/2.57 tff(8078,plain,
% 2.34/2.57 (b(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[357, 8077])).
% 2.34/2.57 tff(8079,plain,
% 2.34/2.57 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1865, 204, 8078, 7639, 4, 8072])).
% 2.34/2.57 tff(8080,plain,
% 2.34/2.57 (r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7225, 8079])).
% 2.34/2.57 tff(8081,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4983, 8080, 3])).
% 2.34/2.57 tff(8082,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[284, 8081])).
% 2.34/2.57 tff(8083,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4987, 8080, 3])).
% 2.34/2.57 tff(8084,plain,
% 2.34/2.57 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[134, 8083])).
% 2.34/2.57 tff(8085,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1540, 8084, 8082, 8076, 8074, 8072])).
% 2.34/2.57 tff(8086,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8087,plain,
% 2.34/2.57 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8086, 4, 3, 2])).
% 2.34/2.57 tff(8088,plain,
% 2.34/2.57 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[108, 8087])).
% 2.34/2.57 tff(8089,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(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(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(8090,plain,
% 2.34/2.57 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(8091,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[8090])).
% 2.34/2.57 tff(8092,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[8091, 8089])).
% 2.34/2.57 tff(8093,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(8094,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[8093, 8092])).
% 2.34/2.57 tff(8095,plain,
% 2.34/2.57 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8094, 204, 8088, 7639, 4, 8072])).
% 2.34/2.57 tff(8096,plain,
% 2.34/2.57 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[134, 8095])).
% 2.34/2.57 tff(8097,plain,
% 2.34/2.57 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4987, 8096, 3])).
% 2.34/2.57 tff(8098,plain,
% 2.34/2.57 (b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7225, 8097])).
% 2.34/2.57 tff(8099,plain,
% 2.34/2.57 (~r(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1887, 339, 2])).
% 2.34/2.57 tff(8100,plain,
% 2.34/2.57 (b(z, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[306, 8099])).
% 2.34/2.57 tff(8101,plain,
% 2.34/2.57 (~r(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7209, 261, 3, 339])).
% 2.34/2.57 tff(8102,plain,
% 2.34/2.57 (b(s(s(s(z))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[402, 8101])).
% 2.34/2.57 tff(8103,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4953, 285, 8102, 6625, 261, 4])).
% 2.34/2.57 tff(8104,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8105,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8104, 339, 3, 4])).
% 2.34/2.57 tff(8106,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[641, 8105])).
% 2.34/2.57 tff(8107,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1993, 8106, 8100, 8020, 8072, 8098])).
% 2.34/2.57 tff(8108,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8109,plain,
% 2.34/2.57 (~r(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8108, 4, 3, 2])).
% 2.34/2.57 tff(8110,plain,
% 2.34/2.57 (b(z, s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[357, 8109])).
% 2.34/2.57 tff(8111,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1865, 204, 8110, 7639, 4, 8072, 8098])).
% 2.34/2.57 tff(8112,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(8113,plain,
% 2.34/2.57 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[8112, 3, 2])).
% 2.34/2.57 tff(8114,plain,
% 2.34/2.57 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[190, 8113])).
% 2.34/2.57 tff(8115,plain,
% 2.34/2.57 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6380, 8114, 2])).
% 2.34/2.57 tff(8116,plain,
% 2.34/2.57 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6528, 8115])).
% 2.34/2.57 tff(8117,plain,
% 2.34/2.57 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3043, 8114, 2])).
% 2.34/2.57 tff(8118,plain,
% 2.34/2.57 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[244, 8117])).
% 2.34/2.58 tff(8119,plain,
% 2.34/2.58 (~r(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[294, 286, 3])).
% 2.34/2.58 tff(8120,plain,
% 2.34/2.58 (b(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[558, 8119])).
% 2.34/2.58 tff(8121,plain,
% 2.34/2.58 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6672, 7363, 1, 443, 8120])).
% 2.34/2.58 tff(8122,plain,
% 2.34/2.58 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[108, 8121])).
% 2.34/2.58 tff(8123,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7960, 204, 8120, 7363, 4780, 8122, 7639])).
% 2.34/2.58 tff(8124,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8125,plain,
% 2.34/2.58 (~r(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8124, 8114, 8118, 3])).
% 2.34/2.58 tff(8126,plain,
% 2.34/2.58 (b(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[306, 8125])).
% 2.34/2.58 tff(8127,plain,
% 2.34/2.58 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6366, 8126, 8020, 8118, 8116])).
% 2.34/2.58 tff(8128,plain,
% 2.34/2.58 (r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[641, 8127])).
% 2.34/2.58 tff(8129,plain,
% 2.34/2.58 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6366, 362, 8020, 443, 2404])).
% 2.34/2.58 tff(8130,plain,
% 2.34/2.58 (r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[641, 8129])).
% 2.34/2.58 tff(8131,plain,
% 2.34/2.58 ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[371, 7639])).
% 2.34/2.58 tff(8132,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8131, 362, 8020, 361])).
% 2.34/2.58 tff(8133,plain,
% 2.34/2.58 (r(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[335, 8132])).
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% 2.34/2.58 tff(8136,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[357, 8136])).
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% 2.34/2.58 tff(8140,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8139, 2])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8143, 361, 8141])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[558, 8144])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[386, 8145, 2])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[108, 8146])).
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% 2.34/2.58 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3043, 1, 2])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[244, 8148])).
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% 2.34/2.58 (~b(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7998, 378, 8141, 1, 8149])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[558, 8150, 8075])).
% 2.34/2.58 tff(8152,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8153,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8152, 1, 2])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[108, 8153])).
% 2.34/2.58 tff(8155,plain,
% 2.34/2.58 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[4788, 339, 1])).
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% 2.34/2.58 tff(8158,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8159,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8158, 1, 2])).
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% 2.34/2.58 (b(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[357, 8159])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8135, 8160, 1, 8149, 7213])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[306, 8161])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[7699, 8153, 8141, 8160])).
% 2.34/2.58 tff(8164,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[402, 8163])).
% 2.34/2.58 tff(8165,plain,
% 2.34/2.58 (~r(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2003, 8164, 8162])).
% 2.34/2.58 tff(8166,plain,
% 2.34/2.58 (b(s(s(s(z))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[558, 8165])).
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% 2.34/2.58 tff(8168,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8169,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8168, 2])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[190, 8169])).
% 2.34/2.58 tff(8171,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[6388, 204, 8141, 4780, 8170])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8171, 361])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[641, 8172])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[7699, 8146, 8141, 361])).
% 2.34/2.58 tff(8175,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[402, 8174])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[7505, 8147, 8141, 361])).
% 2.34/2.58 tff(8177,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[335, 8176])).
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% 2.34/2.58 tff(8179,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8180,plain,
% 2.34/2.58 (~b(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8179, 2])).
% 2.34/2.58 tff(8181,plain,
% 2.34/2.58 (r(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[357, 8180])).
% 2.34/2.58 tff(8182,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[1887, 8181, 2])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[306, 8182])).
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% 2.34/2.58 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8062, 57, 8170, 110])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[108, 8184, 387])).
% 2.34/2.58 tff(8186,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8187,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8186, 110, 2])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[558, 8187])).
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% 2.34/2.58 (~b(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7973, 204, 8188, 8141, 4780, 7639])).
% 2.34/2.58 tff(8190,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[357, 8189])).
% 2.34/2.58 tff(8191,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[1887, 8190, 2])).
% 2.34/2.58 tff(8192,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[306, 8191])).
% 2.34/2.58 tff(8193,plain,
% 2.34/2.58 (~b(s(s(s(z))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7528, 8192, 8020, 8141, 8188])).
% 2.34/2.58 tff(8194,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[402, 8193])).
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% 2.34/2.58 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1479, 8194, 8190])).
% 2.34/2.58 tff(8196,plain,
% 2.34/2.58 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[108, 8195])).
% 2.34/2.58 tff(8197,plain,
% 2.34/2.58 (~b(s(z), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7546, 8192, 8020, 8141, 8188])).
% 2.34/2.58 tff(8198,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[478, 8197])).
% 2.34/2.58 tff(8199,plain,
% 2.34/2.58 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2643, 8198, 110])).
% 2.34/2.58 tff(8200,plain,
% 2.34/2.58 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[284, 8199])).
% 2.34/2.58 tff(8201,plain,
% 2.34/2.58 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3023, 204, 8188, 7639, 8170])).
% 2.34/2.58 tff(8202,plain,
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[8201, 8200, 8196])).
% 2.34/2.58 tff(8203,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8204,plain,
% 2.34/2.58 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8203, 2])).
% 2.34/2.58 tff(8205,plain,
% 2.34/2.58 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[244, 8204])).
% 2.34/2.58 tff(8206,plain,
% 2.34/2.58 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7561, 153, 405, 4, 339])).
% 2.34/2.58 tff(8207,plain,
% 2.34/2.58 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[284, 8206])).
% 2.34/2.58 tff(8208,plain,
% 2.34/2.58 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6366, 1469, 8020, 443, 362])).
% 2.34/2.58 tff(8209,plain,
% 2.34/2.58 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6528, 8208])).
% 2.34/2.58 tff(8210,plain,
% 2.34/2.58 (~r(s(z), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7567, 8209, 264])).
% 2.34/2.58 tff(8211,plain,
% 2.34/2.58 (b(s(z), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[478, 8210])).
% 2.34/2.58 tff(8212,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(8213,plain,
% 2.34/2.58 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(8214,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[8213])).
% 2.34/2.58 tff(8215,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[8214, 8212])).
% 2.34/2.58 tff(8216,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[558, 8238])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[431, 8243])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[7225, 8282])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[7715, 8285, 8244])).
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% 2.34/2.58 inference(unit_resolution,[status(thm)],[1993, 362, 443, 363, 1469])).
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% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
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% 2.34/2.58 inference(modus_ponens,[status(thm)],[8300, 8299])).
% 2.34/2.58 tff(8302,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8301, 67, 8295, 8293, 8291])).
% 2.34/2.58 tff(8303,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8304,plain,
% 2.34/2.58 ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8303, 7639])).
% 2.34/2.58 tff(8305,plain,
% 2.34/2.58 (~b(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8304, 8156, 8020, 8244, 8281])).
% 2.34/2.58 tff(8306,plain,
% 2.34/2.58 (r(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[306, 8305])).
% 2.34/2.58 tff(8307,plain,
% 2.34/2.58 (~r(s(s(s(z))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[2003, 8306, 8289])).
% 2.34/2.58 tff(8308,plain,
% 2.34/2.58 (b(s(s(s(z))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[402, 8307])).
% 2.34/2.58 tff(8309,plain,
% 2.34/2.58 (~r(z, s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8124, 8306, 1, 8281])).
% 2.34/2.58 tff(8310,plain,
% 2.34/2.58 (b(z, s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[259, 8309])).
% 2.34/2.58 tff(8311,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(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(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(8312,plain,
% 2.34/2.58 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(8313,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[8312])).
% 2.34/2.58 tff(8314,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[8313, 8311])).
% 2.34/2.58 tff(8315,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(8316,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[8315, 8314])).
% 2.34/2.58 tff(8317,plain,
% 2.34/2.58 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8316, 204, 8020, 8310, 8308, 8156, 8281, 8283])).
% 2.34/2.58 tff(8318,plain,
% 2.34/2.58 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[284, 8317])).
% 2.34/2.58 tff(8319,plain,
% 2.34/2.58 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7567, 8318, 8287])).
% 2.34/2.58 tff(8320,plain,
% 2.34/2.58 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6528, 8319])).
% 2.34/2.58 tff(8321,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7380, 204, 8020, 8156, 8320, 8281, 8283])).
% 2.34/2.58 tff(8322,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(8323,plain,
% 2.34/2.58 (~r(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8322, 1])).
% 2.34/2.58 tff(8324,plain,
% 2.34/2.58 (b(z, s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[357, 8323])).
% 2.34/2.58 tff(8325,plain,
% 2.34/2.58 (~b(z, s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6376, 8324, 8020, 8244])).
% 2.34/2.58 tff(8326,plain,
% 2.34/2.58 (r(z, s(s(s(z))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[259, 8325])).
% 2.34/2.58 tff(8327,plain,
% 2.34/2.58 (~r(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8124, 8326, 1, 8281])).
% 2.34/2.58 tff(8328,plain,
% 2.34/2.58 (b(z, s(z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[306, 8327])).
% 2.34/2.58 tff(8329,plain,
% 2.34/2.58 ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3512, 7639])).
% 2.34/2.58 tff(8330,plain,
% 2.34/2.58 (~b(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8329, 8328, 8020, 8244])).
% 2.34/2.58 tff(8331,plain,
% 2.34/2.58 (r(s(s(s(s(z)))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[335, 8330])).
% 2.34/2.58 tff(8332,plain,
% 2.34/2.58 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[8304, 8328, 8020, 8244, 8281])).
% 2.34/2.59 tff(8333,plain,
% 2.34/2.59 (r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[641, 8332])).
% 2.34/2.59 tff(8334,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4784, 8333, 8331, 1])).
% 2.34/2.59 tff(8335,plain,(~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8336,plain,
% 2.34/2.59 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[190, 8335])).
% 2.34/2.59 tff(8337,plain,
% 2.34/2.59 (~r(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8272, 361])).
% 2.34/2.59 tff(8338,plain,
% 2.34/2.59 (b(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[478, 8337])).
% 2.34/2.59 tff(8339,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7930, 8338, 8244])).
% 2.34/2.59 tff(8340,plain,
% 2.34/2.59 (r(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[558, 8339])).
% 2.34/2.59 tff(8341,plain,
% 2.34/2.59 (~r(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[294, 8340, 8268])).
% 2.34/2.59 tff(8342,plain,
% 2.34/2.59 (b(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[306, 8341])).
% 2.34/2.59 tff(8343,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7318, 204, 8342, 8338, 8244, 361, 4780])).
% 2.34/2.59 tff(8344,plain,(~b(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8345,plain,
% 2.34/2.59 (r(z, s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[357, 8344])).
% 2.34/2.59 tff(8346,plain,
% 2.34/2.59 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3631, 286, 194, 308, 339])).
% 2.34/2.59 tff(8347,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[431, 8346, 4407])).
% 2.34/2.59 tff(8348,plain,((~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8349,plain,
% 2.34/2.59 ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8348, 4780])).
% 2.34/2.59 tff(8350,plain,
% 2.34/2.59 (~r(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8349, 286, 8345])).
% 2.34/2.59 tff(8351,plain,
% 2.34/2.59 (b(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[402, 8350])).
% 2.34/2.59 tff(8352,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8053, 204, 8020, 8351, 4780, 7639])).
% 2.34/2.59 tff(8353,plain,
% 2.34/2.59 (r(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[558, 8352])).
% 2.34/2.59 tff(8354,plain,
% 2.34/2.59 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3954, 238, 8244, 8345, 8353])).
% 2.34/2.59 tff(8355,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2663, 3521, 286])).
% 2.34/2.59 tff(8356,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[641, 8355, 8354])).
% 2.34/2.59 tff(8357,plain,(b(s(s(s(s(s(s(z)))))), s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8358,plain,
% 2.34/2.59 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8357, 286])).
% 2.34/2.59 tff(8359,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7674, 8358, 8244, 8336])).
% 2.34/2.59 tff(8360,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[218, 8359])).
% 2.34/2.59 tff(8361,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8104, 3, 8345, 8336])).
% 2.34/2.59 tff(8362,plain,
% 2.34/2.59 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[641, 8361])).
% 2.34/2.59 tff(8363,plain,
% 2.34/2.59 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1922, 3, 8345])).
% 2.34/2.59 tff(8364,plain,
% 2.34/2.59 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[108, 8363])).
% 2.34/2.59 tff(8365,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7990, 8364, 8244])).
% 2.34/2.59 tff(8366,plain,
% 2.34/2.59 (r(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[558, 8365])).
% 2.34/2.59 tff(8367,plain,
% 2.34/2.59 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3954, 8366, 8244, 8345, 8362])).
% 2.34/2.59 tff(8368,plain,
% 2.34/2.59 (~b(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7715, 8364, 8244])).
% 2.34/2.59 tff(8369,plain,
% 2.34/2.59 (r(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[478, 8368])).
% 2.34/2.59 tff(8370,plain,
% 2.34/2.59 (~r(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1738, 8369, 3])).
% 2.34/2.59 tff(8371,plain,
% 2.34/2.59 (b(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[306, 8370])).
% 2.34/2.59 tff(8372,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8304, 8371, 8367, 8020, 8244, 8362])).
% 2.34/2.59 tff(8373,plain,(~r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8374,plain,
% 2.34/2.59 (b(z, s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[259, 8373])).
% 2.34/2.59 tff(8375,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6577, 204, 8020, 8374, 8244, 4780])).
% 2.34/2.59 tff(8376,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[335, 8375])).
% 2.34/2.59 tff(8377,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7874, 8358, 8244, 8376])).
% 2.34/2.59 tff(8378,plain,
% 2.34/2.59 (b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[641, 8377])).
% 2.34/2.59 tff(8379,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(8380,plain,
% 2.34/2.59 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(8381,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8380])).
% 2.34/2.59 tff(8382,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[8381, 8379])).
% 2.34/2.59 tff(8383,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(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))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(8384,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[8383, 8382])).
% 2.34/2.59 tff(8385,plain,
% 2.34/2.59 (~b(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8384, 204, 8020, 8351, 4780, 7639])).
% 2.34/2.59 tff(8386,plain,
% 2.34/2.59 (r(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[478, 8385])).
% 2.34/2.59 tff(8387,plain,
% 2.34/2.59 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7682, 8358, 8244, 8336])).
% 2.34/2.59 tff(8388,plain,
% 2.34/2.59 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6528, 8387])).
% 2.34/2.59 tff(8389,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7567, 8388, 8386])).
% 2.34/2.59 tff(8390,plain,
% 2.34/2.59 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[284, 8389])).
% 2.34/2.59 tff(8391,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1783, 8390, 8374, 8351, 8378])).
% 2.34/2.59 tff(8392,plain,
% 2.34/2.59 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[134, 8391])).
% 2.34/2.59 tff(8393,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7561, 8390, 8336, 8374, 8345])).
% 2.34/2.59 tff(8394,plain,
% 2.34/2.59 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[108, 8393])).
% 2.34/2.59 tff(8395,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(8396,plain,
% 2.34/2.59 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(8397,plain,
% 2.34/2.59 (((~![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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8396])).
% 2.34/2.59 tff(8398,plain,
% 2.34/2.59 (((~![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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[8397, 8395])).
% 2.34/2.59 tff(8399,plain,
% 2.34/2.59 ((~![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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(8400,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[8399, 8398])).
% 2.34/2.59 tff(8401,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8400, 67, 8394, 8392, 8360])).
% 2.34/2.59 tff(8402,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8403,plain,
% 2.34/2.59 (b(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[306, 8402])).
% 2.34/2.59 tff(8404,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7990, 444, 8244])).
% 2.34/2.59 tff(8405,plain,
% 2.34/2.59 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[108, 8404])).
% 2.34/2.59 tff(8406,plain,
% 2.34/2.59 (~b(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7528, 444, 8020, 8374, 8403])).
% 2.34/2.59 tff(8407,plain,
% 2.34/2.59 (r(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[402, 8406])).
% 2.34/2.59 tff(8408,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1479, 8407, 8405, 8345])).
% 2.34/2.59 tff(8409,plain,(~b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8410,plain,
% 2.34/2.59 (r(s(s(s(z))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[558, 8409])).
% 2.34/2.59 tff(8411,plain,
% 2.34/2.59 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3954, 238, 8244, 8345, 8410])).
% 2.34/2.59 tff(8412,plain,
% 2.34/2.59 (r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[641, 8411])).
% 2.34/2.59 tff(8413,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4943, 8412, 8376])).
% 2.34/2.59 tff(8414,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[218, 8413])).
% 2.34/2.59 tff(8415,plain,
% 2.34/2.59 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8062, 3521, 8336, 8410])).
% 2.34/2.59 tff(8416,plain,
% 2.34/2.59 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[108, 8415])).
% 2.34/2.59 tff(8417,plain,
% 2.34/2.59 (~r(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1479, 8416, 8345])).
% 2.34/2.59 tff(8418,plain,
% 2.34/2.59 (b(s(s(s(z))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[402, 8417])).
% 2.34/2.59 tff(8419,plain,
% 2.34/2.59 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | b(s(s(s(s(s(s(z)))))), z) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~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(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3243, 7639])).
% 2.34/2.59 tff(8420,plain,
% 2.34/2.59 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8419, 8418, 8020, 8374, 8411, 8376, 3521, 8345])).
% 2.34/2.59 tff(8421,plain,
% 2.34/2.59 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[822, 8420])).
% 2.34/2.59 tff(8422,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3251, 67, 8421, 8376])).
% 2.34/2.59 tff(8423,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3173, 8422])).
% 2.34/2.59 tff(8424,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3259, 67, 8421, 8376])).
% 2.34/2.59 tff(8425,plain,
% 2.34/2.59 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[766, 8424])).
% 2.34/2.59 tff(8426,plain,
% 2.34/2.59 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3267, 204, 8425, 8423, 8414, 8336])).
% 2.34/2.59 tff(8427,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[846, 67, 8421, 8412])).
% 2.34/2.59 tff(8428,plain,
% 2.34/2.59 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[850, 50, 8427])).
% 2.34/2.59 tff(8429,plain,
% 2.34/2.59 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8428, 8426])).
% 2.34/2.59 tff(8430,plain,
% 2.34/2.59 (~b(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2494, 204, 8020, 8403, 8374, 8418])).
% 2.34/2.59 tff(8431,plain,
% 2.34/2.59 (r(s(z), s(s(s(z))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[478, 8430])).
% 2.34/2.59 tff(8432,plain,
% 2.34/2.59 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8429])).
% 2.34/2.59 tff(8433,plain,
% 2.34/2.59 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[664, 8432, 121])).
% 2.34/2.59 tff(8434,plain,
% 2.34/2.59 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(z))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8433])).
% 2.34/2.59 tff(8435,plain,
% 2.34/2.59 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[875, 8434, 119])).
% 2.34/2.59 tff(8436,plain,
% 2.34/2.59 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(z)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8435])).
% 2.34/2.59 tff(8437,plain,
% 2.34/2.59 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[699, 8436, 20])).
% 2.34/2.59 tff(8438,plain,
% 2.34/2.59 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8437])).
% 2.34/2.59 tff(8439,plain,
% 2.34/2.59 (s(s(elem!1)) = s(s(z))),
% 2.34/2.59 inference(transitivity,[status(thm)],[754, 8438, 83])).
% 2.34/2.59 tff(8440,plain,
% 2.34/2.59 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8439])).
% 2.34/2.59 tff(8441,plain,
% 2.34/2.59 (s(elem!1) = s(z)),
% 2.34/2.59 inference(transitivity,[status(thm)],[919, 8440, 78])).
% 2.34/2.59 tff(8442,plain,
% 2.34/2.59 (inj_0(s(elem!1)) = inj_0(s(z))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8441])).
% 2.34/2.59 tff(8443,plain,
% 2.34/2.59 (elem!1 = z),
% 2.34/2.59 inference(transitivity,[status(thm)],[1009, 8442, 15])).
% 2.34/2.59 tff(8444,plain,
% 2.34/2.59 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8443])).
% 2.34/2.59 tff(8445,plain,
% 2.34/2.59 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.34/2.59 inference(symmetry,[status(thm)],[8444])).
% 2.34/2.59 tff(8446,plain,
% 2.34/2.59 (b(s(z), elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[8020, 8445])).
% 2.34/2.59 tff(8447,plain,
% 2.34/2.59 (~b(s(s(z)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3388, 8446, 3521, 8418, 8410, 8403, 8431, 8429])).
% 2.34/2.59 tff(8448,plain,
% 2.34/2.59 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8429])).
% 2.34/2.59 tff(8449,plain,
% 2.34/2.59 ((s(s(s(s(s(s(z)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.34/2.59 inference(symmetry,[status(thm)],[8448])).
% 2.34/2.59 tff(8450,plain,
% 2.34/2.59 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 2.34/2.59 inference(symmetry,[status(thm)],[8438])).
% 2.34/2.59 tff(8451,plain,
% 2.34/2.59 (s(s(z)) = s(s(elem!1))),
% 2.34/2.59 inference(transitivity,[status(thm)],[84, 8450, 753])).
% 2.34/2.59 tff(8452,plain,
% 2.34/2.59 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(z)))))) = s(s(elem!1)))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8451])).
% 2.34/2.59 tff(8453,plain,
% 2.34/2.59 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[8452, 8449])).
% 2.34/2.59 tff(8454,plain,
% 2.34/2.59 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8453])).
% 2.34/2.59 tff(8455,plain,
% 2.34/2.59 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[182, 8454])).
% 2.34/2.59 tff(8456,plain,
% 2.34/2.59 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8435, 8429])).
% 2.34/2.59 tff(8457,plain,
% 2.34/2.59 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[8456, 163])).
% 2.34/2.59 tff(8458,plain,
% 2.34/2.59 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.59 inference(symmetry,[status(thm)],[8457])).
% 2.34/2.59 tff(8459,plain,
% 2.34/2.59 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[8458])).
% 2.34/2.59 tff(8460,plain,
% 2.34/2.59 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[185, 8459])).
% 2.34/2.59 tff(8461,plain,
% 2.34/2.59 (inj_0(s(z)) = inj_0(s(elem!1))),
% 2.34/2.59 inference(symmetry,[status(thm)],[8442])).
% 2.34/2.59 tff(8462,plain,
% 2.34/2.59 (z = elem!1),
% 2.34/2.59 inference(transitivity,[status(thm)],[2194, 8461, 902])).
% 2.34/2.59 tff(8463,plain,
% 2.34/2.59 (elem!1 = z),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2211, 8462])).
% 2.34/2.59 tff(8464,plain,
% 2.34/2.59 (~r(s(s(z)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6460, 8463, 8376, 8421, 8460, 8455])).
% 2.34/2.59 tff(8465,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3393, 8464, 8447])).
% 2.34/2.59 tff(8466,plain,(b(s(s(s(s(s(s(z)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(8467,plain,
% 2.34/2.59 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[8304, 8466, 8020, 8244, 8403])).
% 2.34/2.59 tff(8468,plain,
% 2.34/2.59 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7874, 8466, 8244, 8376])).
% 2.34/2.59 tff(8469,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[641, 8468, 8467])).
% 2.44/2.60 % SZS output end Proof
% 2.44/2.60 % E exiting
%------------------------------------------------------------------------------